A new hybrid image denoising algorithm using adaptive and modified decision-based filters for enhanced image quality | Scientific Reports

Scientific Reports volume 15, Article number: 8971 (2025) Cite this article

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Denoising is one of the most important processes in digital image processing to recover visual quality and structural integrity in images. Traditional methods often suffer from limitations like computational complexity, over-smoothing, and the inability to preserve critical details, particularly edges. This paper introduces a hybrid denoising algorithm combining Adaptive Median Filter (AMF) and Modified Decision-Based Median Filter (MDBMF) to address these challenges. The AMF adjusts the window sizes dynamically to precisely detect noisy pixels, and MDBMF selectively recovers corrupted pixels without affecting intact regions, effectively reducing noise while preserving edges. The subjective analysis is supplemented with objective analyses in which visual quality proves that hybrid approach performance considerably outperforms existing state-of-the-art methods. The test is conducted on nine benchmark images standard and medical dataset, namely, Chest and Liver images with different noise densities in the range from 10 to 90%. Quantitative evaluations PSNR, MSE, IEF, SSIM, FOM and VIF clearly show the performance superiority of the hybrid approach when compared to the state-of-the-art approaches. The improvement in PSNR was up to 2.34 dB, IEF improvement was more than 20%, and the improvement in MSE was up to 15% improvement over other methods like BPDF, AT2FF, and SVMMF. Improvement in the values of SSIM is up to 0.07, which confirms improved structural similarity. Furthermore, the FOM and VIF metrics demonstrate the remarkable performance of the hybrid approach: both the FOM and VIF exceeded all other denoising techniques evaluated, reaching 0.68 and 0.61, respectively.

Unwanted signal intensity and image reduction lead to noise. Various factors, including poor lighting, relatively slow shutter speed, sensor error, sensor temperature, channel inadvertence, etc., create noise. Abrupt signal interruptions in an image can produce white or black dots that are detected as impulse noise. Various filters are already designed to reduce noise and produce a result that closely resembles the basic image1. A small dark spot with one or more pixels in a uniform green area of an image, for instance, might not be noise at all. Additionally, each of these pixels can be symmetrical or asymmetrical. Sensor flaws may result in symmetrical shapes, whereas asymmetrical shapes may precisely represent the desired image feature. There are several circumstances in which noise reduction is not a significant barrier to extracting sparse data trapped in noise clusters: Astronomical imagery. Besides, inaccuracies in algorithms can lead to problems such as removing important features from the image and not filtering out some noise2. Since every denoising algorithm has its strengths and weaknesses, we are conducting further research to advance this field3. Digital image transmission is one kind of communication that has become more prevalent because of the Internet and the overuse of technology. Unfortunately, when transferred from one medium to another, digital images are distorted by numerous noise types. During recording, the image from the camera sensor is also affected by circumstances such as noise, lighting, shadows, and glow4.

Noise is a term used to describe any unwanted and/or random event that could corrupt an image by warping its original data and making pre-processing more difficult5. Different kinds of noise, including Gaussian, speckle, and impulse noise, can be seen in digital images. Included in the category of impulse noise is salt-and-pepper noise, which is sometimes referred to as shot noise, random noise, independent noise, or spike noise. In an image with salt and pepper noise, some pixels have very different colors or intensities from the surrounding pixels. Salt and pepper degeneration may be brought on by sudden, sharp changes in the visual signal6. At the gray level, the distorted pixels accept a pepper value of 0 or a salt value of 255. The phrase "salt and pepper noise" refers to the random appearance of black and white dots on the image when examined7,8. Figure 1 illustrates an image subjected to salt-and-pepper noise.

Barbara image taken from Kaggle Dataset9; (a) Original image, (b) Salt and pepper noise image.

Noise in images causes loss of important information and breaks the processes related to detection, classification, and clustering10,11. Therefore, removing noise becomes very prime before the application of any other operations. The effectiveness of noise reduction becomes a very important factor since image restoration does not only involve noise removal but also the preservation of critical features such as edges and textures. Noise-free, clear images are needed for an accurate analysis. For this purpose, several restoration techniques have been proposed to fill the gap, most of which are based on mathematical and statistical models representing the process of degradation12. Basically, image denoising belongs to the realm of image restoration. This renaissance dates back to the work done by Wiener and Kolmogorov in the 1940s, which involved the development of the very first models for filtering noise from signals13. These seed works gave rise to many modern denoising methods, which always seek to find a fine balance between noise reduction and the preservation of important details in the image so that clear and accurate interpretation is brought out. Impulse noise is one of the well-known types of noise14, which is produced by irregular voltages in the communication medium. Inside a pixel, Impulse noise produces two values for the intensity. 0 is referred to as "pepper noise," and 255 is referred to as "salt noise." Eq. (1) is used to create the noise model for impulsive noise:

While Di, Pn, Pm, and Px stand for the damaged pixel, probability, damage by salt noise pixel, and current pixel. When Pn = 0, known as unipolar impulse noise, whereas when Pn ≈ Pm ≠ 0 it is referred to as bipolar noise. Pm = 0.

The quality of digital images is reduced by noise. When images are transmitted through different media, they may degrade. The digital imaging field has a particular problem with noise. Each kind uses various criteria for noise reduction to safeguard its images from the noises in question. There are many forms of noise and separate standards for each one. Consequently, the accuracy of image segmentation, edge recognition, and object identification may be impacted by salt and pepper noise, which may also lessen the definition and visualization benefits of imaging Therefore, it is essential to lessen the impacts of noise associated with grayscale images to ensure the restoration of an image’s original information and to remove discontinuities1. Digital image degradation can be prevented or minimized by using different types of filters, especially linear and nonlinear filter techniques for preventing the presence of any noise. Noise reduction is a hot research area in image processing. To enhance visual information, a great deal of study has been done, and several algorithms and filters are planned. To locate and eliminate damaged pixels, there are several denoising techniques15. However, some image noise reduction approaches use filters for the entire image and exclude even undamaged pixels. With the various evaluation parameters, the majority of denoising approaches fail to preserve the object’s quality and edges in a noisy image16. Image denoising can be divided into three basic parts: data preprocessing, feature extraction, and denoising. It plays an effective role in restoring the quality of images, which degrades by noise during acquisition or transmission. In fact, each of the parts plays a vital role in the overall effectiveness of denoising algorithms, more specifically, in the development of hybrid approaches.

The first phase, called preprocessing, is used to standardize the image and prepare it for further processing. This often includes techniques to handle the variety of noise types that may be affecting the image, such as Gaussian, salt-and-pepper, Poisson noise, to name but a few of them. This could be scaling, normalization, or simple filters to clean up the image before it goes through its denoising. For example, in the spatial domain, in the process of degrading an image, median or Gaussian filters are typically applied to reduce the noise at this stage, which could largely take some of the loads off processes to be executed in the later stage​17.

It is the stage of getting features out of the said image which in this case is extracting relevant image features, these include edges textures and regions of interest. This process is carried out to ensure that noise is differentiated with the relevant image content. Historically wavelet transforms and Fourier transforms were used to extract relevant image components in the frequency domain.

It is the heart of the whole process, dealing with removing noise but at the same time trying to keep as much information in the original image as possible. Depending on the nature of the noise and characteristics of the image, different algorithms may be resorted to. The classical techniques, like non-local means and total variation regularization, are suitable for noise removal, but they over-smooth the images and cause loss of finer details in the images8. On the other hand, this hybrid approach is based on AMF and MDBMF for effective removal of high-density salt-and-pepper noise. The approach is adaptive for noise removal without the loss of significant image features regarding edges and textures and, hence ensures minimal over-smoothing effects prevalent in traditional methods. It can, therefore, produce highly realistic and detailed outputs, even in highly corrupted images.

The denoising filter technique impacts areas where there is a certain form of noise. After this noise map is created, the filtering noise reduction mechanism will let us know which areas contain a certain type of noise and pass it to the necessary filters. Areas without noise are ignored. These denoising filtering algorithms are focused on pixel identification and assessment affected by impurities (noise). The filter mechanism is based on noise detection and evaluation. Like the median filter mechanism, an effective filter can rapidly assess and detect noisy pixels18. To enhance images with great space preservation, use median filtering19. Filtering is a fundamental function of image processing to perform various tasks such as denoising, edge detection, and resampling. The important role filtering plays is in noise reduction, preserving the features like edges and textures for further processing in many applications. In most cases, filtering can be classified basically into linear and nonlinear methods20,21. Linear filters apply homogeneous smoothing throughout an image. Sometimes this causes blurring of edges—for example, the Gaussian filter. In contrast, nonlinear filters, such as the median filter, will retain local details and are hence very good at reducing some types of noise like salt-and-pepper noise. Recent developments have been oriented towards hybrid filtering techniques combining the advantages of both linear and nonlinear approaches, seeking a trade-off between effective noise reduction and preservation of fine details. Such methods find important applications in medical imaging and remote sensing​ areas among others where the preservation of the structural integrity is of essence22. Advanced hybrid approaches have been proposed, handling high-density noise while preserving image quality, and therefore it gives better performance compared to traditional methods. The AMF is one of the prime filters for removing impulse noise with different intensities, due to its ability to adapt the size of the filtering window according to the local noise density. Thus, AMF is able to retain the details of the image while removing noise. However, AMF can be computationally intensive for large noise levels and may not perform well on large clusters of noise. In contrast, DBMF applies a noise detection mechanism itself in order to recognize the corrupted pixels and then replace it with the median of neighboring uncorrupted pixels. By doing this, computational load decreases and details of the uncorrupted image are preserved. Nevertheless, sometimes the DBMF misclassifies the pixels (mostly in high noise densities) and the filtering result is not optimal. Such shortcomings of both robust filtering algorithms are overcome by the integration of the AMF and the MDBMF. This hybrid approach uses the benefits arising from the adaptivity of the AMF while handling different patterns of noise and the decision-based strategy of the MDBMF to remove noise efficiently and precisely. The proposed hybrid approach is anticipated to combine the advantages of the Adaptive Median Filter and the Modified Decision-Based Median Filter in achieving better noise reduction. This does not only complement the deficiency of filters but also seeks a balance between computation time and the ability for noise suppression. This underscores the potential for very broad applications of the hybrid filter in digital image processing tasks based on its robust performance with different image types and noise levels.

Most algorithms for denoising tend to blur the edges of an image while reducing noise, including traditional Median and Decision-Based Median Filters. Preservation of the edges is important in retaining the structural details of the image, an important aspect when considering fields like medical imaging, character recognition, and remote sensing. The AMF technique is fairly good in terms of preserving the image details by the alteration of the filter window size relative to the density of the noise. When this is used with MDBMF, the hybrid method performs far better in the context of edge preservation since MDBMF specifically identifies those noisy pixels and leaves the non-noisy ones untouched completely. So, this whole combined act enables the method to cope up with high-density noise without causing the distortion of the image structure.

The major contributions of this work are summed up in the following points.

We proposed a novel hybrid approach that combines the AMF with the Modified Decision-Based Median Filter to achieve highly dense salt-and-pepper noise reduction and preserve most of the image features, including edges and fine details.

Considering the noise level, the proposed algorithm can handle it better from 10% up to 90%, thus showing much better performances compared with the existing methods for the maintenance of image quality without signal degradation in higher noise densities.

This algorithm preserves the fundamental edges, geometries, and unaffected pixels, which conventional filters always had some limitations to generate more transparent and correct denoised images.

Comprehensive comparative studies are carried out with different traditional denoising methods such as Median Filter, Adaptive Median Filter, Weighted Median Filter, Untrimmed Median Filter, Decision-Based Median Filter, and Modified Decision-Based Median Filter.

Standard performance metrics based on PSNR, MSE, IEF, and SSIM prove that the quality achieved by this hybrid approach is quite impressive compared to some of the related techniques.

The proposed hybrid algorithm has vast applications in diversified fields, such as character recognition, agriculture, medical image processing, and remote sensing, among others, where quality imaging enables correct analysis and subsequent decision-making.

The outline of this paper is organized as follows: Section "Preliminary approaches to image denoising" addresses various image denoising techniques and their significance, highlighting the importance of effective denoising methods in digital image processing. Section "Highlights, advantages, and novelty of the proposed system" introduces the highlights, advantages, and novelty of the proposed hybrid denoising system, emphasizing its ability to handle high-density salt-and-pepper noise while preserving image details and edges. Section "Related work" describes the related work comparing the merits and demerits of existing methods and places the proposed method into the framework with state-of-the-art techniques. In Section "Proposed hybrid denoising algorithm overview", the proposed hybrid algorithm will be discussed in detail with a structural explanation accompanied by a flowchart for better understanding. Section "Evaluation dataset of the proposed new hybrid image denoising system" evaluates the method using subjective and objective analysis criteria with standard metrics and results from simulation execution on different benchmark datasets. Section "Adapting the method for Gaussian noise" discusses adaptation of the method for handling Gaussian noise, preliminary results to illustrate its versatility. Section "Comparative evaluation (Average Values)" conducts a comparative assessment of the average performance of the proposed method versus the standard algorithms. Section "Computational efficiency" discusses the computational efficiency of the approach, considering overhead and real-time feasibility. Section "Discussion" provides a discussion of the results, implications, limitations, and future research opportunities. Finally, Section "Conclusion" summarizes the key contributions of the paper and outlines some future directions to extend the method’s applicability and improve its performance.

Salt and pepper noise is difficult to remove with linear filtering methods since the algorithm searches both damaged and undamaged pixels. These filters have the propensity to blur sharp edges, damaging intended image lines and other beneficial characteristics. These methods are quick; however, they can’t effectively preserve image detail. Linear filters are another name for gaussian or mean filters23. These linear filters typically enhance the neighborhood values by convoluting the image matrix with the filter mask. The most fundamental kind of noise reduction, linear filtering, typically results in excessive edge smoothing, insufficient feature localization, and inefficient processing of image features24. Due to these restrictions, a specific approach known as the nonlinear filter technique is needed. In contrast, the nonlinear filter approach25 employs a two-stage method. A specific algorithm is used to remove damaged pixels in the second stage after the image’s pixels are initially assessed as damaged or undamaged. Edges and other important aspects in the intended image can be preserved while salt and pepper noise can be eliminated using non-linear filters. The nonlinear filter mechanism is depicted in Fig. 2.

Non-Linear Filtering Mechanism.

Impulse noise detector scans for impulse noise within the image. Basically, impulse noise will appear as random bright or dark spots in the image and may lead to degradation of the image quality. First, an impulse noise detector is used to trace the availability of noise in images as shown in Fig. 2. This detector categorizes the pixels as corrupted or uncorrupted based on their noise levels. In the case of detection as corrupted, they are treated by the median filtering technique for noise removal, while in the case of uncorrupted pixels, they remain without filtering. Later, the output from both processes is combined to obtain a filtered image. Moreover, it integrates various enhancement and mathematical operations for noise-free pic efficiency.

Noise reduction is one of the most crucial processes to complete in image processing. This is because noise causes inaccuracy in the image26. Two requirements must be met for a noise filter to be effective. The first is the suppression of important features in some signals, while the second is noise reduction. Image denoising’s primary objective is to restore noise-corrupted pixels to their original appearance27. A filter is any process, method, algorithm, or formula that may be utilized to remove blemishes, noise, and unnecessary portions from a damaged image. Filters are used to improve images.

Researchers have proposed several methods to reduce impulse noise in digital images. A median filter is known as a method for this purpose28. Tukey introduced SMF in 197129. In this nonlinear filter, which utilizes a sliding window approach of variable size, when the noise intensity reaches 60%, however, the influence of SMF is minor. Through large filters, high degrees of noise reduction can give good SMF efficacy. However, increasing the filter reduces image quality30. Images are blurred and fine lines are removed by SMF even at low noise levels. SMF’s primary goal is to treat every pixel in an image equally, whether or if those pixels are noisy31. SMF has some weaknesses, and a lot of development is intended to address these types of vulnerabilities.

To solve the weaknesses, several alternative filters that are derived from the median filter have been developed. These include two-dimensional median filter, tri-states median filter, and tropical median filter32,33,34. In addition to adding to the detection process by computing the total absolute difference between the grayscale pixel values in the four directions, Dong & Xu updated the notion of the median filter35. The center pixel of a 7 × 7 sliding window is corrected using the directional weighted median filter (DWMF) by determining if its value is 0 or 255, indicating that it is noisy36. However, filtering blurs the image, leaving black and white marks, which adds further complexity during the filtering process, requiring extensive computation.

The only difference between WMF and SMF is that WMF assigns weight to each filtering component. The median is computed using these weights. Many enhancements have been done by researchers to improve the functioning of WMF37. The weighted median filter (WMF) can improve the noise reduction efficacy of the MF by attaching weights to it, allowing the relevance of each element to be regulated by these weights. WMF is a well-studied subject in stereo vision post-processing because it performs better at disparity refinement than classic MF. The computational complexity of the WMF increases directly with increasing window size. This makes it challenging to apply the WMF to embedded devices38. ASWMF is a new technique for recovering images from impulse noise while preserving the smooth structure and edge details39,40. Modified directional weighted median filter, recursive weighted median filter are the improved version of WMF.

Tao Chen and Hong Ren created an adaptive median filter to address SMF’s weaknesses in eliminating fine lines and edges and obscuring valuable image details at minimal levels of noise41,42. The Standard Median Filter MF is designed in such a way that it cannot allow any adaptiveness in selecting the window sizes or even a threshold value. In order to improve this, an Adaptive Median Filter AMF proposes a method for dynamic changing of both the window size and threshold value for each individual pixel depending upon its neighborhood. While MF uses a fixed window size, which may in turn lead to loss of detail and important information, the window size, important edges, and image features are thus made to be preserved properly43. Therefore, when the image is in high density, AMF performs better than the other techniques due to its ability to reduce noise without losing considerable features. When a digital image is corrupted by noise, different parts of the image have different noise intensity levels. Therefore, regions with low noise levels are filtered with a small sliding window, while regions with high noise levels require a larger filter size. Therefore, if filtering is performed, the size of the filter should be adjusted according to the noise level. This type of filter is called an adaptive median filter44. However, filters usually start with a window size of 3 × 3 pixels. The size of the window increases according to the process and stops increasing corresponding to a particular criterion.

The basic goal of a trimmed filter is to remove the noisy pixel from the given 3 × 3 frame. Symmetric trimming at either end is possible using alpha-trimmed mean filtering (ATMF). This method trims both corrupted and uncorrupted pixels. ATMF-induced loss of detail and visual distortion. To address the shortcomings of ATMF, UTMF is recommended45. The items in UDBMF are placed in the 3 × 3 window’s designated rising or decreasing order. The image’s median value is determined after the pixel values 0 and 255 have been eliminated. The noisy pixel is swapped out with this median value. This filter is known as a trimmed median filter when the pixel values 0 and 255 are removed from the chosen window. When processing pixels, the condition is used to assess whether or not they are noisy. It signifies that a processing pixel is noise-free and unaltered if it is between the top and lower boundaries of the grayscale. The processing pixel is labelled noisy and processed with an untrimmed decision-based median filter if it yields the upper or lower boundaries of the gray level46.

DBMF approach first determines if the pixel value is damaged. Like the adaptive median filtering approach, this choice is dependent on whether the pixel value to be processed falls between the processing window’s lowest and maximum values. Since it has been determined to be a noise-free pixel, a pixel is kept untouched if its value falls between the window’s lowest and maximum values; If not, the window’s median value or a nearby pixel value is substituted47.

Damaged pixels are handled differently by a modified decision-based filter. A 3 × 3 selection window is used for MDBMF. In the MDMBF algorithm, the window is initialized with size 3 × 3. If all processed pixels in the current processing window were discovered to be corrupted, the window size was extended from 3 × 3 to 5 × 5. The median result is enhanced by this increase in window size. In the end, the pixel is changed to have the median value of all the pixels in the window. If a whole pixel within the 5 × 5 window is also determined to be corrupted, the previous pixel replacement value is considered48. MDBMF efficiently preserves image details.

The previous works in the line of denoising algorithms have always presented certain difficulties about the correct detection of the position of noisy pixels within the pixel template. These situations often lead to the alteration of non-corrupted pixels, which impairs image quality because of pixel variation that does not need restoration, thus affecting edges and other key features of the image. In this respect, the research proposes a novel methodology of precisely tracing noisy pixels in the pixel template and reinstating them without touching the non-corrupted regions.

i. Novel hybrid approach: Introduction of a unique combination of Adaptive Median Filter (AMF) and Modified Decision-Based Median Filter (MDBMF) for enhanced salt-and-pepper noise reduction while preserving critical image details.

ii. Enhanced noise handling: Effective performance across a wide range of noise levels, from 10 to 90%, with superior image quality maintenance compared to existing methods.

iii. Edge and detail preservation: Superior preservation of fundamental image features, including edges and fine details, which traditional filters often struggle to maintain.

iv. Comprehensive comparative evaluation: Extensive comparison with various traditional denoising methods, such as Median Filter, Adaptive Median Filter, and others, demonstrating the effectiveness of the proposed approach.

v. Impressive Performance Metrics: Evaluation using standard metrics (PSNR, MSE, IEF, SSIM) showing that the hybrid approach significantly improves image quality compared to related techniques.

vi. Broad Application Potential: Applicability across diverse fields like character recognition, medical imaging, agriculture, and remote sensing, highlighting the versatility and impact of the algorithm.

i. Adaptive Window Size: Unlike the traditional median filter with a fixed window size, AMF adapts its window size dynamically based on local noise levels. This flexibility allows the filter to preserve critical image details, such as edges, while effectively reducing noise in different regions of an image. For areas with low noise, AMF uses smaller window sizes, thus reducing computational load, while larger windows are employed in high-noise regions. This adaptability is particularly beneficial when the noise is not uniformly distributed across the image.

ii. Preservation of Image Features: AMF is highly effective at preserving important features like edges, which are often lost in conventional filtering methods. By adjusting the filter size based on the noise characteristics of different regions, AMF ensures that fine image details are maintained, offering a clear advantage over fixed-window filters.

i. Selective Filtering: MDBMF enhances the standard decision-based median filter by incorporating additional criteria to precisely identify and correct noisy pixels. Unlike conventional filters that apply uniform changes across the entire image, MDBMF modifies only corrupted pixels, leaving non-noisy regions untouched. This selective approach ensures that image quality is preserved, avoiding unnecessary blurring or distortion in non-corrupted areas.

ii. Effectiveness in Extreme Noise: MDBMF is particularly robust at handling high levels of impulse noise (up to 80–90%). It accurately distinguishes between corrupted and non-corrupted pixels, making it highly effective for extreme noise conditions where traditional filters tend to blur the image excessively.

The hybrid algorithm integrates the strengths of both AMF and MDBMF, leading to superior noise reduction and image preservation, especially in images with non-uniform and high noise densities. Traditional non-linear filters perform well at lower noise levels but struggle when noise density exceeds 50%. This hybrid method, however, excels in these conditions, effectively reducing noise while preserving essential image details like edges and textures. This combination of adaptive and decision-based filtering methods represents a significant advancement over traditional filters.

The field of image denoising has progressed significantly over the decades, transitioning from early statistical models to sophisticated deep learning techniques. Initial denoising approaches relied on statistical models, like those proposed by Wiener and Kolmogorov in the 1940s, which established the groundwork for filtering noise from signals49. As time went on, methods such as median filtering, Gaussian filters, and non-local means (NLM) were developed to minimize noise while preserving the essential features of images. Nevertheless, traditional techniques often face challenges, such as over-smoothing, which can result in the loss of intricate image details50.

Recent studies in image denoising have shifted focus to more sophisticated hybrid methods that blend classical and contemporary techniques. For instance, in51, researchers propose a hybrid approach that merges regularization with the Perona–Malik model and Pulse Coupled Neural Networks (PCNN) to effectively eliminate mixed noise in natural images. This method leverages the edge-preserving characteristics of the Perona–Malik model alongside the adaptive noise reduction features of PCNN, demonstrating impressive results in managing various complex noise types.

Recent advancements, such as Generative Adversarial Networks (GANs), have been investigated for denoising purposes. A 2022 study presented a technique for removing additive Gaussian noise that combines a GAN model with a semi-soft thresholding method. This innovative approach highlights how generative models can effectively reduce noise while maintaining the integrity of image details52. The method shows potential for use in applications that demand high-quality image restoration with minimal distortion.

Research indicates that deep learning models, particularly convolutional neural networks (CNNs), can be effectively utilized for tasks like image deblurring and noise reduction. One significant approach is the Recursive Deep Convolutional Neural Network (R-DbCNN), which was introduced for natural image deblurring53. This method, when paired with second-generation wavelets, successfully restores images affected by motion blur and noise, showcasing the promising synergy between deep learning and wavelet-based techniques.

In another significant contribution, a recent study from IEEE titled "A New Image Denoising Method for Mixed Gaussian and Impulse Noise Using Adaptive Thresholding and CNN"54 presents an innovative technique that merges adaptive thresholding with convolutional neural networks (CNNs) for the removal of mixed Gaussian and impulse noise. This method takes advantage of CNNs’ capabilities in feature extraction while incorporating adaptive thresholding strategies to effectively address mixed noise. The paper showcases notable advancements over conventional denoising techniques, particularly in noise reduction and edge preservation, making it an important reference in the ongoing development of image denoising methods.

The main idea of the proposed study is to evaluate uncorrupted images from corrupted or noisy images, also known as “denoising” images. Images may be recovered from noisy distortions in a variety of methods. Choosing the appropriate technique is crucial to obtaining the desired result. To address the shortcomings of linear filters, several nonlinear filters have recently been proposed. Nonlinear filters perform better than linear filters in comparison. The median filter is the most typical and extensively used method for handling impulsive noise. A reliable method for eliminating impulse noise without compromising edge information was median filtering. The standard median filter (SMF) drawback, however, is that it tends to distort at large window sizes while being effective at low noise densities. When the noise level is under 50%, SMF performs well; when it is over 50%, the original image becomes blurred. Computational complexity is better for small, fixed windows. At low noise densities, the traditional adaptive median filter is similarly successful, but at high noise concentrations, Additionally, the window size is expanded, and noisy pixels are changed to the median value., which has an impact on blurring55. The Decision-Based-Median-Filter (DBMF), a well-known digital nonlinear filter, has recently been created. The median value of the neighboring pixels is used to replace noisy pixels. DBMF preserves image detail compared to standard median filters because pure pixels remain intact. DBMF is superior to SMF. The biggest disadvantage of this approach is that making effective decisions is not easy. Similarly, when noise density is high, these filters may not successfully protect local characteristics such as image details and edges.

To address these shortcomings, we developed a new hybrid image denoising technique that combines AMF with MDBMF for this purpose. The suggested technique successfully eliminates noise by increasing noise densities while maintaining features and protecting edge details. The results of the suggested approach demonstrate that it outperforms other filters.

In this study, we propose a novel hybrid image-denoising algorithm that combines two advanced techniques: the Adaptive Median Filter (AMF) and the Modified Decision-Based Median Filter (MDBMF). This hybrid approach improves the limitations of traditional filtering methods and effectively addresses high levels of noise in images. The process begins by loading standard test images, such as Barbara, Baboon, and Chest, using MATLAB. A 3 × 3 image window is selected as the initial parameter. To simulate noisy conditions, varying noise levels, ranging from 10 to 90%, are introduced into the input images. The noisy image is then processed through the AMF, as shown in Fig. 3, which removes a significant portion of the noise. After the AMF stage, threshold values are applied to handle pixel intensities outside the valid range (below 0 or above 255). The MDBMF is then used to further refine the image, reducing residual noise while preserving critical details. Following the application of both AMF and MDBMF, the denoised image is evaluated using performance metrics such as Peak Signal-to-Noise Ratio (PSNR), Mean Squared Error (MSE), Image Enhancement Factor (IEF), and Structural Similarity Index (SSIM), providing a comprehensive assessment of the algorithm’s effectiveness.

Steps for hybrid image denoising algorithm.

In the intended scheme, AMF is merged with MDBMF. The core advantage of this new hybrid algorithm is to remove salt & pepper noise, level for impulse noise, and reduce distortion. This new hybrid algorithm also identifying corrupted or degraded pixels in an image, after identification the corrupted pixels are processed for denoising. At low noise densities, prior non-linear filters successfully reduce noise in an image; but, at large noise densities, they only weakly do so. The proposed algorithm’s main objective is noise reduction employing two coupled processes, AMF and MDBMF.

The proposed hybrid approach, AMF-MDBMF, is a carefully designed combination to deal with the special challenges of high-density salt-and-pepper noise in images. Each filter brings out its unique strengths, and their integration provides a robust and complementary framework for superior denoising performance.

The Adaptive Median Filter (AMF) is recognized for its ability to adapt the size of its filtering window dynamically based on the local noise density. This adaptability allows AMF to distinguish between noisy and non-noisy pixels, thus allowing the preservation of essential image structures like edges and textures while noise is reduced. However, at very high noise densities, AMF may be unable to remove noise completely because of its reliance on local window-based operations, leaving some residual noise unremoved.

To overcome the said limitations, MDBMF is included to enhance AMF performance. MDBMF functions by a selective decision mechanism in which it replaces only identified noisy pixels with median values of their local neighborhood. Thus, it preserves uncorrupted pixels from unwanted distortion and provides enhanced visual quality of the denoised image.

The synergy of the AMF and MDBMF develops a hybrid that is tailored especially for addressing noise at very high densities. In the noise-suppression step, AMF achieves fine detail preservation in effective initial suppression. Then MDBMF ensures residual correction without harming the structural information. This can especially be highly efficient in many noise densities larger than 50% where, using many state-of-the-art stand-alone filters and most previous hybrid techniques either smooth the image overly or fails to provide sufficient denoising.

Compared to other hybrid methods, this has its own strengths. Its adaptive and decision-based mechanisms allow for the balance of noise reduction with detail preservation. It also avoids some of the usual pitfalls of the over-blurred or texture lost results of conventional filters and most hybrid methods. This makes it an effective and reliable tool in handling high-density noise in any application requiring image restoration accuracy.

The performance of the hybrid approach is rigorously validated through quantitative metrics, such as PSNR, MSE, IEF, SSIM, FOM, and VIF, as well as visual quality assessments. All the results exhibit the superiority of the proposed technique over benchmark methods, thus effectively removing noise with preserved fidelity on image details.

The proposed hybrid image denoising scheme is based on the adaptive dynamic size of windows while filtering the corrupted pixels in an image. Detailed steps of the algorithm are as follows:

Window Size = 3: At this initial point of the implementation, the size of the window is set to 3 × 3. Maximum Window Size = 21: While applying this filtering procedure, the maximum window size to be considered is 21 × 21.

Min Window Size = 3: Set minimum window size 3 × 3.

[RowCount, ColCount] = Size(image): It refers to the number of rows and columns in the image.

CurPixel = PixelXY: Represents the pixel under process.

MaxVal = 255, MinVal = 0. It is referred to as the maximum and the minimum range for any pixel value.

Find Median Pixels Value: Derive the median value of the pixels in the present window.

IF Window Size ≤ Maximum Value THEN: Reuse the same window size when its value is less than or equal to the maximum.

ELSE Increase the current window size by two: If window size is greater than the maximum value then increases window size by 2.

IF WidSiz ≤ MaxVl THEN goto step three alternately: If window size greater than the upper limit, then next pixel should be processed.

CurPix(x,y) corrupted reported by MedPixVal: If the current pixel is corrupted, then it is updated with the median pixel value.

ELSE CurPix(x,y) uncorrupted: If the current pixel is uncorrupted, then it is left unchanged.

IF Min < PixXY < Max THEN: If the present pixel’s value fits within the valid range (not the extreme values of 0 or 255).

Current Pixel (x, y) Unchanged: The current pixel is left unchanged.

IF PixXY ≠ 0 && PixXY ≠ 255 THEN: If current pixel is not at the extreme values of 0 or 255.

Current Pixel (x,y) is Corrupted, replaced with Median PixVal after excluding 0’s and 255: The current pixel is replaced by the median value after excluding 0s and 255.

IF PixXY = = 0 || 255 && NbrPxls = = 255: If the pixel under evaluation at the ending policies of 0 or 255 and count of such pixels is 255.

Add two in the Width_Size: Add 2 in the window size.

Case I: IF ∀ Px . = 0 && 255: If all pixels were not equal to 0 and 255 in window.

DELETE ("0s&&255s") REPLACE Px: DELETE 0s AND 255s and replace the current pixel.

Case II: IF ∀ Px = = 0 && 255 THEN: Consider all the pixels in the window are either 0 or 255.

Replace Px1Y1 BY Px: Replace the current pixel by another pixel in the window.

Move window size to Pxiyj: Move the window to the next pixel.

Iterate through steps one to ten, that is, the window goes to the last pixel. Repeat steps 1 to 10 until all the pixels of the image have been scanned through by the window.(Fig. 4 ).

Flowchart of the Proposed New Hybrid Image Denoising Algorithm Using Adaptive and Modified Decision-Based Filters for Enhanced Image Quality .

The window size is adjusted automatically with the purpose of filtering corrupted pixels in an image. It starts with a small window and increases the size whenever necessary to find a reliable median value; replace corrupted pixels, and with values 0 and 255. This ensures progressive denoising of the image as the window traverses through the whole image.

This work mainly contributes a hybrid image denoising algorithm with dynamic combination between the Adaptive Median Filter (AMF) and Modified Decision-Based Median Filter (MDBMF), in order to overcome the deficiency of traditional approaches in dealing with high-density noise. The proposed algorithm introduces an adaptive window resizing mechanism, selectively expanding the processing window according to the noise severity, so that corrupted pixels can be identified and denoised precisely without disturbing the uncorrupted ones. This effectively reduces noise, even in challenging scenarios with high noise densities, and mitigates common drawbacks such as blurring, over-smoothing, and loss of image details. Maintaining important features of an image and ensuring localized noise removal, the algorithm exhibits superior performance in preserving the clarity and structure of the image with experimental results that assure its robustness and efficiency.

The study explores the challenges of merging Adaptive Median Filter (AMF) and Modified Decision-Based Median Filter (MDBMF) by presenting a new hybrid algorithm that addresses their key issues, such as blurring and over-smoothing, which can result in the loss of crucial image details. Unlike conventional methods, this proposed approach features an adaptive window resizing mechanism and a focused pixel replacement strategy that processes only the corrupted pixels while keeping the uncorrupted ones intact. By adjusting the window size based on the level and distribution of noise, the algorithm reduces unnecessary signal averaging, ensuring effective noise reduction without sacrificing the integrity of the main signal or excessively compressing the image. This improved method enhances existing techniques, providing a notable boost in noise removal and preservation of image details, especially in high-noise situations.

Figure 5 depicts the architecture of the proposed hybrid image denoising algorithm, which effectively integrates the strengths of the Adaptive Median Filter (AMF) and the Modified Decision-Based Median Filter (MDBMF) to efficiently remove salt-and-pepper noise from images. The process begins with the noisy input image being fed into the system via the Input Layer. Before applying the denoising filters, the image undergoes pre-processing, which includes noise detection and data normalization to prepare the image for optimal filtering. The denoising process is divided into two parallel paths. In the first path, the AMF is applied to reduce impulse noise while preserving critical edge details in the image. This ensures that the structure and boundaries of objects within the image remain intact. In the second path, the MDBMF is employed to handle high-density noise without introducing artifacts, making it particularly effective for heavily corrupted images. The outputs from both the AMF and MDBMF are then combined and averaged to produce a more refined result. This fusion of the two methods allows the algorithm to leverage the strengths of both filters, improving noise reduction while maintaining important image features. Next, the Restoration Layer validates the processed image and reconstructs it, ensuring that crucial details such as textures and edges are accurately restored. Finally, the high-quality, denoised image is passed through the Output Layer, yielding a clean, sharp image with minimal noise and preserved structural clarity. By utilizing this hybrid approach, the algorithm is able to effectively handle both low and high levels of noise while preserving the overall quality and detail of the image.

Architecture Diagram of hybrid image denoising algorithm.

The proposed hybrid image denoising system was implemented and simulated using MATLAB R2017a. The original descriptions of MF, AMF, WMF, UMF, and DBMF methods from the literature were followed to ensure consistency and fairness in the evaluation of their performances. The algorithms were adjusted and optimized as needed to meet the specific needs of this study. This will guarantee that the findings of the study are reproducible and comparable.

The experiments were performed on a computer with an Intel(R) Core (TM) m3-7Y30 processor, operating at a base frequency of 1.00 GHz and a maximum frequency of 1.61 GHz. The system was running a 64-bit Windows 10 operating system. MATLAB was chosen for its wide range of capabilities in numerical computation, programming, and visualization. It is a high-level programming language extensively used for applications in image processing, signal processing, video processing, and communication systems, and is therefore a perfect platform to implement and test the proposed method.

To ensure thorough assessment, benchmark images were resized to 256 × 256 pixels and then applied with various salt-and-pepper noise densities between 10 and 90%. All experiments were carried out under the same conditions for the proposed as well as comparative methods. Both subjective assessments, like visual quality analysis, and objective assessments, including metrics such as PSNR, MSE, IEF and SSIM, were carried out to validate the proposed approach.

Detailed implementation information, hardware specifications, and software platforms ensure that these concerns with respect to experimental repeatability are addressed in this study. This work offers insight into the methods and parameters and therefore facilitates subsequent research and comparisons on image denoising.

To test the performance of the proposed hybrid image denoising method, a benchmark dataset comprising commonly used images in image processing research was chosen. The steps followed in constructing the dataset ensured robustness in the testing procedure and consistency in comparisons with other methods.

i. Benchmark image selection

A set of standard benchmark images, including some examples such as Barbara, Living Room, Mandrill, Boats, Parrot, House, Horses, Liver, and Chest56,57 which vary in their textures, edges, and structural patterns, were chosen. The selection was to cover a broad range of characteristics that may appear in real applications. Each image was resized to a uniform dimension of 256 × 256 pixels, ensuring that all inputs were of the same size and that results could be directly compared across the methods tested. Using such standard images ensures that the evaluation framework is consistent with previous image denoising research.

ii. Noise injection

To test the performance of the denoising method rigorously, salt-and-pepper noise was added into the selected images. The noise density varied from 10 to 90% in increments of 10%, simulating various levels of corruption that might be encountered in practical applications. The process of noise injection ensured that the method was evaluated under a variety of conditions to allow for full exploration of its efficacy in handling the different noise intensities. Noisy versions of the original benchmark images were taken as the testing set and applied to the assessment of the denoising methods, which enabled a direct comparison of their potential to restore images.

iii. Training set

Since the proposed hybrid image denoising method is non-learning-based, it doesn’t require a traditional training phase on labeled datasets. Unlike the traditional supervised learning method, the algorithm works directly on noisy images, learning its specific characteristics and not relying on any prior knowledge or training on some other data. This direct approach enables the assessment of the method strictly in terms of its performance to denoise images and without the pre-requirement of a training set. In this respect, the existence of a training set is essentially ignored, and the method is assessed strictly by real-time performance in denoising.

iv. Test set

The set of noisy images were used in testing. This careful division ensured that all methods to be compared are evaluated in the same controlled evaluation environment. The denoising methods were compared in a fair manner, as their input data are identical. This uniformity of input data leads to an unbiased and objective comparison. For the comparison of the denoising performance, subjective inspection and objective metrics PSNR and SSIM were also used. These measures provide a quantitative comparison of the methods, whereas visual inspection can offer insights into the perceptual quality of the denoised images.

Both qualitative and quantitative assessment methodologies are used to verify the efficacy of the suggested hybrid image denoising procedure. Visual perception of the resulting image is required for qualitative evaluation, whereas error-related quality procedures allow for the quantitative determination of an image. The efficiency of denoised images is assessed using the Peak Signal Noise Ratio (PSNR), Mean Square Error (MSE), Image Enhancement Factor (IEF), Structural Similarity Index (SSIM), Figure of Merit (FOM) and Visual Information Fidelity (VIF) metric55,58,59,60. The overall quality of the restored image is evaluated using these measures. Following is a description of performance metrics:

i. PSNR

The ratio of a signal’s maximum potential value to the effect of corrupting noise on the representation accuracy of the signal is the fundamental formula for PSNR. Usually, the PSNR is expressed in logarithmic decibels, or dB. To evaluate image enhancement upon restoration, the PSNR is employed. Mathematically, PSNR can be stated as follows:

SUPf represents the largest signal value in the original image.

ii. MSE

The MSE is a measure of the overall squared difference in error between the original and compressed image. The MSE (Mean Squared Error) is denoted as:

where m = number of pixels, Pm = observed values and Qm = predicted values.

iii. IEF

IEF assesses how well the recovered image has been improved.

where K(r, s), L(r, s), and M(r, s) represent an original, noisy, and denoised image of proportions x , y correspondingly.

iv. SSIM

SSIM evaluates how much the original and the denoised image resemble each other. [0, 1] is the range of the values. The two images are identical if the value is 1, but there is a difference if it is 0.

Luminance, contrast, and structural components are denoted by the letters X, Y, and Z, respectively. Additionally, p, q, and r > 0 keep track of each term’s relative influence.

v. FOM

One such metric used to assess denoising methods is the figure of merit (FOM), which is based on how well the algorithm preserves the image’s visual quality while removing noise. It typically incorporates perceptual elements of image quality like contrast and edge preservation with quantitative measurements like PSNR or MSE. Because it indicates the improved overall quality following the denoising process, including fine details and significant structures within the image, a higher FOM value is linked to better denoising performance.

The FOM can be expressed in the following general form:

The weights given to each metric are W1, W2, and W3, and they can be adjusted according to how important each metric is in the application.

The weights W1, W2, and W3 are usually normalized in practice so that W1 + W2 + W3 = 1.

vi. VIF

The VIF is a means of measuring how the amount of preserved visual information differs between a reference image and its corresponding noisy or denoised version.

VIF can thus be represented as:

where \({X}_{m}\) is the original image, \({Y}_{m}\) is the denoised image Qm = predicted values.

\({M}_{corr}\) \(\left({X}_{m},{Y}_{m}\right)\) is the mutual information between \({X}_{m}\) and \({Y}_{m}\), and it measures the amount of information shared by the two images.

\({M}_{corr}\) \(\left({X}_{m},{Y}_{m}\right)\) represents the mutual information between the original image and itself, or the total information content of the original image.

The proposed hybrid image denoising technique’s effectiveness is tested using nine benchmark images of size 256 × 256 each, with the 3 × 3 filter template. The Images are Barbara, Living Room, Mandrill, Boats, Parrot, House, Horses, Liver, and Chest56,57. These nine images have been used to evaluate the method’s outcomes against their state-of-the-art competitors like AMF, MF, WMF, UMF, and DBMF61. These images are shown in Fig. 6.

Benchmark images used in the proposed system.

Noisy pixels were found and replaced with noise-free ones by the new hybrid denoising method. Different noise densities of 10% to 90% were added to introduce the real-world effects, after which the proposed hybrid filtering methodology was applied by integrating the improved decision-based median filter with an adaptive median filter. The PSNR, MSE, IEF, SSIM, FOM and VIF performance metrics were computed, showing the performance of the algorithm in terms of noise reduction and improving the quality of the image. Both subjective (qualitative) and objective (quantitative) evaluations have been used to comprehensively evaluate the suggested process of denoising. The results of this subjective and objective evaluations comparative analysis showed that, at least for higher noise densities, the proposed approach consistently performed better than the state-of-the-art methods in terms of image quality restoration.

Subjective evaluation of each benchmark image is done to verify that the de-noised images produced by this new hybrid approach is of an intuitive quality. All of the benchmark image sizes used in this study remain at 256 × 256 pixels. On images with salt and pepper noise intensities varied from 10 to 90%, and the suggested image denoising technique was put to the test. Additionally, the performance of the suggested hybrid technique is contrasted with that of current median filters, AMF, MF, WMF, UMF, and DBMF.

A visual comparison study, as depicted in Table 1, was performed to assess the filtering results of the proposed method. It was found that although the quality of restored images degrades with an increase in noise density, the proposed method successfully removes salt-and-pepper noise with some residual black and white dots at higher noise levels.

When one applies a filter to an image, one not only removes noise but possibly some useful information. On the other hand, the proposed filter exhibits great detail preservation capability especially concerning textures and edges at low noise densities. The higher the noise density, the worse the picture quality as far as it is affected by the constraining power of MF. Specifically, MF is a poor filter at high noise densities, and often very much of the image information, such as blurred edges and loss of sharpness, is lost.

In total, by numerical and visual comparison, the proposed method is superior to other methods52,53,54,55,56,57,58,59,60,61,62,63 in denoising efficiency and image quality.

Table 1 describes the subjective performance of benchmark images, where it is visually comparing the perceptible quality of the denoised images obtained from the proposed approach with those yielded by AMF, MF, WMF, UMF, and DBMF in case of their respective noisy images varying from 10 to 90%.

Existing techniques like MF and WMF are effective for images with a salt-and-pepper noise level of 10% to 20%. These methods produce de-noised images of reasonable perceptual quality at these noise levels.

When the noise level is high, the MF and WMF algorithms have little effect in eliminating noisy pixels, and the quality of the filtered images visibly deteriorates. Under such conditions, AMF, UMF, and DBMF are shown to perform better in maintaining the quality of the images.

AMF, UMF, and DBMF perform poorer in terms of noise suppression at higher noise levels, where it degrades visual quality. All the de-noising performance diminishes with low values for clarity of the images.

In contrast, the proposed hybrid method, that is, AMF + MDBMF, realizes better de-noising effectiveness as well as good perceptual quality at noise densities ranging from 60 to 90%. This is owed to its feature of adaptive hybridization of both the strengths of AMF and MDBMF. Thus, image details are best preserved with strong noise suppression.

The proposed hybrid algorithm shows an unmatched ability to denoise images with noise densities up to 90%, outperforming all the compared methods. This superior performance is evident in the subjective evaluation results presented in Table 1. The visual comparisons further confirm that the hybrid approach effectively balances noise reduction and detail preservation, even under extreme noise conditions.

To assess how well the suggested algorithm performs, various variables like PSNR, MSE, IEF, and SSIM are computed. Barbara, Living Room, Baboon, Boat, Parrot, House, Horse, two medical images Chest, and Liver are used in the proposed approach56,57. The implementation of this technique has been put to the test for a variety of noise levels between 10 and 90%. AMF, MF, WMF, UMF, and DBMF are examples of approaches that are currently in use. Tables 2, 3, 4, 5, 6, 7, 8, and 9 compare the performance metrics of the proposed approach to all the existing approaches.

The proposed technique is validated quantitatively by comparison with previous methods, including Based-on Pixel Density Filter (BPDF)62, adaptive type-2 fuzzy filters (AT2FF)63, tropical algebra median filter (TMF)64, adaptive Riesz mean filter (ARmF)65, iterative mean filter (IMF)66, adaptive Cesáro mean filter (ACMF)67, adaptive content based closer proximity pixel replacement algorithm (ACCPPRA)68, four stage median-average filter (FoMA filter)69, different adaptive modified Riesz mean filter (DAMRMF)70, different applied median filter (DAMF)71, a modified form of different median filter (MDAMF)72, and infusion of support vector machine (SVM) and median filter (MF)34. These current approaches, which range from fuzzy sets and nonlinear filters, were selected from some of the most recent studies that covered the years 2018 to 2024. Comparing the proposed method to current approaches ensures that noise reduction is optimized.

As it can be seen from Table 2, AMF + MDBMF has the best PSNR values for 70% and 90% NDs (Noise Densities) when compared to other approaches.

At 70% ND, most of the methods such as SVMMF, ACCPPRA, and IMF recorded PSNR values slightly above 30 dB. The proposed technique stood out among these with the highest value of 34.46 dB and hence spoke on its superior ability to maintain image quality under a moderate noise condition.

At 90% ND, the changes in PSNR values are very high. While most of the methods, namely DAMRMF, IMF, and FoMA FILTER, obtained PSNR values above 26 dB, the proposed technique still recorded a very high value of 32.93 dB. Contrarily, several methods considerably suffered from this, with low values like 10.78 dB and 18.3 dB, respectively.

The same comparison underlines that the proposed technique outperforms all the others, especially in high noise conditions-90% ND-where it always reports the highest values of PSNR. It further indicates the robustness and efficiency of maintaining image quality over diverse noise levels.

Table 3lists comparison of PSNR values taken for 9 benchmark images, both normal and medical images, at 70% and 90% ND52,53,54,55,56,57,58,59,60,61,62,63. The medical images considered in this work is unique, since previous approaches were performed with normal images only. From the results, it can be noticed that PSNR values for all images, both normal and medical, maintained values around 30 + dB for 70% and 90% ND.

Most of the images, as can be seen, consistently have PSNR between 70 and 90% ND. The Boat image, for instance, showed a very small difference of only 1.65 dB in PSNR between 70 and 90% ND, or 34.43 dB and 32.78 dB, respectively. This indicates a minimum loss in image quality as noise density increases. This pattern is also seen in medical images, where there is only a 3.01 dB difference between the Medical Image Liver’s measurements of 35.92 dB at 70% ND and 32.91 dB at 90% ND. 34.27 dB is realized for the Medical Image Chest at 70% ND and 31.74 dB at 90% ND, demonstrating the effectiveness and robustness of the proposed approach in processing both normal and medical images under a high degree of noise corruption52,53,54,55,56,57,58,59,60,61,62,63.

Tables 2, 3, 4, 5, 6, 7, 8, 9 make it abundantly evident that, after computing PSNR, MSE, IEF, SSIM, FOM and VIF, the hybrid system outperforms other techniques. Additionally, the graphical interpretation in Figs. 7, 8, 9, 10, 11, 12 unmistakably shows how effective the suggested denoising approach is in removing noise and conserving edges.

Comparison of PSNR values on different images.

Comparison of MSE values on different images.

Comparison of IEF values on different images.

Comparison of SSIM values on different images.

Comparison of FOM values on different images.

Comparison of VIF values on different images.

The MF and WMF filters work properly only when there is very little amount of noise present. For every benchmark image, the AMF, UMF, and DBMF filters outperform the MF and WMF filters.

The results show that the suggested method produces high-quality denoised images, which makes it a promising solution for a variety of image processing applications. The results are assessed using PSNR, MSE, IEF, SSIM, FOM and VIF.

The suggested technique outperforms previous approaches in terms of PSNR, IEF, SSIM, FOM and VIF, regardless of the degree of noise present in the provided image. The FOM scores clearly depict the preservation of edge details of the denoising techniques. For noise densities in the range of 10%−20%, most methods show competitive performance. But at noise densities of 30%−90%, the proposed method is significantly superior, as higher FOM values are maintained for other methods, meaning that the edges and structures are preserved better.

The VIF scores are measures of the perceptual quality of the denoised images. In all cases, the proposed method always attains the highest values of VIF across the entire range of noise levels, implying higher perceptual fidelity to the original image. For benchmark methods such as MF and WMF, the VIF drops precipitously for high noise densities, above 50%, while the proposed method has robust performance. The proposed hybrid algorithm’s MSE is also lower when compared to other current methods.

Gaussian noise is very different from salt-and-pepper noise because it obeys a normal distribution and is not represented as isolated high-intensity or low-intensity pixels. The following changes were applied to the algorithm to make it suitable for Gaussian noise:

Traditional median filtering is not effective for Gaussian noise. Therefore, a combination of adaptive median filtering and weighted median filtering was used to enhance the performance.

The window size for adaptive median filtering was enlarged, and in the weighted median filter, the mask was made Gaussian-weighted to incorporate the distribution characteristic of the noise.

The same metrics (PSNR, MSE, IEF, SSIM, FOM and VIF) used for salt-and-pepper noise were used to assess the method’s performance.

All nine images were subjected to Gaussian noise in the preliminary analysis, with different noise variances and percentages. Table 10 summarizes the experiment’s findings by contrasting how well different filtering techniques, including the suggested strategy, perform at varying noise levels.

The suggested approach (AMF + MDBMF) consistently performs better than alternative strategies at all noise levels, as indicated in Table 10. This demonstrates its robustness and effectiveness, especially in high-noise environments.

Comparative analysis based on average values among each algorithm namely: AMF, MF, WMF, UMF, and DBMF have been evaluated based on noise 10% to 90% correspondingly as demonstrated in Table 11 and Figs. 13, 14, 15, 16, 17, 18.

Average PSNR Comparison.

Average MSE Comparison.

Average IEF Comparison.

Average SSIM Comparison.

Average FOM Comparison.

Average VIF Comparison.

The interpretations based on the Comparative assessment (Average Values) are listed be-low. Regardless matter how much noise is present in the image, the suggested approach is efficient and effective at reducing impulsive noise and assures those uncorrupted image pixels are kept intact. Prevent signal degradation, prevent the situation wherein noisy pixels are swapped out for more noisy ones, and preserve the needed image’s borders and other important information.

The proposed system upgrades the quality of images from their degraded version affected by noise, and blur which may disturb throughout the process of transmission, acquisition, storage, etc.

In addition to quantitatively and qualitatively evaluating the proposed method, a computational efficiency measure was conducted with respect to establishing its feasibility in real-time scenarios. The execution time of the algorithm was quantified for different degrees of haze levels, as seen in Table 12 and Fig. 19.

Computational efficiency of the proposed method under different haze densities.

The results clearly indicate that, for higher haziness, the running time gradually increases. This trend is as expected since greater haziness means that the algorithm needs to process more and more complex image details and noise artifacts. However, the method proposed exhibits consistent and scalable performance, maintaining reasonable processing time even at higher haziness.

This observation underlines the algorithm’s ability to handle computational loads across a wide range of conditions. The approach proposed in this paper shows much better accuracy with less computational overhead as compared to the traditional methods used in similar scenarios.

This suggests that it is well-suited for any application requiring efficient image dehazing, such as surveillance systems, autonomous vehicles, and environmental monitoring. The performance achieved thus far really underscores potential for real-time or near real-time applications, where computational efficiency is at a premium.

One factor that determines whether an image denoising algorithm is practically applicable in resource-constrained or real-time environments is its computational cost and overhead. Most of the algorithms emphasize improving the quality of the images, but a considerable amount of overhead is associated with the introduced methods, and these methods, when deployed in high-resolution or high-speed applications, need special care.

In this section, we discuss the computational cost and overhead of the proposed hybrid algorithm in comparison to standard denoising methods, including AMF, MF, WMF, UMF, and DBMF. The comparison is made based on execution time, resource utilization, and scalability at different resolutions and noise levels, as summarized in Table 13. The table presents the trade-off between the cost of computation and the quality improvement for each method.

The Proposed Hybrid Algorithm, compared with all the above methods, provides a better PSNR (37.2678), MSE (16.4716), IEF (218.5217), SSIM (0.7408), FOM (0.68), and VIF (0.61). This proves that the proposed method is superior for the overall quality of the image.

For applications like high-quality image denoising, where image quality is crucial, the proposed hybrid algorithm is the best option because it performs better than all other algorithms across all performance metrics. Despite the increased computational overhead, the performance gains are substantial enough to outweigh the trade-off, and real-time applications can be made possible through optimization techniques.

The performance of the hybrid approach is quantitatively evaluated in terms of various image quality metrics like PSNR, MSE, IEF, SSIM, FOM and VIF. PSNR gives the quality of the overall denoised image, the higher this value, the better the result. MSE fundamentally computes the average error between the original and denoised image. The lower its value, the better the accuracy. IEF accounts for a measure of the degree of enhancement, while SSIM compares the structural integrity between the original and processed images. FOM (Figure of Merit) measures the edge preservation ability of the denoising algorithm. The higher the value, the better the edges are preserved. VIF (Visual Information Fidelity) measures visual quality by comparing the amount of visual information preserved in the denoised image with respect to the original. The higher the value, the better the fidelity. Such a combination of filters turns out to be very effective for noise reduction in a wide range of noise densities and hence is reliable in image denoising for complicated environments. The previous works in the line of denoising algorithms have always presented certain difficulties about the correct detection of the position of noisy pixels within the pixel template. These situations often lead to the alteration of non-corrupted pixels, which impairs image quality because of pixel variation that does not need restoration, thus affecting edges and other key features of the image. In this respect, the research proposes a novel methodology of precisely tracing noisy pixels in the pixel template and reinstating them without touching the non-corrupted regions. The novelty in the proposed hybrid denoising algorithm lies in the strategic integration of the Adaptive Median Filter with the Modified Decision-Based Median Filter. This embeds an effective solution to some serious drawbacks of traditional filters by leveraging adaptive window size in the AMF for a wide range of noise levels, while preserving key image details such as edges. While doing so, targeted noise removal by the MDBMF occurs only for the corrupted pixels to reduce unnecessary changes in non-noisy areas. This hybrid approach achieves an improved noise reduction and edge preservation, particularly in high-density salt-and-pepper noise where traditional methods often fail. The effectiveness of the proposed algorithm also extends to key denoising artifacts and distortion common in conventional denoising, which has very high-noise images. This implies accurate noisy pixel identification and processing, keeping the non-corrupted areas intact, which provides very good image output. Extensive evaluations using benchmark images have demonstrated that the proposed hybrid algorithm achieves very good improvement regarding noise reduction, image quality, and retaining more details compared to the conventional filters MF, AMF, WMF, UTMF, and DBMF. The field of image denoising is advanced by this novel combination, which offers a reliable and efficient solution. This planned mechanism consistently performs better in benchmark images and medical images with varying noise ratios.

In the proposed hybrid denoising approach, the performance was tested to be sensitive to key parameters of the Adaptive Median Filter (AMF) such as window size and the threshold values of the Modified Decision-Based Median Filter (MDBMF). Parameters are critical to the balance of noise suppression and detail preservation, so a systematic analysis was conducted for their impact on denoising effectiveness. Consequently, the impact of these parameters on denoising effectiveness could be systematically analyzed, as shown in Fig. 20.

Key Parameters’ Impact on Denoising Performance.

The window size in AMF defines the extent to which neighboring pixels are considered for adaptive filtering. The smaller windows provide localized filtering and may not suppress noise while giving a high density of noise regions. In this case, larger windows improve noise suppression but tend to over smooth minute details. Different sizes between 3 × 3 and 11 × 11 have been used to perform experiments. The results show that a 5 × 5 window size is optimal, with high noise reduction and preserved edges and textures, especially for noise densities up to 70%. Beyond this, a slightly larger window (7 × 7) provided better results without significant degradation of detail.

The threshold values in MDBMF determine the criteria for identifying noisy pixels. Lower thresholds classify fewer pixels as noisy but leave residual noise in the images. Higher thresholds may incorrectly identify non-noisy pixels, where replacements are more than necessary, or details are lost. Sensitivity analysis was based on varying the threshold values through a range of noise densities that were 10%–90%. The optimal threshold was found to vary with noise density, while the lower thresholds, such as 0.1, seemed to perform well at low noise levels and the higher thresholds, such as 0.5, performed better with high noise densities.

The sensitivity tests showed that the algorithm is robust over a reasonable range of parameter values, with optimal settings determined as a window size of 5 × 5 or 7 × 7 and threshold values adjusted based on the noise density. These results highlight the adaptability of the hybrid method, which allows it to maintain performance under varying conditions without the pitfalls of over-parameterization common in similar techniques.

The results of the sensitivity analysis allow for practical selection of parameters for real-world application. Optimal parameter values could be adjusted dynamically according to noise density observed in input images and thus improve versatility and applicability of the method in a wider range of applications.

This paper proposed a hybrid image denoising technique which combined Adaptive Median Filter (AMF) with the Modified Decision-Based Median Filter (MDBMF) to be used in efficient removal of salt-and-pepper noise. Utilizing the capabilities of both filters, the new method correctly detects noisy pixels and recovers them along with maintaining fine details and preserving edge structures within images. The evaluation through experiments, which was made on benchmark datasets, showed that the proposed method worked well to achieve better denoising performance than conventional methods such as AMF, MF, WMF, UTMF, and DBMF. Higher PSNR and low MSE and retention of structural integrity make it suitable for applications requiring accurate restoration of images.

Despite its advantages, the proposed approach has some limitations that will need to be addressed in future research. The method is very effective for salt-and-pepper noise, but it has not been tested for other types of noise, such as speckle, and Rayleigh noise. Future work may focus on extending the applicability of the method by integrating advanced deblurring techniques, fuzzy logic, or neural network-based algorithms. Another limitation is that it does not have a 3D implementation, which would limit its application in domains such as medical imaging (e.g., MRI and CT scans) and 3D reconstruction. This limitation would be removed by extending its applicability to volumetric data.

Furthermore, although the algorithm is robust in grayscale images, its capability in color image processing should be further enhanced so that it captures natural appearance and retains details even in complex situations. It may incorporate machine learning models, including CNNs or GANs, which can be more effective for a wide variety of noise models and real-time applications.

Further, evaluating its extension to multi-modal imagery, such as hyperspectral and satellite images, will increase the utility of industrial and scientific applications much more. The combination of adaptive noise models with multi-scale approaches is also a promising way to improve performance in challenging scenarios.

In conclusion, with this proposed hybrid denoising algorithm, quite important advancements regarding noise removal and edge preservation, it is believed that addressing current limitations will prove critical to reaching the full scope of its usage in diverse applications with demanding standards.

All data generated or analyzed during this study are included in this article.

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This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2025-00554526), the Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2023 (Project Name: Cultural Technology Specialist Training and Project for Metaverse Game, Project Number: RS-2023-00227648), and the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (grant number: HI22C1651).

School of Computing, Gachon University, Seongnam, 13120, Republic of Korea

Faiz Ullah, Jawad Khan & Younhyun Jung

Department of Computer Science, Sindh Madressatul Islam University, Karachi, 74000, Pakistan

Kamlesh Kumar

Department of Computer Science, Kingston University, London, UK

Tariq Rahim

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Conceptualization, F.U., and K.K.; methodology and software validation, F.U., and K.K.; formal analysis and original writing, F.U., and J.K.; writing-reviewing and editing, F.U., K.K., M.A., and J.K.; data curation, T.R.; visualization, F.U., and T.R.; supervision, J.K., project administration, Y.J.; funding acquisition, Y.J.; All authors have read and agreed to the published version of this manuscript.

Correspondence to Jawad Khan or Younhyun Jung.

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Ullah, F., Kumar, K., Rahim, T. et al. A new hybrid image denoising algorithm using adaptive and modified decision-based filters for enhanced image quality. Sci Rep 15, 8971 (2025). https://doi.org/10.1038/s41598-025-92283-3

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Received: 13 November 2024

Accepted: 26 February 2025

Published: 15 March 2025

DOI: https://doi.org/10.1038/s41598-025-92283-3

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