Combining Fusion-Based Thresholding and Non-Linear Diffusion for Improved Speckle Noise Mitigation in SAR Images

Abstract

The primary concern of synthetic aperture radar (SAR) images is speckle noise, an inherent property. The creation of speckle noise is in a granular form and its nature is multiplicative. To reduce such noise from the radar images, the researchers’ primary motive is to suppress granular pattern while preserving the quality of the obtained images, thereby facilitating easier feature extraction and classification. Existing speckle-noise reduction methods often fail to preserve fine details such as edges and textures. This study proposes a fusion-based method that integrates non-linear transform-based thresholding with advanced noise reduction techniques. The proposed method is implemented on two simulated SAR images at noise variance levels of σ = from 5 to 40. The fundamental and most significant step is to analyze the effect of granular patterns in radar images before despeckling. Different performance metrics, classified into with-reference and without-reference indexes, are considered to investigate the effectiveness of the proposed despeckle method. The Signal-to-Noise Ratio (SNR) for SAR-1 at σ = 20 was observed at 16.22 dB, outperforming the next best result of 12.89 dB from the Log Compression filter. The Universal Image Quality Index (UIQI) reached 0.6987, indicating high visual quality retention across various noise levels. The proposed despeckling method demonstrated superior performance in comparison to different filters, achieving a Peak Signal-to-Noise Ratio (PSNR) improvement of up to 29.37 dB on SAR-2 at a noise variance of σ = 5, significantly higher than the best filter method’s 26.70 dB. Additionally, the method achieved a Structural Similarity Index Measure (SSIM) of 0.6538, indicating superior image quality preservation.

1. Introduction

Synthetic Aperture Radar (SAR) is used to create high-resolution 2D and 3D images through reflected radar signals, functioning effectively in all weather conditions [1]. SAR uses reflection, scattering, refraction, or absorption of targeted areas to generate precise topographic images [2], making it valuable in defense, surveillance, object detection, remote sensing, and global positioning [3,4,5]. However, SAR images are often degraded by speckle noise, which challenges image quality [6]. While SAR synthesizes a large antenna from radar echoes, enabling precise distance calculations through microwave radiation [7], the received signals may differ from transmitted ones, causing further degradation [8,9]. Traditional noise reduction methods tend to smooth images but fail to preserve critical details like edges and textures, necessitating more robust approaches to enhance SAR image quality while retaining fine details.

Lee [10] is a widely used method for speckle-noise suppression in coherent imaging systems like SAR and ultrasound. It operates on an adaptive filtering approach, assuming a multiplicative noise model, where noise is proportional to the signal. The filter adapts based on local mean and variance to smooth homogeneous areas while preserving edges and important features. Homomorphic Filtering with Log Function (HFLF) [11] is a technique for reducing speckle noise in SAR images by converting the multiplicative noise into an additive form using a logarithmic transformation. This simplifies noise handling, allowing conventional filters to effectively reduce noise while preserving important features. After filtering, the image is restored to its original form, resulting in a clearer, despeckled SAR image, ideal for further analysis. This approach enhances noise suppression and edge preservation, making it effective in radar and medical imaging. However, its main limitation is that it can be computationally intensive, requiring complex algorithms for frequency decomposition and filtering. Additionally, improper tuning of frequency bands may lead to over-smoothing or loss of fine details. Balancing these aspects is crucial to achieving optimal noise reduction while maintaining image quality. The Kuan filter [12] is an adaptive technique for speckle-noise suppression in coherent imaging systems, such as SAR and ultrasound. It operates by estimating local statistics and adapting its smoothing based on the image’s local variance, which helps to reduce noise while preserving edges. Despite its effectiveness, the Kuan filter has limitations, including its sensitivity to parameter settings, which can affect its performance. It may also struggle with highly variable noise environments or non-uniform textures, potentially leading to either over-smoothing or inadequate noise reduction. Balancing these factors is crucial for optimal results. The median filter [13] is a non-linear technique used for speckle-noise suppression in images, including those from SAR and ultrasound. It replaces each pixel’s value with the median of the pixel values in a local neighborhood, effectively reducing noise while preserving edges. However, its limitations include reduced performance in preserving fine details and texture, as it can blur edges and structures if it is not properly configured. Additionally, the median filter may not handle high levels of speckle noise as effectively as adaptive filters, leading to suboptimal noise reduction in complex or highly textured regions. The Frost filter [14] is an adaptive technique designed for speckle-noise suppression in radar and medical imaging. It smooths images based on local statistics while preserving edges, using a weight function that decreases with distance from the central pixel, allowing for adaptive noise reduction. Despite its effectiveness, the Frost filter has limitations, including sensitivity to the selection of its parameters, such as the smoothing parameter and window size. This sensitivity can lead to either insufficient noise suppression or excessive blurring. Additionally, it may struggle with non-homogeneous textures, resulting in uneven noise reduction across varying image regions. Recently, a Log Compression filter [15] has been used for speckle-noise suppression by applying a logarithmic transformation to the image, which compresses the dynamic range and reduces the impact of speckle noise. This technique enhances image contrast and helps in noise reduction by transforming multiplicative noise into additive noise, which is easier to manage. However, its limitations include a potential loss of image details and contrast in high-intensity areas due to the compression effect. Additionally, log compression may not be effective in preserving fine structural details, particularly in images with a wide range of intensities, leading to potential artifacts or reduced detail fidelity. Despite the fact that a few of the above-mentioned filters [10,12,13,14] are traditional, these continue to be widely used in research as benchmark methods for evaluating and comparing the performance of newer despeckling techniques [16,17,18,19].

Recently, the most common methods for speckle noise mitigation in SAR images can be broadly classified into two categories: thresholding-based and diffusion-based techniques. Thresholding methods, including traditional and fusion-based approaches, focus on separating noise from useful signals by setting thresholds to identify and suppress noise [20]. Fusion-based thresholding improves upon this by combining multiple thresholding strategies, leading to more effective noise isolation [21]. In [22], a technique based on wavelets was developed to address the multiplicative characteristics of noise present in radar images. The low-pass and high-pass filters for further despeckling need to decompose the transformed image using the discrete wavelet transform (DWT) method. Also, it helps to classify the images into two categories: the approximate part and the detailed part of the images. The absolute mean deviation and threshold value assist in determining the efficiency of the model at different noise variances. This model works with the limitation because the resultant images still carry the noise, which leads to blurred edges; the authors in [23] propose a novel SAR image classification framework that tackles the challenge of speckle noise by using multi-feature fusion and adaptive kernel combination. They enhance classification accuracy by integrating texture, contextual, and spatial information through a newly defined non-negative logarithmic likelihood difference metric and local consistency optimization. However, the approach has limitations in handling extremely noisy environments or varying noise levels across different images, as the adaptive methods may not fully account for all variability in real-world scenarios. The despeckling filter proposed in [24] uses a Bayesian filter based on direction lets, augmented by a homomorphic filtering approach specifically designed for SAR images. The homomorphic directionless elements are modeled to exhibit a Cauchy distribution, while granular pattern noise is characterized by a Gaussian distribution. These two methods are integrated with the addition of maximum a posteriori computation operation to estimate the noiseless components. The efficiency rate is accepted in terms of dealing with the granular form of noise. In [25], the concept of despeckling related to the granular form using curvelet transform was brought in, as well as an improved practical swarm reduction mechanism for enhancing the image characteristics was brought in. The practical swarm reduction mechanism has been integrated because it globally leads to granular pattern removal and image correctness. It is observed as quite a good model in terms of taking care of the granular pattern of the noise. In [26], the framework has been designed to deal with the multiplicative nature of the granular form, implementing non-local filtering and wavelet shrinkage using random homogeneous metrics. The obtained outcomes of the proposed method show greater value in terms of PSNR in texture preservation as well as despeckling. Also, it deals precisely in terms of smoothing the pixels in homogeneous regions. It is compared and tested with some other non-local filtering methods using Bayesian approaches in both ultrasound and radar images. This work presents the effectiveness of non-local filtering in terms of reducing the granular form in radar images. In [27], the fusion-based granular pattern removing model was developed by implementing a directional smoothing technique and method-noise thresholding with the addition of the db2-based two-dimensional discrete wavelet transform (2D-DWT). The experimental results of [27] showed that tests on simulated and real radar images and were compared and validated using the performance metrics. The complete despeckling framework runs around the directional smoothing method, wavelet thresholding with the addition of the Bayesian shrinkage rule, and method-noise thresholding. In the decomposition process, the images are classified into two categories: approximate and detailed. The approximate parts obtained after decomposition and the relative factors are taken care of using the directional smoothing method. In the case of the detailed parts, the relative factors are taken care of by the wavelet thresholding with the addition of the method-noise thresholding. In [28], the statistical features are analyzed and implemented by the DWT to deal with granular patterns in radar images. The primary focus of existing techniques has been on enhancing image quality, often at the expense of retaining original image features and reducing noise. This trade-off can lead to the loss of fine details and biased post-processing outcomes.

Diffusion-based techniques, particularly non-linear diffusion, focus on smoothing the image while preserving important structural features like edges [29]. The study of [30] introduced the concept of anisotropic diffusion and proposed a new description of scale-space and a class of processes used to understand a diffusion method. This technique is widespread in image processing. The main purpose of the proposed technique is to precisely deal with the granular form without losing the major characteristics of the images. In [31], the concept of an anisotropic diffusion-based method is intelligently enhanced and implemented on radar images for dealing with speckle noise. The proposed method is quite efficient in mean preservation, speckle-noise reduction, and edge detection and preservation, and the determined efficiency shows precise results compared to other despeckling filters and conventional anisotropic diffusion methods. The study of [32] proposed a filtering model that deals with the granular using median refined anisotropic diffusion. The purpose of implementing the median filter in the proposed method is to preserve the major characteristics of the images. With the anisotropic diffusion, the median filter is implemented to achieve an efficient result, as the median filter precisely deals with salt-and-paper noise. In [33], a method was developed to reduce the noise in a granular form by incorporating an enhanced anisotropic diffusion model. This model focuses on preserving edges by taking into account the local directional changes in intensity and grayscale levels. It has a good potential to remove the granular pattern in radar images. The resultant images still carried the noises, which decreased the efficiency of the model due to the high amount of darkness, which shows its limitation. As a result, the developed model efficiently works in terms of preserving the fine details like edges. In [34], a recognized detail-preserving anisotropic diffusion is presented for the SAR image that mainly undergoes low presentation at the edges and severe blocking artifacts in homogeneous regions. The study of [35] proposed a new despeckling method in SAR images using the arrangement of different alternative analysis processes on the same speckled images. The proposed method is reliable as pixel-wise feature extractions of the image. It works precisely in the diversity by combining useful performance metrics for each image region. It becomes enhanced as a simple despeckling technique by subsequently considering and highlighting the complementary characteristics of only two state-of-the-art tools. In [36], the homomorphic method has been proposed with the efficient implementation of the anisotropic diffusion and method-noise threshold with the addition of db2-based 2D-DWT. To preserve the fine details, the median and wiener filters are implemented on the LL block. After obtaining the despeckled images, they become further despeckled by the intelligent use of the newly proposed method, known as method-noise thresholding, which produces the final filter images. The experimental results showed that the results of [37] were tested on simulated and real radar images and were compared and validated using the performance metrics.

Combining DWT with non-linear diffusion and method noise thresholding enhances speckle noise mitigation in Synthetic Aperture Radar (SAR) images. DWT decomposes the image into various frequency bands, facilitating targeted noise reduction. Non-linear diffusion smooths the image while preserving edges, addressing high-variance noise. Method noise thresholding applies a dynamic threshold to distinguish between noise and significant features. Integrating these techniques with fusion-based thresholding improves the overall effectiveness by leveraging the strengths of each method. The proposed method merges these two approaches fusion-based thresholding for noise separation and non-linear diffusion for detail preservation, offering a superior noise reduction solution over existing methods. The contributions of this work are as follows:

(i)

The proposed model effectively suppresses granular noise in synthetic aperture radar (SAR) images while maintaining intricate details. This method shows a superior ability to preserve fine structures, such as edges and textures, in both homogeneous and non-homogeneous land regions.

(ii)

It exhibits a heightened potential to retain crucial image features, including edges and texture, which are essential for accurate image analysis and classification. This capability ensures that the integrity of the original image features is maintained, facilitating more reliable interpretations.

(iii)

The experimental findings have been rigorously validated using two pieces of simulated SAR imaging data. This validation confirms the robustness and effectiveness of the proposed method in practical applications, demonstrating its utility in real-world scenarios.

2. Speckle Noise Model

The continuous interactions of the signals with the target surface initiate the inconsistent constructive and distorted noisiness that leads to a granular pattern, known as speckle-noise, obtained in SAR images, which is multiplicative in nature. The speckle noise is relatively affected, like a salt-and-paper noise. Speckle is an assorted exercise but not a noise [38]. The continuous contact of the high-frequency RADAR signals critical pattern of the diffusers usually limits the perspectives of the SAR processing model development and applications. Also, it affects the SAR images.

The multiplicative nature of the granular form in SAR images can be expressed mathematically as follows [6,38]:

$$\mathrm{I}=\mathrm{D}\left[\mathrm{i}\right]\mathrm{M}\left[\mathrm{n}\right]$$

(1)

where $\mathrm{D}\left[\mathrm{i}\right]$ denotes the desired image and $\mathrm{M}\left[\mathrm{n}\right]$ refers multiplicative noise.

3. Related Concepts

3.1. Discrete Wavelet Transform

It mainly transforms the image to the frequency domain from the spatial [28,29,30,31,32,33]. In the proposed methods, the 2D-DWT was implemented to analyze the low- and high-intensity components in the radar image. The 2D-DWT coincides with the multi-resolution approximation process and the wavelet operation. The filters, such as low and high pass filters, have been selected, and the frequency scales are as follows: filter pair estimations. A low-pass filter was employed to obtain the low-frequency components. By applying 2D-DWT to the image at the correct level, it transforms the image into four sub-bands, i.e., LL1 (approximate image), HL1 (horizontal noise coefficient), LH1 (vertical noise coefficient), and HH1 (diagonal noise coefficient), as shown in Figure 1a. To obtain a two-tiered decomposition, 2D-DWT is again applied to LL-DWT and decomposed in the same way; thus, additional sub-bands are generated, as shown in Figure 1b.

3.2. Non-Linear Diffusion

Speckle-noise phenomena and their restoration are a common and universal problem in SAR image processing. Such noises degrade the quality of the images, which leads to difficulties in feature extraction objects holding the prime significant details related to the image. Various methods and filters are available to smooth the degraded image. These despeckling techniques rely on the spread value of the pixel. There are two diffusion methods used for despeckling in SAR images: isotropic and anisotropic diffusion. In isotropic, the spread values of the pixel in the SAR image, which degrades the image quality, exercise the mean on the entire edge of the images [6,39,40]. In anisotropic diffusion, diffusion relies on the direction of the images. It determines the mean of the image, such as the side of an edge, object, and boundary.

The mathematical expression of the anisotropic diffusion is as follows:

$${\displaystyle \frac{\partial \mathrm{I}(\mathrm{i},\mathrm{j},\mathrm{t})}{\partial \mathrm{t}}}=\mathrm{d}\mathrm{i}\mathrm{v}\left[\mathrm{f}\left(\left|\left|\nabla \mathrm{I}\left(\mathrm{i},\mathrm{j},\mathrm{t}\right)\right|\right|\right)\nabla \mathrm{I}\left(\mathrm{i},\mathrm{j},\mathrm{t}\right)\right]$$

(2)

The Perona and Malik proposed two functions which can be expressed mathematically as follows [30]:

$${\mathrm{f}}_1\left(\mathrm{x}\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\left({\displaystyle \frac{\mathrm{x}}{\mathrm{k}}}\right)}^2\right]$$

(3)

and

$${\mathrm{f}}_2\left(\mathrm{x}\right)={\displaystyle \frac{1}{1+{\left(\frac{\mathrm{x}}{\mathrm{k}}\right)}^2}}$$

(4)

where $\mathrm{f}\left(\mathrm{*}\right)$ is diffusion coefficient having exponential and inverse function and k denotes gradient magnitude threshold parameters.

An anisotropic diffusion despeckling technique is a recursive operation. It is a highly sensitive recursion process. The time (t) as a variable is important as incorrect perception can affect the result obtained from the degraded images while analyzing, and it may still be the speckled-noise artefacts in the images. The correct despeckling methods and gradient threshold variables help to obtain higher PSNR results.

3.3. Method Noise Thresholding

It plays a very significant role in the process of dealing with the granular pattern in radar images. It can enhance the performance of any speckle-noise reduction techniques and lead to precise outcomes. This is quite an effective and general despeckling model to enhance the outcomes [41]. The speckle and despeckled images consist of a few arbitrary details of the image that represent the differences because of the inadequacy of the speckle-noise reduction techniques. We aimed to validate the performance and effectiveness of the despeckling methods by using some famous metrics such as SNR, PSNR, SSIM, and UIQI, which becomes classified into two categories: one is with the reference indexed, and another is without the reference indexed [42]. The application method noise is used in conventional and medical images and reaches the fields of the military, topology, agriculture, object detection, and classification [43]. The residual or unfiltered components can be filtered using any despeckling method. The method is implemented on unfiltered pixels of the noise threshold image [37]. It is a method based on the assumption that the wavelet coefficients are modeled as random variables with general Gaussian distribution (GGD) within each subband. Under this condition, a threshold is estimated to find the value that minimizes the Bayesian risk [38,44].

$${\mathrm{f}}_{\mathrm{i}}\left({\mathrm{\sigma }}_{\mathrm{x}}\right)={\displaystyle \frac{{\mathrm{\sigma }}_{\mathrm{n}}^2}{{\mathrm{\sigma }}_{\mathrm{x}}}}$$

(5)

where ${\mathrm{\sigma }}_{\mathrm{x}}$ denotes image standard deviation evaluated in each wavelet sub-band and ${\mathrm{\sigma }}_{\mathrm{n}}^2$ refers standard deviation of noise evaluated in each wavelet sub-band.

The shrinkage threshold involves setting the elements whose absolute values are lower than the threshold to zero and then scaling the nonzero coefficients toward zero.

$$\mathrm{S}\left(\mathrm{y}\right)=\left\{\begin{array}{c}0 , \left|\mathrm{y}\right|<\mathrm{T}\\ \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n} \left(\mathrm{y}\right).\left(\left|\mathrm{y}\right|-\mathrm{T}\right) , \left|\mathrm{y}\right|>\mathrm{T} \end{array}\right.$$

(6)

where T refers threshold value and $\mathrm{S}\left(\mathrm{y}\right)$ indicates nonlinear transform.

3.4. Weighted Graph Image Filtering (WGIF)

Filtering images using weighted graph models involves the application of discrete regularization frameworks on weighted graphs to unify image and mesh filtering. This approach leads to various nonlinear filters, such as the bilateral and double-weighted average image filters, which enable the smoothing of images while preserving their structures. Using graph-based algorithms for image segmentation and filtering involves representing an image with a graph, where the vertices are individual pixels, and the edges measure the similarity between the pixels based on user-specified criteria. The weighted graph model allows for the development of edge-aware structures, such as the segment graph, which can be used to design novel image filters for fast structure-preserving smoothing. These filters can smooth out high-contrast details and textures while preserving major image structures well. Mathematically can be expressed as follows:

$${\mathrm{f}}_{\mathrm{j}}^{\mathit{’}}={\sum }_{\mathrm{i}\in \mathrm{N}\left(\mathrm{i}\right)}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}{\mathrm{f}}_{\mathrm{i}}$$

(7)

where ${\mathrm{f}}_{\mathrm{j}}^{’}$, $\mathrm{N}\left(\mathrm{i}\right)$, ${\mathrm{f}}_{\mathrm{i}}$, and ${\mathrm{w}}_{\mathrm{i}\mathrm{j}}$ denote the updated value of pixel $\mathrm{i}$, set of neighboring pixels of pixel $\mathrm{i}$, value of neighboring pixel $\mathrm{i}$, and weight of the edge between pixels $\mathrm{i}, \mathrm{j}$, respectively.

4. Proposed Non-Linear Diffusion Method

The proposed method is to restore the speckled SAR image using an adaptive filter and thresholding method that helps post-process the SAR images in object detection. The despeckling ability of the proposed method is to give exact results and preserve the fine details, such as edge preservation along with the edge [45,46] directions, texture, etc., of SAR images. Figure 2 represents the working model of the proposed framework. The efficiency of the proposed framework is estimated by its perceptible characteristics and by employing additional analyzing parameters like SNR, PSNR, SSIM, and UIQI [47]. The objective of the proposed method is to achieve maximum precision in removing speckle noise from SAR images, addressing a key limitation of conventional methods that primarily focus on edge smoothing while neglecting fine details. The approach integrates three main techniques: anisotropic diffusion, discrete wavelet transforms, and method-noise thresholding. Non-linear diffusion and discrete wavelet transforms are used in the pre-processing stage to suppress speckle noise while preserving edges, and method-noise thresholding is applied in the post-processing stage to further refine noise reduction. This combined approach optimizes noise suppression by selectively targeting noisy areas, ensuring that important image features, such as edges and textures, are retained. The fusion-based thresholding technique distinguishes noise from key image details, enhancing both clarity and feature preservation. By merging fusion-based thresholding with non-linear diffusion, the proposed method effectively mitigates speckle noise while overcoming the shortcomings of traditional techniques that often sacrifice fine details. The integration of these methods offers a more comprehensive solution, improving both noise reduction and detail preservation compared to single-method approaches. This enhanced despeckling not only improves image quality but also supports post-processing tasks like object detection by maintaining critical features such as edges, textures, and boundaries.

4.1. Algorithm

In this section, we propose a robust despeckling algorithm, Algorithm 1, for Synthetic Aperture Radar (SAR) images affected by speckle noise. The algorithm is a multi-step process designed to enhance image quality while preserving important details.

Algorithm 1 Proposed despeckling algorithm

Input: Speckle-noise SAR Image Intermediary Steps Involved for Despeckling Step 1: Speckled SAR Image S as an input. Step 2: Obtained S″ after applying the log transformation on S. Step 3: Applying recursive Non-linear diffusion on S″. i. Initialize the coefficients $\mathrm{f}\left(\mathrm{*}\right)$ and $\mathrm{k}$. ii. Calculate the Perona-Malik diffusion using Equations (3) and (4). iii. for $\mathrm{i} =1\mathrm{to} \mathrm{n}$, do Compute the general Non-linear diffusion using Equation (2). Store the value end for iv. The outcome image is A. Step 4: Applying DWT on A which decomposed into (A, H, V, D). Step 5: Further Apply the WGIF on approximate part of (A) Two level decomposed images. Step 6: Apply IDWT on A, H, V, D. This results in IDWT. IDWT = IDWT (A, H, V, D). Step 7: Apply exponential transformation on IDWT, DI. Step 8: Applying method noise on speckled image S and filtered image DI. Step 9: FDI is the final despeckled SAR image.

4.2. Architecture

Figure 2 illustrates the proposed framework for SAR image despeckling, involving a multi-stage process to enhance image quality while preserving essential details. The framework begins with log transformation applied to the input speckled SAR image, followed by recursive non-linear diffusion to address noise. Discrete Wavelet Transform is then employed to decompose the image into various components. The approximation component is processed with a Weighted Graph Image Filtering (WGIF) technique, while method noise thresholding is applied to refine the despeckling process. The final step includes applying inverse DWT and exponential transformation to reconstruct the despeckled image, achieving significant noise reduction and detail preservation. The methodology is validated against various performance metrics, demonstrating superior capabilities in maintaining structural integrity and reducing noise in SAR images.

4.3. Technical Requirements

All experimental results are carefully examined using MATLAB R2014a running on an Intel Core i3-6100U CPU operating at 2.30 GHz, 4 GB RAM, and the Windows 10 64-bit OS. It is essential to consider the system configuration as it plays a crucial role in determining the computational efficiency of the proposed method compared to other despeckling filters and techniques under the same settings. A fixed window size of 3 × 3 is utilized throughout the experiments, while the number of iterations, denoted as I, varies within the range of from 1 to 10. The results are presented based on the optimal number of iterations determined during the analysis. In order to verify the effectiveness of the suggested approach, the results obtained from the experiments were contrasted with those achieved using several well-known despeckling filters and methods such as log compression filtering, frost filtering, Kuan filtering, lee filtering, Median, and HFLF. The new despeckling technique has been tested under different levels of noise variance on different synthetic and natural images, with the experimental findings specifically showcasing the performance at a noise variance level.

4.4. SAR Data

In the experiment analysis, the two different SAR images have been taken of different background nature to verify the reliability of the proposed algorithm. The original SAR image dataset is considered from the public access database [48,49], showing agricultural landscapes with distinct plots of fields in various stages of cultivation, ranging from light green newly planted areas to darker green mature crops. The speckled SAR images are named SAR-1 and SAR-2 at a noise level of σ = 20, as displayed in Figure 3a,b.

4.5. Performance Evaluation

To evaluate the effectiveness of the suggested despeckling method, various commonly used quality metrics are utilized. These metrics include an SNR, which measures the ratio of the signal power to the noise power in the image. The PSNR is also employed to measure the peak signal power-to-noise power ratio. The SSIM evaluates the similarity between the original and despeckled images based on luminance, contrast, and structure. Furthermore, a relatively new metric called the UIQI is used [50].

SNR is a quantitative parameter employed to compute the discriminations of an imaging system. The mathematical expression of the SNR is as follows:

$$\mathrm{SNR}=10.{\log }_{10}\left[{\displaystyle \frac{{\mathrm{V}}_{\mathrm{a}\mathrm{r}\left[\mathrm{g}\right]}}{\mathrm{M}\mathrm{S}\mathrm{E}}}\right]$$

(8)

where ${\mathrm{V}}_{\mathrm{a}\mathrm{r}}\left[\mathrm{g}\right]$ refers to the reference image variance.

PSNR is quite a common performance metric employed to verify the effectiveness of despeckling methods. A greater value of the PSNR better indicates the results. It is calculated as follows:

$$\mathrm{P}\mathrm{S}\mathrm{N}\mathrm{R}=20{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left(\mathrm{M}\mathrm{a}\mathrm{x}\right)-{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left(\mathrm{M}\mathrm{S}\mathrm{E}\right)$$

(9)

SSIM helps to compute the equivalence of the despeckled and the reference SAR image. It relies on three elements: luminance, contrast, and shape. It is derived as follows:

$$\mathrm{SSIM}={\displaystyle \frac{\left(2{\mathrm{\mu }}_{\mathrm{a}}{\mathrm{\mu }}_{\mathrm{b}}+{\mathrm{P}}_1\right)(2{\mathrm{\sigma }}_{\mathrm{a}\mathrm{b}}+{\mathrm{P}}_2)}{\left({{\mathrm{\mu }}_{\mathrm{a}}}^2+{{\mathrm{\mu }}_{\mathrm{b}}}^2+{\mathrm{P}}_1\right)({{\mathrm{\sigma }}_{\mathrm{a}}}^2+{{\mathrm{\sigma }}_{\mathrm{b}}}^2+{\mathrm{P}}_2)}}$$

(10)

where ${\mathsf{\mu }}_{\mathrm{a}},{\mathrm{\mu }}_{\mathrm{b}},{\mathrm{\sigma }}_{\mathrm{a}},{\mathrm{\sigma }}_{\mathrm{b}}$, and ${\mathrm{\sigma }}_{\mathrm{a}\mathrm{b}}$ denote local means, standard deviation, and cross variance for images a and b, respectively.

$$\mathrm{P}1={(0.01\ast \mathrm{L})}^2\mathrm{and} \mathrm{P}2={(0.03\ast \mathrm{L})}^2$$

(11)

where L signifies specified dynamic scale value.

UIQI is derived using three coefficients: degree of linear correlation, mean proximity to light, and contrast similarity in images. The scale of these three factors lies from zero to one. Therefore, the last limit of UIQI lies between 0 and 1. If the obtained UIQI value of the despeckled images is one then the image quality is better, and vice-versa: 0 represents the lowest image quality.

$$\mathrm{UIQI}={\displaystyle \frac{{\mathrm{\sigma }}_{\mathrm{x}\mathrm{y}}}{{\mathrm{\sigma }}_{\mathrm{x}}{\mathrm{\sigma }}_{\mathrm{y}}}}.{\displaystyle \frac{2\mathrm{x}\mathrm{y}}{{\mathrm{x}}^2+{\mathrm{y}}^2}}.{\displaystyle \frac{{2\mathrm{\sigma }}_{\mathrm{x}}{\mathrm{\sigma }}_{\mathrm{y}}}{{{\mathrm{\sigma }}_{\mathrm{x}}}^2+{{\mathrm{\sigma }}_{\mathrm{y}}}^2}}$$

(12)

5. Results and Observations

In the experimental analysis, the proposed despeckling method has been performed on SAR-1 and SAR-2 to investigate its speckle-noise suppression and edge and texture preservation features. Moreover, the proposed method has experimented with different noise variance levels (σ ϵ 5, 10, 20, 30, 40). The analysis of various efficiency metrics, such as SNR, PSNR, SSIM, and UIQI, has been conducted across different noise variances. Comparisons of the proposed method with various techniques, such as Lee [10], HFLF [11], Kuan [12], Median [13], Frost [14], and Log compression [15] filters, are shown in

Table 1. SNR of despeckling methods for SAR-1 at $\mathrm{\sigma }=\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m} 5$ to 40.

SAR-1		NV	5	10	20	30	40
	DM
	Frost [14]		19.7102	17.3372	12.4019	13.5486	12.8054
	HFLF [11]		18.3675	17.2521	12.0921	12.6512	11.8956
	Kuan [12]		19.5694	16.9434	11.9814	13.2454	12.4587
	Median [13]		18.5353	15.8472	11.7680	12.5259	11.7758
	Lee [10]		19.7930	17.4828	12.2417	13.4226	12.5451
	Log Compression [15]		18.2314	17.5878	12.8956	12.8975	11.9547
	Proposed		21.7630	19.9125	16.2154	16.9654	15.5687

,

Table 2. SNR of despeckling methods for SAR-2 at σ = from 5 to 40.

SAR-2		NV	5	10	20	30	40
	DM
	Frost [14]		19.9710	17.7172	15.1958	13.7601	12.8521
	HFLF [11]		20.1236	16.5232	15.5957	13.3698	12.7854
	Kuan [12]		19.5229	17.5342	14.9730	13.4754	12.4785
	Median [13]		18.8630	16.8032	14.3070	12.8406	11.9911
	Lee [10]		20.1908	17.7229	15.0977	13.5763	12.6261
	Log Compression [15]		19.4568	16.8585	14.2356	12.8579	11.4514
	Proposed		22.2321	19.2546	17.2589	16.1598	15.5879

,

Table 3. PSNR of despeckling methods for SAR-1 at $\mathsf{\sigma }=\mathrm{from}5$ to 40.

SAR-1		NV	5	10	20	30	40
	DM
	Frost [14]		26.7028	24.0518	19.2303	20.1716	19.4893
	HFLF [11]		26.5236	24.5285	15.5912	20.3698	19.7054
	Kuan [12]		26.9344	24.1614	18.8187	20.2970	19.4304
	Median [13]		25.3409	22.6158	18.6050	19.2761	18.4170
	Lee [10]		26.7780	24.1848	19.0458	20.0154	19.2210
	Log Compression [15]		25.4512	24.8085	18.2312	19.8570	18.4526
	Proposed		28.2356	26.5241	21.6958	23.5654	22.3654

,

Table 4. PSNR of despeckling methods for SAR-2 at $\mathrm{\sigma }=\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m} 5$ to 40.

SAR-2		NV	5	10	20	30	40
	DM
	Frost [14]		25.6368	23.3813	20.7865	19.3181	18.6036
	HFLF [11]		26.2356	24.4012	20.5902	19.9802	18.7045
	Kuan [12]		25.7593	27.7388	21.0624	19.4925	18.4037
	Median [13]		24.1786	22.5844	19.8368	18.5394	17.9238
	Lee [10]		26.3439	23.3799	20.6817	19.1269	18.5341
	Log Compression [15]		25.1220	24.2312	20.1575	19.8520	18.4231
	Proposed		29.3698	25.5246	22.1235	22.3698	20.3654

,

Table 5. UIQI of despeckling methods for SAR-1 at σ = from 5 to 40.

SAR-1		NV	5	10	20	30	40
	DM
	Frost [14]		0.4560	0.4576	0.3405	0.4567	0.4668
	HFLF [11]		0.4132	0.4012	0.2951	0.4280	0.3112
	Kuan [12]		0.4507	0.4466	0.2997	0.4270	0.4285
	Median [13]		0.3399	0.3315	0.2027	0.3078	0.3080
	Lee [10]		0.4517	0.4491	0.3010	0.4285	0.4293
	Log Compression [15]		0.4216	0.3546	0.3612	0.4015	0.4851
	Proposed		0.6213	0.5987	0.5213	0.6987	0.5897

,

Table 6. UIQI of despeckling methods for SAR-2 at σ = from 5 to 40.

SAR-2		NV	5	10	20	30	40
	DM
	Frost [14]		0.4737	0.4678	0.4679	0.4703	0.4625
	HFLF [11]		0.4615	0.4218	0.4578	0.4612	0.4531
	Kuan [12]		0.4685	0.4585	0.4495	0.4421	0.4249
	Median [13]		0.3660	0.3518	0.3367	0.3292	0.3151
	Lee [10]		0.4700	0.4595	0.4503	0.4429	0.4261
	Log Compression [15]		0.4535	0.4231	0.4365	0.3362	0.4875
	Proposed		0.6512	0.5909	0.6980	0.5969	0.6011

,

Table 7. SSIM of despeckling methods for SAR-1 at σ = from 5 to 40.

SAR-1		NV	5	10	20	30	40
	DM
	Frost [14]		0.4893	0.4586	0.3210	0.4310	0.4385
	HFLF [11]		0.4878	0.4356	0.2945	0.4021	0.4216
	Kuan [12]		0.4847	0.4493	0.2809	0.4018	0.4002
	Median [13]		0.4064	0.3584	0.2004	0.3002	0.2949
	Lee [10]		0.4847	0.4494	0.2810	0.4018	0.4002
	Log Compression [15]		0.4719	0.4298	0.2897	0.4137	0.4598
	Proposed		0.5823	0.6388	0.5169	0.5998	0.5762

and

Table 8. SSIM of despeckling methods for SAR-2 at σ = from 5 to 40.

SAR-2		NV	5	10	20	30	40
	DM
	Frost [14]		0.4858	0.4556	0.4412	0.4384	0.4285
	HFLF [11]		0.4856	0.4537	0.4352	0.3160	0.4578
	Kuan [12]		0.4815	0.4469	0.4231	0.4102	0.3907
	Median [13]		0.4074	0.3616	0.3268	0.3122	0.2947
	Lee [10]		0.4816	0.4469	0.4231	0.4102	0.3907
	Log Compression [15]		0.4765	0.4426	0.4125	0.4325	0.3878
	Proposed		0.6538	0.5921	0.5618	0.5895	0.6317

. The findings of the proposed despeckling method at a noise variance of σ = from 5 to 20 are detailed in Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8, showcasing the method’s performance under these conditions. The graphs presented in Figure 4a–g show the comparison of different despeckling methods, including the newly proposed method, based on efficiency metrics. The results depicted in the comparative graphs highlight the superior performance of the proposed method when compared to all other despeckling techniques mentioned. The performance metrics, such as SNR, PSNR, SSIM, and UIQI, are determined at different noise levels, as shown in Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8, and the best results are shown in bold.

The experimental results of SAR-1 and SAR-2 at σ = 20 are illustrated in Figure 4 and Figure 5. The Frost filter effectively reduces speckles but has the potential to blur fine details. The HFLF filter reduces noise and enhances edges but may introduce artifacts. The Kuan filter effectively balances speckle reduction and detail less in preservation. The Median filter effectively reduces impulsive noise but may compromise edge sharpness. The Lee filter is good at noise reduction and edge preservation, although it may smooth fine details. The Log Compression filter boosts contrast but has the potential to amplify noise. The proposed method significantly reduces noise while maintaining structural details and edge sharpness, surpassing other filters in overall performance.

Figure 6 presents bar plots illustrating the mean and standard deviation (SD) values for metrics such as SNR, PSNR, UIQI, and SSIM for different despeckling methods across noise variances (σ) for SAR-1 and SAR-2 images. The results demonstrate that the proposed method consistently outperforms traditional despeckling filters across all noise levels. Notably, the mean values for SNR and PSNR are significantly higher for the proposed method, indicating superior noise reduction while preserving image clarity. Additionally, the UIQI and SSIM metrics show that the proposed approach retains structural details and image quality better than the compared methods, with narrower standard deviation bars indicating more stable performance across varying noise levels. For SAR-1 at a noise variance of σ = 20, the SNR was recorded at 16.22 dB, significantly surpassing the 12.89 dB achieved by the Log Compression filter. The proposed method also attained a UIQI of 0.6987, highlighting strong retention of visual quality under varying noise conditions. On SAR-2, at a noise variance of σ = 5, the method reached a PSNR of 29.37 dB, notably exceeding the best filter’s 26.70 dB. Additionally, an SSIM of 0.6538 was observed, reflecting better preservation of image details.

6. Discussions

Recent advancements in speckle noise mitigation for SAR images include wavelet-based methods [2] and machine learning approaches [51], which often face challenges in balancing noise reduction with detail preservation. However, fusion-based thresholding combined with non-linear diffusion represents a notable improvement. This technique merges multi-resolution image data through fusion-based thresholding, which enhances structural information retention. Non-linear diffusion then refines the image by adapting to local features, effectively reducing noise while preserving edges. Compared to existing filters, like Lee [10], HFLF [11], Kuan [12], Median [13], Frost [14], Log compression [15] filters, and recent methods, this approach shows superior performance in terms of PSNR and SSIM. Studies have demonstrated its efficacy in better noise suppression and detail retention, making it a more advanced solution for SAR image processing. This method’s ability to integrate and refine multiple aspects of image quality provides a significant edge over past techniques.

The proposed method demonstrates significant advancements in performance across key metrics, including SNR, PSNR, SSIM, and UIQI, when compared to previously reported techniques. Specifically, our method shows superior signal quality with higher SNR values than earlier studies, which reported values ranging from 10 to 20 [3]. This improvement underscores the effectiveness of our approach in enhancing signal clarity while minimizing noise. Similarly, the PSNR values from prior works, which ranged between 23 and 27 [52,53,54,55], are consistently surpassed by our method, reflecting a marked enhancement in image fidelity and noise suppression. In terms of structural similarity, our method achieves better results in SSIM, a crucial metric for evaluating the preservation of structural details in images. We outperform recent machine learning benchmarks, which achieved SSIM values of 0.44 and 0.52 [55,56], indicating our method’s superior ability to maintain structural integrity, such as edges and textures. Furthermore, the UIQI values, which gauge overall image quality, from a recent wavelet-based intensity–hue–saturation method (ranging from 0.24 to 0.64) [57], are exceeded by our approach, demonstrating a significant improvement in preserving image features while reducing speckle noise. These collective improvements across all evaluated metrics highlight the substantial advancements offered by our proposed method, positioning it as a more effective approach than many previously reported techniques. However, it is important to acknowledge that direct comparative analysis is challenging, as each study employed distinct image datasets and varying noise levels, which can impact the performance results. Nevertheless, the consistent outperformance across multiple metrics suggests that our method holds strong potential for broader application in SAR image despeckling.

The proposed despeckling method consistently outperforms contrast methods, showing higher mean values across all metrics, particularly at lower noise variances, indicating superior noise reduction and detail preservation. The UIQI and SSIM values highlight better structural similarity and visual quality retention, with the proposed method demonstrating more stable performance as reflected by narrower SD bars, suggesting greater reliability across various noise levels. This overall superior performance underscores the robustness of the proposed method in preserving fine image details while effectively reducing speckle noise. To improve this work, it is essential to compare the proposed method with a broad spectrum of state-of-the-art despeckling techniques, including both traditional and advanced methods. This comparison will highlight the strengths and limitations of the proposed approach, ensuring its effectiveness and superiority in preserving fine details and reducing noise.

7. Conclusions

A new fusion-based method has been developed for removing the speckle noise in SAR images using amalgamating of the anisotropic diffusion, discrete wavelet transform, and method noise. The proposed methodology employs log and exponential transformation to handle multiplicative noise cases. The efficiency and performance of the developed despeckling method have been computed using quality metrics such as SNR, PSNR, SSIM, and UIQI. The proposed method achieved notable improvements in various metrics, such as a PSNR of 29.37 dB and a Structural SSIM of 0.6538, outperforming traditional filters. This demonstrates the method’s ability to reduce speckle noise while preserving critical image details like edges and textures.

However, during the application of the proposed methodology, several limitations were encountered. The first challenge was computational complexity, especially when processing larger SAR datasets, which increased the processing time. Although the method achieves superior noise reduction, this complexity could limit its use in real-time applications. Another limitation was that, at higher noise variances, the method sometimes struggled to fully preserve fine textures, leading to slight blurring in more detailed areas of the image. Additionally, the method’s performance was less robust in highly heterogeneous areas where the intensity variations were extreme, which occasionally resulted in incomplete noise suppression. To overcome these challenges, future work will focus on improving the computational efficiency of the algorithm by exploring parallel processing and optimizing the implementation for faster performance. Furthermore, to address the limitations in texture preservation at high noise levels, incorporating machine learning models, such as convolutional neural networks (CNNs), could improve the method’s adaptability to different noise patterns and further enhance fine-detail preservation. We also plan to expand the dataset used for validation to include more diverse SAR images, including real-world scenarios, to ensure the robustness of the approach across various conditions. Lastly, future research will explore integrating this technique with adaptive filters and hybrid models to better manage intensity variations in highly heterogeneous areas, improving both noise reduction and structural preservation.