A wavelet denoising method and system for SAR image and electronic equipment

Abstract

The application discloses a wavelet denoising method and system for SAR images and electronic equipment, and relates to the technical field of remote sensing image processing. The method comprises the following steps: determining a wavelet and a wavelet decomposition level, and calculating a wavelet coefficient matrix obtained by wavelet decomposition of a to-be-processed SAR image; determining an initial adaptive threshold and a corresponding estimated wavelet coefficient matrix according to the wavelet coefficient matrix based on a preset adaptive threshold estimation function; removing a wavelet coefficient when any wavelet coefficient is less than the initial adaptive threshold; when any wavelet coefficient is greater than or equal to the initial adaptive threshold, constructing a risk function based on the wavelet coefficient and the estimated wavelet coefficient matrix; performing minimum calculation on the risk function based on a minimum maximum estimation criterion to obtain optimal wavelet coefficients after threshold processing; and performing wavelet reconstruction on the optimal wavelet coefficients to obtain a denoised SAR image. The application effectively removes noise in the image while better maintaining the image edge, thereby improving the denoising effect.

Description

Technical Field

[0001] This invention relates to the field of remote sensing image processing technology, and in particular to a wavelet denoising method, system and electronic device for SAR images. Background Technology

[0002] Images are a crucial medium for information transmission, and almost every field relies on multimedia for image delivery. However, noise significantly impacts image generation, processing, transmission, and post-processing in various image-related tasks, potentially affecting image clarity. If noise is not addressed promptly, it can severely hinder image acquisition. Therefore, image denoising is a critical step in image processing. Traditional denoising methods easily lose image details, while wavelet transform-based denoising methods effectively address this issue. After wavelet transform, noisy images retain both frequency and spatial information. Thus, wavelet transform-based denoising is a vital image processing technique.

[0003] In existing technologies, there are three image denoising methods based on wavelet transform, one of which is wavelet thresholding. Wavelet thresholding removes noise signals from the decomposed wavelet coefficients using a set threshold function. This method is highly effective in denoising Gaussian noise. In wavelet image denoising, the choice of threshold plays a decisive role, and controlling the threshold size is crucial. A large threshold will set most wavelet coefficients to zero, and effective information in the image will be treated as noise; a small threshold will set only a small portion of the wavelet coefficients to zero, and not all noise information in the image can be selected. The image denoising process is based on the prediction of the ideal image, and theoretically, achieving a completely flawless result is impossible, which is the main challenge of image denoising. Simultaneously, image denoising also involves the problem of image noise identification. In addition to selecting denoising methods, it is also necessary to consider the type of noise and its distribution in the image; identifying the distribution characteristics of noise information in the image is particularly important. Therefore, constructing a noise model is a crucial step in image denoising. Image denoising primarily relies on experiments using corresponding noise models to obtain effective denoising methods. Currently, the definition of a noise model mainly focuses on constructing models for subtle factors, emphasizing the description of noise distribution. Typical noise models include Gaussian distribution models, Gaussian-resolution mixture distribution models, and Gaussian-Laplacian mixture distribution models. Based on these noise models, image denoising still faces challenges such as: the optimal selection of threshold functions and thresholds, the removal of various mixed noises, and the need for noise model construction and validation. Summary of the Invention

[0004] The purpose of this invention is to provide a wavelet denoising method, system, and electronic device for SAR images, which effectively removes noise from images while better preserving image edges, thereby improving the denoising effect.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] In a first aspect, the present invention provides a wavelet denoising method for SAR images, comprising:

[0007] Acquire the SAR image to be processed;

[0008] The wavelet and wavelet decomposition level are determined, and the wavelet coefficient matrix obtained after wavelet decomposition of the SAR image to be processed is calculated; the wavelet coefficient matrix includes multiple wavelet coefficients.

[0009] Based on the preset adaptive threshold estimation function, the initial adaptive threshold and the corresponding estimated wavelet coefficient matrix are determined according to the wavelet coefficient matrix.

[0010] When any wavelet coefficient is less than the initial adaptive threshold, the wavelet coefficient is removed.

[0011] When any wavelet coefficient is greater than or equal to the initial adaptive threshold, a risk function is constructed based on the wavelet coefficient and the estimated wavelet coefficient matrix.

[0012] Based on the minimization-maximization estimation criterion, the risk function is minimized to obtain the optimal wavelet coefficients after threshold processing;

[0013] Wavelet reconstruction is performed on the optimal wavelet coefficients to obtain the denoised SAR image.

[0014] Optionally, the preset adaptive threshold estimation function is:

[0015]

[0016] Where, ρ T (x) represents the estimated wavelet coefficients obtained using the preset adaptive threshold estimation function, sat(x) represents the sliding switch function, P represents the adjustment factor, x represents the wavelet coefficients, T represents the threshold used to process the wavelet coefficients, i.e. the initial adaptive threshold; sigmoid(x) represents the smoothing function.

[0017] Optionally, the step of minimizing the risk function based on the minimization-maximization estimation criterion to obtain the optimal wavelet coefficients after threshold processing specifically includes:

[0018] Based on the preset orthogonal basis conditions and the noise distribution in the SAR image to be processed, the risk function is solved to obtain the extreme points;

[0019] Calculate the minimum risk based on the extreme points and the risk function;

[0020] Based on the minimum risk, an optimal adaptive threshold is determined, and the wavelet coefficient matrix is ​​subjected to threshold quantization processing according to the optimal adaptive threshold to obtain the optimal wavelet coefficients after threshold processing.

[0021] In a second aspect, the present invention provides a wavelet denoising system for SAR images, comprising:

[0022] Image acquisition module, used to acquire SAR images to be processed;

[0023] The wavelet decomposition module is used to determine the wavelet and the wavelet decomposition level, and to calculate the wavelet coefficient matrix obtained after wavelet decomposition of the SAR image to be processed; the wavelet coefficient matrix includes multiple wavelet coefficients.

[0024] An adaptive threshold determination module is used to determine an initial adaptive threshold and a corresponding estimated wavelet coefficient matrix based on a preset adaptive threshold estimation function and the wavelet coefficient matrix.

[0025] The first processing module is used to remove the wavelet coefficient when any wavelet coefficient is less than the initial adaptive threshold.

[0026] The second processing module is used to construct a risk function based on the wavelet coefficients and the estimated wavelet coefficient matrix when any wavelet coefficient is greater than or equal to the initial adaptive threshold.

[0027] The risk minimization module is used to minimize the risk function based on the minimization-maximization estimation criterion to obtain the optimal wavelet coefficients after threshold processing.

[0028] The image reconstruction module is used to perform wavelet reconstruction on the optimal wavelet coefficients to obtain a denoised SAR image.

[0029] Thirdly, the present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform a wavelet denoising method for SAR images.

[0030] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0031] This invention discloses a wavelet denoising method, system, and electronic device for SAR images. The method involves wavelet decomposition of the SAR image to be processed to obtain a wavelet coefficient matrix. Based on a preset adaptive threshold estimation function, an initial adaptive threshold and a corresponding estimated wavelet coefficient matrix are determined according to the wavelet coefficient matrix. The wavelet coefficients and the initial adaptive threshold are evaluated; if the wavelet coefficients are less than the initial adaptive threshold, they are removed; otherwise, a risk function is constructed based on the wavelet coefficients and the estimated wavelet coefficient matrix. The risk function is minimized based on a minimization-maximization estimation criterion to obtain the optimal wavelet coefficients after threshold processing. Wavelet reconstruction is then performed to obtain the denoised SAR image. This invention is based on wavelet denoising technology and optimizes the threshold selection for wavelet denoising by combining adaptive thresholding and a minimization-maximization estimation criterion. This results in a more intuitive denoised image, smoothing of uniform regions, and good support for edge regions, thereby significantly reducing image noise and improving the denoising effect. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a flowchart illustrating the wavelet denoising method for SAR images according to the present invention.

[0034] Figure 2 The graph shows the result parameters of various noise reduction methods in the experimental examples of this invention;

[0035] Figure 3 This is a schematic diagram of the wavelet denoising system for SAR images according to the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] This invention provides a wavelet denoising method, system, and electronic device for SAR images, belonging to the field of remote sensing SAR image denoising technology, to make the target outlines in SAR images clear and effectively eliminate erroneous information for tasks such as land-sea segmentation and target detection.

[0038] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] Example 1

[0040] like Figure 1 As shown, this embodiment provides a wavelet denoising method for SAR images, including:

[0041] Step 100: Acquire the SAR (Synthetic Aperture Radar) image to be processed. In a specific practical application, coastline images from both the MSAR and SSDD datasets can be acquired.

[0042] Step 200: Determine the wavelet and wavelet decomposition level, and calculate the wavelet coefficient matrix obtained after wavelet decomposition of the SAR image to be processed; the wavelet coefficient matrix includes multiple wavelet coefficients.

[0043] Step 300: Based on the preset adaptive threshold estimation function, determine the initial adaptive threshold and the corresponding estimated wavelet coefficient matrix according to the wavelet coefficient matrix.

[0044] Specifically, to better approximate the minimum risk, an adaptive threshold estimation operator needs to be designed and selected. When |x| is greater than the threshold T, the sat(x) sliding switch function is used to smooth the adjustment factor P. When |x| is less than the threshold T, the sigmoid(x) function is used to smooth and optimize the adaptive threshold estimation operator. The threshold function is directly truncated, which causes an oscillation effect. The specific operator, i.e., the preset adaptive threshold estimation function, is as follows:

[0045]

[0046] Where, ρ T (x) represents the estimated wavelet coefficients obtained using the preset adaptive threshold estimation function, sat(x) represents the sliding switch function, P represents the adjustment factor, P can be dynamically adjusted according to different wavelet coefficient sizes to achieve the purpose of adaptively selecting the threshold; x represents the wavelet coefficient, T represents the threshold used to process the wavelet coefficient, i.e. the initial adaptive threshold; sigmoid(x) represents the smoothing function.

[0047] Step 400: When any wavelet coefficient is less than the initial adaptive threshold, it indicates that the wavelet coefficient is a low-frequency component and the wavelet coefficient needs to be removed.

[0048] Step 500: When any wavelet coefficient is greater than or equal to the initial adaptive threshold, it indicates that the wavelet coefficient is a high-frequency component. A risk function needs to be constructed based on the wavelet coefficient and the estimated wavelet coefficient matrix.

[0049] In a specific example, the mean square distance, i.e., the squared Euclidean norm, is used to describe the degree of signal estimation. The corresponding risk function is:

[0050] r(D,f)=E{||DX-f|| 2}

[0051] Step 600: Based on the minimization-maximization estimation criterion, the risk function is minimized to obtain the optimal wavelet coefficients after thresholding. Specifically, the minimization-maximization estimation criterion minimizes the maximum risk of the aforementioned risk function. The specific formula for calculating the upper limit of the aforementioned risk function is as follows:

[0052]

[0053] Its minimal risk is the lower bound calculated on all linear or nonlinear operators D, and the calculation formula is as follows:

[0054]

[0055] Among them, O n Let be the set of operators D.

[0056] Furthermore, step 600 specifically includes:

[0057] 1) Based on the preset orthogonal basis conditions and the noise distribution in the SAR image to be processed, the risk function is solved to obtain the extreme points.

[0058] In one specific embodiment, the L-shaped wavelet formed by scaling and translation is... 2 (R) A spatially orthonormal basis is denoted as B = {g m} 0≤m＜n The noisy signal is decomposed into X on the basis of B. B (m)= <X,g m >,f B (m)= <f,g m >,e B (m)= <e,g m >, and X B (n)=f B (n)+e B (n).

[0059] The operator D can be defined as follows:

[0060]

[0061] When a(m) does not depend on X B When (m), operator D is called a linear operator; otherwise, it is called a nonlinear operator.

[0062] To minimize risk, the risk function needs to be estimated. Generally, for a quadratic equation, its first derivative is taken, and then its derivative is set to zero to obtain an extreme point. Specifically, let the pre-defined orthogonal basis condition ||g m ||=1, the noise e in the SAR image to be processed follows N(0,σ) 2 If the distribution is such that the risk function described above can be transformed into the following formula:

[0063]

[0064] E{|f B (m)-a(m)X B (m)| 2}=E{|f B (m)-a(m)[f B (m)+e B (m)]| 2}

[0065] =E{|f B (m) 2 -2a(m)f B (m)[f B (m)+e B (m)]+a(m) 2 [f B (m)+e B (m)] 2 |};

[0066] =|f B (m)| 2 (1-a(m)) 2 +σ 2 a(m) 2

[0067] Where r(D,f) represents the risk value, E{} represents the expected value of the squared Euclidean norm, and f represents the original signal in the SAR image to be processed. Let D represent the estimated value of the original signal, and let D represent the estimation operator used to estimate the original signal f to obtain the estimated value of the signal. X represents the wavelet coefficient matrix, |||| 2 Let L2 norm be N, total signal length be N, and a(m) be the correction parameter. 2 The L2 norm is represented by the square of the absolute value of the difference between the decomposed signal and the estimated signal, used to specifically calculate the value of the L2 norm; σ represents the scaling parameter in the normal distribution; the orthogonal basis B = {g m} 0≤m＜n The noisy signal is decomposed into X on the orthogonal basis B. B (m)= <X,gm >,f B (m)= <f,g m >,e B (m)= <e,g m >,d m This represents a partial value obtained after performing calculations on the estimation operator D and the decomposed signal.

[0068] Taking the derivative of the risk function after the above transformation and setting its derivative to 0, we obtain the following formula:

[0069] |f B (m)| 2 (2a(m)-2)+2σ 2 a(m)=0.

[0070] Further solving yields the extreme points:

[0071]

[0072] 2) Calculate the minimum risk based on the extreme points and the risk function. Specifically, by substituting the calculated extreme points into the risk function, the risk r(D,f) is minimized, resulting in:

[0073]

[0074] Where, r inf (f) represents the minimum risk value, but this minimum risk value is a value achieved under ideal conditions. In reality, since the value of a(m) is a variable value, it depends on f. B The value of (m) is such that no wavelet basis can approximate it infinitely in practice.

[0075] In practical applications, to simplify the analysis of operator D, a compromise is usually adopted: limiting the range of values ​​for a(m) to minimize the risk to r. inf (f). Specifically, when D is a linear operator, a linear estimation approximation is performed, and the following settings are made:

[0076] The formula for calculating minimum risk is:

[0077]

[0078] When D is a nonlinear operator, an approximation of the nonlinear estimate is performed, and the following settings are made:

[0079] The formula for calculating minimum risk is:

[0080]

[0081] Where, ε l(M) represents the linear approximation error, and M represents the length of a portion of the signal.

[0082] 3) Based on the minimum risk, determine the optimal adaptive threshold, and perform threshold quantization on the wavelet coefficient matrix according to the optimal adaptive threshold to obtain the optimal wavelet coefficients after threshold processing.

[0083] Step 700: Perform wavelet reconstruction on the optimal wavelet coefficients to obtain the denoised SAR image.

[0084] In a specific example, wavelet reconstruction was performed using the high-frequency components processed by this invention, LEE filtering was used to denoise the SAR image, traditional wavelet denoising was used to denoise the SAR image, and stationary wavelet denoising was used to denoise the SAR image, respectively, and the corresponding denoising results were obtained.

[0085] Peak Signal-to-Noise Ratio (PSNR) is used to compare the denoising results of each image. For the processed image, decibels (dB) are used as the evaluation unit. A higher PSNR indicates better image information preservation compared to the original image; a lower PSNR indicates a greater difference between the two images, meaning the effect is less ideal. Peak Signal-to-Noise Ratio is often simply defined using Mean Squared Error (MSE). For two monochrome images I and K, where (i,j) represents the coordinates of pixels in the image, if one image is a noisy approximation of the other, then their mean squared error is defined as:

[0086]

[0087] Peak signal-to-noise ratio is defined by the following formula:

[0088]

[0089] MAX1 represents the maximum value of the color of a point in the image.

[0090] The four different denoising methods described above were applied to 50 sets of images for denoising. The PSNR parameter values ​​of the denoised results are shown below. Figure 2 As shown; some of the data is shown in Table 1.

[0091] Table 1 Simulation results and parameters for various denoising methods

[0092]

[0093] from Figure 2Based on the data in Table 1, the following conclusions can be drawn: Filtering offers the worst denoising effect, and in practical SAR image processing, it is difficult to obtain the crucial guide map, thus limiting its practical application value. While traditional wavelet transform improves image quality somewhat, the results are not particularly ideal. Wavelet transform denoising, improved by stationary wavelet transform, achieves superior image quality compared to traditional methods and does not require a guide map, making it convenient and feasible for practical applications. Furthermore, the denoising method based on wavelet threshold minimization maxima estimation adopted in this invention achieves a higher PSNR value than stationary wavelet transform. Therefore, this invention can significantly reduce image noise, contributing to SAR image target localization and recognition.

[0094] In summary, the denoising method of this invention can effectively preserve the edge features of an image while removing noise, making it an effective SAR image denoising method. Images denoised using this invention are more intuitive, with smoothed uniform regions and well-preserved edge regions. Furthermore, case studies demonstrate that the method employed in this scheme significantly reduces image noise, aiding in SAR image target localization and recognition. Preliminary results show that the PSNR of the denoising method based on wavelet threshold minimization maximization estimation exceeds 30 dB.

[0095] Example 2

[0096] like Figure 3 As shown, in order to implement the technical solution in Embodiment 1 and achieve the corresponding functions and technical effects, this embodiment also provides a wavelet denoising system for SAR images, including:

[0097] Image acquisition module 101 is used to acquire SAR images to be processed.

[0098] Wavelet decomposition module 201 is used to determine the wavelet and wavelet decomposition level, and to calculate the wavelet coefficient matrix obtained after wavelet decomposition of the SAR image to be processed; the wavelet coefficient matrix includes multiple wavelet coefficients.

[0099] The adaptive threshold determination module 301 is used to determine the initial adaptive threshold and the corresponding estimated wavelet coefficient matrix based on the preset adaptive threshold estimation function and the wavelet coefficient matrix.

[0100] The first processing module 401 is used to remove the wavelet coefficient when any wavelet coefficient is less than the initial adaptive threshold.

[0101] The second processing module 501 is used to construct a risk function based on the wavelet coefficients and the estimated wavelet coefficient matrix when any wavelet coefficient is greater than or equal to the initial adaptive threshold.

[0102] The risk minimization processing module 601 is used to minimize the risk function based on the minimization maximization estimation criterion to obtain the optimal wavelet coefficients after threshold processing.

[0103] The image reconstruction module 701 is used to perform wavelet reconstruction on the optimal wavelet coefficients to obtain a denoised SAR image.

[0104] Example 3

[0105] This embodiment provides an electronic device, including a memory and a processor. The memory is used to store computer programs, and the processor runs the computer programs to enable the electronic device to perform the wavelet denoising method for SAR images according to Embodiment 1.

[0106] Alternatively, the aforementioned electronic device may be a server.

[0107] In addition, embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the wavelet denoising method for SAR images in Embodiment 1.

[0108] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0109] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A wavelet denoising method for SAR images, characterized in that, The methods include: Acquire the SAR image to be processed; Determine the wavelet and wavelet decomposition level, and calculate the wavelet coefficient matrix obtained after wavelet decomposition of the SAR image to be processed; The wavelet coefficient matrix includes multiple wavelet coefficients; Based on a preset adaptive threshold estimation function, an initial adaptive threshold and the corresponding estimated wavelet coefficient matrix are determined according to the wavelet coefficient matrix; the preset adaptive threshold estimation function is: Where, ρ T (x) represents the estimated wavelet coefficients obtained using the preset adaptive threshold estimation function, sat(x) represents the sliding switch function, P represents the adjustment factor, x represents the wavelet coefficients, T represents the threshold used to process the wavelet coefficients, i.e. the initial adaptive threshold; sigmoid(x) represents the smoothing function. When any wavelet coefficient is less than the initial adaptive threshold, the wavelet coefficient is removed. When any wavelet coefficient is greater than or equal to the initial adaptive threshold, a risk function is constructed based on the wavelet coefficient and the estimated wavelet coefficient matrix. Based on the minimization-maximization estimation criterion, the risk function is minimized to obtain the optimal wavelet coefficients after thresholding; specifically including: Based on the preset orthogonal basis conditions and the noise distribution in the SAR image to be processed, the risk function is solved to obtain the extreme points; based on the extreme points and the risk function, the minimum risk is calculated; based on the minimum risk, the optimal adaptive threshold is determined, and the wavelet coefficient matrix is ​​threshold quantized according to the optimal adaptive threshold to obtain the optimal wavelet coefficients after threshold processing. The noise distribution in the SAR image to be processed follows a normal distribution; the risk function is: E{|f B (m)-a(m)X B (m)| 2 }=E{|f B (m)-a(m)[f B (m)+e B (m)]| 2 } =E{|f B (m) 2 -2a(m)f B (m)[f B (m)+e B (m)]+a(m) 2 [f B (m)+e B (m)] 2 |}; =|f B (m)| 2 (1-a(m)) 2 +σ 2 a(m) 2 in, r(D,f) represents the risk value, E{} represents the expected value of the squared Euclidean norm, and f represents the original signal in the SAR image to be processed. Let D represent the estimated value of the original signal, and let D represent the estimation operator used to estimate the original signal f to obtain the estimated value of the signal. X represents the wavelet coefficient matrix, || || 2 Let L2 norm be N, total signal length be N, and a(m) be the correction parameter. 2 The square of the absolute value of the difference between the decomposed signal and the estimated signal is represented by σ, which represents the scaling parameter in the normal distribution; the orthogonal basis B = {g m } 0≤m＜n The noisy signal is decomposed into X on the orthogonal basis B. B (m)= <X,g m >,f B (m)= <f,g m >,e B (m)= <e,g m >,d m This represents a partial value obtained after calculating the estimation operator D and the decomposed signal; The formula for calculating the minimum risk is: Where, r inf (f) represents the minimum risk value; Wavelet reconstruction is performed on the optimal wavelet coefficients to obtain the denoised SAR image.

2. The wavelet denoising method for SAR images according to claim 1, characterized in that, The method further includes: When D is a linear operator, set The formula for calculating minimum risk is: When D is a nonlinear operator, set The formula for calculating minimum risk is: Where, ε l (M) represents the linear approximation error, and M represents the length of a portion of the signal.

3. A wavelet denoising system for SAR images, employing the wavelet denoising method for SAR images as described in any one of claims 1-2, characterized in that, The system includes: Image acquisition module, used to acquire SAR images to be processed; The wavelet decomposition module is used to determine the wavelet and the wavelet decomposition level, and to calculate the wavelet coefficient matrix obtained after wavelet decomposition of the SAR image to be processed. The wavelet coefficient matrix includes multiple wavelet coefficients; An adaptive threshold determination module is used to determine an initial adaptive threshold and a corresponding estimated wavelet coefficient matrix based on a preset adaptive threshold estimation function and the wavelet coefficient matrix. The first processing module is used to remove the wavelet coefficient when any wavelet coefficient is less than the initial adaptive threshold. The second processing module is used to construct a risk function based on the wavelet coefficients and the estimated wavelet coefficient matrix when any wavelet coefficient is greater than or equal to the initial adaptive threshold. The risk minimization module is used to minimize the risk function based on the minimization-maximization estimation criterion to obtain the optimal wavelet coefficients after threshold processing. The image reconstruction module is used to perform wavelet reconstruction on the optimal wavelet coefficients to obtain a denoised SAR image.

4. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to cause the electronic device to perform the wavelet denoising method for SAR images according to any one of claims 1 to 2.

Images