Globally weighted least squares filtering method based on RoEWA operator

Abstract

The present invention discloses a global weighted least squares filtering method based on an operator, which mainly solves the problem in the prior art of obtaining gradients based on differences, resulting in poor accuracy. The implementation steps include: 1) obtaining a power map based on the original noisy polarimetric synthetic aperture radar image; 2) obtaining gradients based on the operator on the power map, and calculating the weights in the x and y directions of each pixel; 3) constructing an energy function for filtering using the obtained weights; 4) converting the energy function into a matrix form to obtain the result of minimizing the energy function; 5) applying the aforementioned filtering steps 3) and 4) independently and equally to the nine channels of the image to obtain the output data in each channel, i.e., the filtered image. The present invention can effectively suppress coherent speckle noise and better preserve image detail information, and can be used for coherent speckle suppression in polarimetric synthetic aperture radar images.

Description

Technical Field

[0001] The present invention belongs to the technical field of polarimetric remote sensing image processing, and further relates to a method for suppressing coherent speckle in polarimetric synthetic aperture radar images. Specifically, the present invention is a global weighted least squares filtering method based on the Ratio of Exponentially Weighted Averages (RoEWA) operator, which can be used for suppressing coherent speckle in polarimetric synthetic aperture radar images. Background Art

[0002] Polarimetric Synthetic Aperture Radar (PolSAR) data offers all-weather, all-day mapping capabilities, unaffected by poor nighttime lighting, cloud cover, and other weather conditions. Therefore, it holds enormous potential for remote sensing applications. However, the presence of speckle noise significantly impacts PolSAR image quality, making suppressing speckle noise a crucial preprocessing step before using PolSAR data. Research and exploration into PolSAR data denoising has become an increasingly important topic.

[0003] Considering the need to preserve local image details while removing noise, current research on various polarimetric data denoising methods can be broadly categorized into local denoising, non-local filtering, and other denoising algorithms using optimization models. Among these local denoising methods, the Boxcar filter removes noise by taking the average of all pixels within a sliding window. The Lee filter proposed by Lee et al. is a filtering method based on the statistical properties of pixels within a window. Lee et al. also proposed a local statistical estimator based on the minimum mean square error (MMSE), from which they derived many excellent local filters based on the minimum mean square error. However, these traditional algorithms only utilize local image information, which inevitably leads to blurred edges. Non-local filtering selects uniform pixels based on non-locality and estimates the center pixel using weighted averaging or MMSE. In 2011, Chen et al. proposed the NL-Pretest filter, based on the concept of image matching blocks. This algorithm has excellent noise suppression and edge preservation performance and is one of the most typical non-local mean filtering algorithms in PolSAR image denoising applications. Subsequently, a series of PolSAR image denoising algorithms based on NL-means have been proposed. These non-local methods achieve significantly better denoising results than local denoising methods, but they still suffer from issues such as time-consuming and low denoising efficiency. By optimizing and improving the model, a balance between noise filtering and detail preservation is achieved. This denoising method has gradually become an important means of PolSAR image preprocessing.

[0004] In recent years, PolSAR optimization frameworks have gained increasing popularity. For example, Nie et al. developed the Wishart total variation (WisTV) model based on the statistical properties of PolSAR covariance data and the Bayesian maximum a posteriori criterion, while Daniel et al. introduced anisotropic diffusion into denoising. However, existing optimization-based denoising algorithms struggle to achieve both high-speed and effective denoising. The introduction of regularization terms effectively addresses this issue. Applying the concept of global regularization to PolSAR image denoising, Ren et al. developed a global weighted least squares filter method with a simple and effective regularization term. Solving the global weighted least squares filter is equivalent to solving a large sparse linear system, thus achieving rapid denoising. The goal of this filtering approach is to make the result as close to the original image as possible, requiring smoothing in regions with small gradients and preserving information at edges with large gradients. This goal is achieved by minimizing an energy function, with regularization terms constrained by adaptive parameters and gradient values being crucial components of this minimization. The global weighted least squares filter proposes the creation of a guiding image to accurately calculate image gradients, thereby obtaining filter weights that are more conducive to denoising. The creation of the guiding image also allows single-polarization SAR data processing to be better extended to multi-polarization SAR image processing. However, because the noise generated during the coherent imaging process of PolSAR is multiplicative, the existing differential gradient operator, based on an additive noise model, cannot effectively estimate the local structural information of PolSAR data. Therefore, a suitable gradient operator can further improve the denoising effect. The current global weighted least squares filter denoising method still needs to be improved in the application of gradient methods in the field of PolSAR. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a global weighted least squares filtering method based on the RoEWA operator. By utilizing the spatial structural information of the PolSAR image, the method overcomes the problem of inaccurate gradient calculation caused by differential gradient calculation in the current global weighted least squares filter, so as to improve the ability to extract structural information in the PolSAR image, thereby achieving effective suppression of coherent speckle noise and effective preservation of image detail information.

[0006] The proposed method leverages the RoEWA operator's ability to extract image gradient information from power maps, fully incorporating structural information into the speckle removal process of PolSAR images. First, the total power is calculated from the original noisy polarimetric SAR image. The image gradient is then calculated using the RoEWA operator on the total power map. Finally, the image is processed using a globally weighted least squares filter.

[0007] To achieve the above object, the technical solution of the present invention includes the following steps:

[0008] (1) Calculate the total power SPAN based on the original noisy polarimetric synthetic aperture radar PolSAR image and obtain the power map:

[0009] SPAN=|S HH 2 +2S HV 2 +S VV 2 ,

[0010] Among them, H represents the information sent and received in the horizontal direction, V represents the information sent and received in the vertical direction; S HH 、S VV Represent the co-polarization components in the vertical and horizontal directions, S HV Represents the co-polarization component when horizontal transmission and vertical reception or vertical transmission and horizontal reception are met;

[0011] (2) Obtain the gradient on the power graph using the weighted exponential average ratio ROEWA operator:

[0012]

[0013] where h∈{x,y}, Represents the gradient in the vertical direction x or horizontal direction y; represents the exponentially weighted average value obtained by using the weighting function in the window area i, i = {1, 2};

[0014] (3) Calculate the weights in the x and y directions of pixel point p according to the following formula:

[0015]

[0016]

[0017] Among them, α represents the constraint factor and ε is a constant;

[0018] (4) Using the weights obtained in step (3), construct the energy function J(u) for filtering:

[0019]

[0020] Where f represents the polarimetric SAR image containing noise, u represents the output image after filtering, p represents the position of the pixel point; λ is the smoothing coefficient; and are the partial derivatives of the filtered output image u in the x and y directions respectively;

[0021] (5) In order to obtain the result of minimizing the energy function, the energy function is converted into a matrix form, and according to the properties of matrix operations, the following is obtained:

[0022] (I+λL s )u=f,

[0023] Where I represents the identity matrix; L s is the five-point Laplace matrix calculated using the power map;

[0024] (6) Let A = I + λL s , the output image u is expressed as follows:

[0025] u=F λ (f) = A -1 f,

[0026] Among them, A -1 is the inverse matrix of A;

[0027] (7) According to the properties of PolSAR data, the nine channels of the PolSAR image are filtered in step (6) respectively, and the output image in each channel is obtained according to the following formula:

[0028] u z =F λ (q z )=A -1 q z ,

[0029] Among them, q z represents the input image of the zth channel, z∈{1,2,…,9}; u z Represents the output image of the z-th channel.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] First, the present invention introduces the RoEWA operator into the boundary detection of polarimetric SAR images, thereby avoiding the disadvantage of using the differential method to calculate the gradient of PolSAR images containing multiplicative noise, making better use of spatial structure information and better preserving image details;

[0032] Second, the present invention integrates the gradient operator into the polarimetric SAR filtering under the global framework, and accurately identifies homogeneous regions through precise boundary recognition, so that the homogeneous regions of the denoised image are smoother. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is an implementation flow chart of the present invention;

[0034] Figure 2The results of speckle suppression on a simulated PolSAR image using a global weighted least squares filter and the method of the present invention are shown; (a) is the original image containing noise, (b) is the image obtained after the global weighted least squares filter, and (c) is the image filtered using the method of the present invention;

[0035] Figure 3 The results of speckle reduction on a real PolSAR image of the Flevoland region of the Netherlands using a global weighted least squares filter and the method of the present invention. (a) shows the original image containing noise; the red frame indicates the region selected for the CV value used to evaluate the denoising effect. (b) shows the image obtained after applying the global weighted least squares filter. (c) shows the image after filtering using the method of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings.

[0037] Refer to the attached Figure 1 The present invention proposes a global weighted least squares filtering method based on the RoEWA operator, which is characterized by comprising the following steps:

[0038] Step 1: Calculate the total power SPAN based on the original noisy polarimetric synthetic aperture radar (PolSAR) image to obtain the power map:

[0039] SPAN=|S HH | 2 +2|S HV | 2 +|S VV | 2 ,

[0040] Among them, H represents the information sent and received in the horizontal direction, V represents the information sent and received in the vertical direction; S HH 、S VV Represent the co-polarization components in the vertical and horizontal directions, S HV Represents the co-polarization component when horizontal transmission and vertical reception or vertical transmission and horizontal reception are met;

[0041] Step 2: Obtain the gradient on the power graph using the weighted exponential average ratio ROEWA operator:

[0042]

[0043] where h∈{x,y}, Represents the gradient in the vertical direction x or horizontal direction y; represents the exponentially weighted average value obtained by using the weighting function in the window area i, i = {1, 2};

[0044] Step 3: Calculate the weights in the x and y directions of pixel point p according to the following formula:

[0045]

[0046]

[0047] Among them, α represents the constraint factor and ε is a constant;

[0048] Step 4: Use the weights obtained in step 3 to construct the energy function J(u) for filtering:

[0049]

[0050] In the above energy function expression, the first term, parameter f, represents the noisy polarimetric SAR image, u represents the filtered output image, and p represents the pixel position. The second term, parameter λ, is the smoothing coefficient, which is used to balance the relationship between the first and second terms. A larger parameter λ results in a smoother output image, while a smaller parameter λ results in a higher degree of detail preservation. and are the partial derivatives of the filtered output image u in the x and y directions respectively.

[0051] Here, the first item requires that the image before and after denoising be as similar as possible, which is used to control the degree of detail preservation. The second item is a regularization item used to control the degree of smoothness, which constrains edge areas and homogeneous areas with different gradient sizes through the constraint factor α. When in edge areas with large gradients, the edge information is preserved by reducing the constraint factor α; in homogeneous areas with small gradients, a better denoising effect is achieved by increasing the smoothing factor. The balance between detail preservation and noise removal is achieved by finding the minimum value of the energy function: not only should the output image after filtering be as close as possible to the real image, thereby showing the degree of detail preservation, but the image should also be smoothed by maintaining the continuity of the gradient.

[0052] Step 5: In order to obtain the result of minimizing the energy function, the energy function is converted into a matrix form, which is specifically expressed as follows:

[0053]

[0054] Among them, u T and f T are the transposed matrices of u and f respectively; W x and W y They are respectively W in the energy function x,p (s) and W y,p The sparse diagonal matrix composed of the elements in (s), D x and D yare the backward difference matrices in the x and y directions, and D x and D y The transposed matrix of .

[0055] According to the properties of matrix operations, we can get the following:

[0056] (I+λL s )u=f,

[0057] Where I represents the identity matrix; L s is the five-point Laplace matrix calculated using the power diagram, which is expressed as follows:

[0058]

[0059] Step 6: Let A = I + λL s , the output image u is expressed as follows:

[0060] u=F λ (f) = A -1 f,

[0061] Among them, A -1 is the inverse matrix of A;

[0062] Step 7: According to the properties of PolSAR data, the nine channels of the PolSAR image are filtered in step (6) respectively, and the output image of each channel is obtained according to the following formula:

[0063] u z =F λ (q z )=A -1 q z ,

[0064] Among them, q z represents the input image of the zth channel, z∈{1,2,…,9}; u z Represents the output image of the z-th channel.

[0065] The effect of the present invention is further described below in conjunction with simulation experiments:

[0066] 1. Simulation conditions

[0067] (1) The experiment is divided into two parts: real images and simulated images. For the simulated image part, a 500×500 three-view simulated image is selected for the experiment; for the real image part, a 750×1024 four-view real image of the Netherlands is selected for the experiment.

[0068] (2) According to the characteristics of the image, the gradient operator window size of the filter in the present invention is set to 3×3, and the coefficient is 0.4; the parameters The smoothing factor t in is set to 1, where L represents the number of views of the image; α is set to 3.

[0069] 2. Simulation content and results

[0070] Simulation content: Using a 500×500 three-view simulated image and a 750×1024 four-view real image of the Netherlands, the present invention and the existing global weighted least squares filter method are used to suppress coherent speckle.

[0071] The purpose of this experiment is to compare the suppression effect of the present invention with the existing global weighted least squares filter method on coherent speckle. The experimental results are shown in the accompanying drawings. Figure 2 and Figure 3 As shown. Figure 2 (a) and Figure 3 (a) in the figure is the original image. Figure 2 (b) and Figure 3 (b) in the figure is the image obtained after the global weighted least squares filter. Figure 2 (c) and Figure 3 (c) in FIG. 1 is the image after filtering using the method of the present invention.

[0072] When comparing the present invention with the existing global weighted least squares filter, the PolSAR image speckle suppression evaluation indicators used are as follows: the images before and after filtering are compared and analyzed using the evaluation indicators dBMSE and dMaxBias, structural similarity (SSIM), the evaluation indicators EPD-ROA vertical and EPD-ROA horizontal in the horizontal and vertical directions respectively, the Peak Signal-to-Noise Ratio (PSNR), and the CV indicator of the homogeneous area. The CV value of the selected ROI area is as follows: Figure 3 The red box area in (a) is shown. The evaluation results of various indicators on simulated data and real data are shown in Tables 1 and 2.

[0073]

[0074] Table 1

[0075]

[0076] Table 2

[0077] Simulation results: As can be seen from the figure, the denoising effect of the present invention is significantly improved compared with the global weighted least squares filter. Figure 1 and Figure 2 As can be seen from (b) in the figure, the global weighted least squares filter method has been significantly improved compared to the previous classic non-local filtering method, but it is still lacking in smoothness for homogeneous areas, with obvious patch effects and the loss of edges and point targets. Figure 1 and Figure 2 In (c), we can see that the image's overblurring problem has significantly disappeared; the homogeneous area has been well smoothed, and there is basically no patchy effect; the preservation of point targets, line targets, and details has been significantly improved, and the edge lines are accurately located.

[0078] As can be seen from Tables 1 and 2, the proposed algorithm suppresses speckle noise while effectively preserving the image's scattering characteristics and geometric structure. Compared to the global weighted least squares filter, the proposed algorithm achieves a better balance between preserving PoLSAR image detail and suppressing coherent speckle.

[0079] In summary, the present invention achieves a balance between structural information preservation and speckle suppression in PoLSAR image speckle noise suppression, and obtains a good speckle suppression effect for PoLSAR images.

[0080] The above simulation analysis proves the correctness and effectiveness of the method proposed in the present invention.

[0081] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, for professionals in this field, after understanding the content and principles of the present invention, they may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A global weighted least squares filtering method based on the RoEWA operator, characterized in that: The steps include: (1) Calculate the total power SPAN based on the original noisy polarimetric synthetic aperture radar PolSAR image and obtain the power map: SPAN=|S HH | 2 +2|S HV | 2 +|S VV | 2 , Among them, H represents the information sent and received in the horizontal direction, V represents the information sent and received in the vertical direction; S HH 、S VV Represent the co-polarization components in the vertical and horizontal directions, S HV Represents the co-polarization component when horizontal transmission and vertical reception or vertical transmission and horizontal reception are met; (2) Obtain the gradient on the power graph using the weighted exponential average ratio ROEWA operator: where h∈{x,y}, Represents the gradient in the vertical direction x or horizontal direction y; represents the exponentially weighted average value obtained by using the weighting function in the window area i, i = {1, 2}; (3) Calculate the weights in the x and y directions of pixel point p according to the following formula: Among them, α represents the constraint factor and ε is a constant; (4) Using the weights obtained in step (3), construct the energy function J(u) for filtering: Where f represents the polarimetric SAR image containing noise, u represents the output image after filtering, p represents the position of the pixel point; λ is the smoothing coefficient; and are the partial derivatives of the filtered output image u in the x and y directions respectively; (5) In order to obtain the result of minimizing the energy function, the energy function is converted into a matrix form, and according to the properties of matrix operations, the following is obtained: (I+λL s )u=f, Where I represents the identity matrix; L s is the five-point Laplace matrix calculated using the power map; (6) Let A = I + λL s , the output image u is expressed as follows: u=F λ (f)=A -1 f, Among them, A -1 is the inverse matrix of A; (7) According to the properties of PolSAR data, the nine channels of the PolSAR image are filtered in step (6) respectively, and the output image in each channel is obtained according to the following formula: u z =F λ (q z )=A -1 q z , Among them, q z represents the input image of the zth channel, z∈{1,2,…,9}; u z Represents the output image of the z-th channel.

2. The method according to claim 1, wherein: In step (5), the energy function is converted into a matrix form, which is specifically expressed as follows: Among them, u T and f T are the transposed matrices of u and f respectively; W x and W y They are respectively W in the energy function x,p (s) and W y,p The sparse diagonal matrix composed of the elements in (s), D x and D y are the backward difference matrices in the x and y directions, and D x and D y The transposed matrix of .

3. The method according to claim 2, wherein: The five-point Laplace matrix in step (5) is expressed as follows:

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