High-resolution remote sensing satellite image restoration method combining constrained least square filtering and guiding filtering

Abstract

The invention relates to a high-resolution remote sensing satellite image restoration method combining constrained least square filtering and guiding filtering, and belongs to the field of satellite remote sensing data processing. Carrying out deblurring processing on the to-be-restored input degraded image by adopting constrained least square filtering; and carrying out edge enhancement processing on the obtained deblurred image, outputting an image after edge enhancement, and carrying out denoising processing with edge characteristics by adopting guide filtering to obtain a restored image. The method has the advantages that balance can be kept in edge keeping and noise weakening, edge details are more highlighted, the edge strength is improved, the ringing phenomenon is avoided on the premise that the restoration effect meets a certain signal-to-noise ratio, and the method is high in practicability and can be expanded to multi-spectrum remote sensing images for image restoration.

Description

Technical Field

[0001] The present invention belongs to an image restoration method in the field of satellite remote sensing data processing, and particularly relates to a high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering. Background Art

[0002] When an optical remote sensing satellite is imaging in orbit, due to factors such as the disturbance effect of atmospheric turbulence, the scattering effect of aerosols in the atmosphere, the relative motion between the ground object and the imaging device, the diffraction of the optical system, the defocus of the imaging device, and electronic noise, the obtained remote sensing image will be degraded to varying degrees. The specific manifestations of degradation are noise, blurring, or spectral aliasing in the image, which seriously affects the accuracy of subsequent image processing. Image restoration is to eliminate or weaken the influence of degradation factors on the image quality, restore a clear, content-rich, and nearly real ideal image, and improve the image interpretation ability. Currently, in the field of remote sensing image data processing, restoration work has become an important aspect and has wide application value.

[0003] There are two key issues in the research of image restoration: one is to study the imaging degradation model, and the other is to study the image restoration algorithm. The imaging degradation model should be able to reflect the reasons for image degradation. Since there are many and complex factors causing image degradation and it is not convenient to analyze and establish models one by one, the degradation reasons are usually represented by a linear and space-invariant degradation model, that is, the original image is blurred by the action of a degradation function and then superimposed with an additive noise to finally form the degraded image.

[0004] The degradation process of the image can be described as the two-dimensional convolution of the original image and the degradation function. Therefore, image restoration can be realized by the inverse process of two-dimensional convolution. However, deconvolution is an ill-posed problem. Even when the degradation function that accurately represents the degradation factors is obtained, the degradation factors in the image cannot be completely eliminated, and only an approximate best estimate of the original image can be obtained. Deconvolution can improve the sharpness of the image, but at the same time, it will also amplify the noise.

[0005] Typical image restoration methods include inverse filtering, Wiener filtering, constrained least squares filtering, etc.

[0006] Inverse filtering restoration estimates the original true image by frequency-domain filtering under the condition of ignoring noise. Its advantages are small computational complexity and simple method. Its disadvantage is that it has limitations and is only applicable to degraded images without noise pollution. However, in reality, such degraded images do not exist. In the process of applying inverse filtering to restore degraded images affected by noise, its restoration algorithm will significantly amplify the noise and reduce the signal-to-noise ratio of the restored image. Therefore, the application scope of inverse filtering is not extensive in practical applications.

[0007] Wiener filtering, as a classic restoration method, solves the defect that inverse filtering significantly amplifies noise. The premise is that both the image and the noise are stationary random processes, and it uses the statistical information of the image and the noise to minimize the restoration error. When the frequency characteristics of the image and the noise are known, the effect of Wiener filtering is good. However, in the case of poor signal-to-noise ratio of the image, the restoration effect of Wiener filtering is not good. At the same time, Wiener filtering is based on the premise that the prior knowledge such as the power spectra of the degraded image and the noise is known, and these prior knowledge are often not easy to obtain.

[0008] Constrained least squares filtering is an improvement on the basis of Wiener filtering. It not only solves the problem that the inverse filtering method significantly amplifies noise, but also does not require much prior knowledge of the image. At the same time, in the case of low signal-to-noise ratio, its restoration effect is also better than that of Wiener filtering. Constrained least squares filtering combines a smoothness metric and the least squares criterion, aiming to reduce the noise sensitivity problem. This method finds the optimal restored image by solving an optimization problem, making the difference between the restored image and the original image the smallest, while satisfying the smoothness constraint.

[0009] Constrained least squares filtering is based on the premise that the noise has generalized stationarity. The smoothness constraint in the constrained least squares filtering method is mainly to suppress noise. However, when the noise suppression constraint strength is small, the clarity and contrast of the image can be better improved, the edge details can be restored, but the introduced noise is also large, and the signal-to-noise ratio of the restored image is poor, and even phenomena such as ringing will occur, affecting the interpretation quality of the image. And when the noise suppression constraint strength is large, the overall smoothing of the image is excessive, and the detailed edge information of the image will be lost.

[0010] Generally speaking, there has always been a contradiction between noise smoothing and edge preservation in the process of improving the clarity of the image. How to effectively process edges and noise in the image restoration process so that the restored image can well preserve the edges while weakening the noise is a problem to be solved. Summary of the Invention

[0011] The present invention provides a high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering, aiming to maintain a balance between edge preservation and noise reduction, so that the restoration effect is more prominent in edge details and the edge strength is improved on the premise of meeting a certain signal-to-noise ratio.

[0012] The technical solution adopted by the present invention includes the following steps:

[0013] Step 1, perform deblurring processing on the input degraded image g(x, y) to be restored by using constrained least squares filtering;

[0014] Step 2, for the deblurred image f obtained in Step 1 deblurPerform edge enhancement processing on (x, y) and output the edge-enhanced image f edge_enhance (x, y);

[0015] Step 3: Use guided filtering to perform denoising processing with edge characteristics on the edge-enhanced image f edge_enhance (x, y) to obtain the restored image f restore (x, y).

[0016] The input degraded image g(x, y) to be restored in the present invention adopts a general linear and space-invariant degradation model to characterize the degradation process, that is, the original image f(x, y) is affected by a degradation function h(x, y) and superimposed with noise n(x, y) to form the degraded image g(x, y). Assuming that the operator or system is linear and space-shift invariant, the relationship between the degraded image g(x, y) and the original image f(x, y) is expressed as follows:

[0017]

[0018] Represents the convolution operation symbol;

[0019] The convolution operation of two functions in the spatial domain is equal to the product of their Fourier transforms in the frequency domain. Therefore, the above relationship in the frequency domain is expressed as:

[0020] G(u, v) = H(u, v)F(u, v) + N(u, v)

[0021] G(u, v) is the Fourier transform of the degraded image g(x, y), H(u, v) is the Fourier transform of the degradation function h(x, y), and N(u, v) is the Fourier transform of the noise n(x, y).

[0022] The input image in this step of the present invention is the degraded image g(x, y), and the output image f deblur (x, y) is obtained through constrained least squares filtering processing;

[0023] The expression of the constrained least squares filter in the frequency domain is as follows:

[0024]

[0025] where is the Fourier transform of the output image f deblur (x, y) of this step of deblurring processing, IFFT represents the inverse Fourier transform, and the output image f deblur (x, y) after this step of deblurring processing is obtained through the inverse Fourier transform, H *(u, v) is the complex conjugate of the degenerate function H(u, v), γ is an adjustable regularization parameter, and the value of γ controls the strength of the smoothing constraint; P(u, v) is called the smoothing matrix, and its shape determines the degree to which different frequency components are affected by smoothness. P(u, v) is the Fourier transform of the Laplacian operator p(x, y), and p(x, y) is represented as the following 3*3 matrix:

[0026]

[0027] In the present invention, the value of γ is between 0.7 and 0.9.

[0028] In the present invention, the input image of step 2 is the deblurred image f deblur (x, y) obtained in step 1.

[0029] In step 2 of the present invention, the edge enhancement consists of two parts, namely edge extraction and edge superposition. The 5*5 edge extraction operator r(x, y) is selected to perform a convolution operation on the image f deblur (x, y) to obtain the edge image f edge (x, y). The edge image f edge (x, y) and the input image f deblur (x, y) are superimposed to obtain the edge-enhanced image f edge_enhance (x, y), and the specific expression is as follows:

[0030]

[0031] f edge_enhance (x, y) = f deblur (x, y) + δf edge (x, y)

[0032] In the above formula, represents the convolution operation symbol, δ is an adjustable edge superposition parameter, and the value of δ controls the strength of edge detail superposition.

[0033] In the present invention, the value of δ is between 0.1 and 0.2.

[0034] In step 3 of the present invention, the edge-enhanced image f edge_enhance (x, y) obtained in step 2 is used as the input image of the guided filter.

[0035] In step 3 of the present invention, f edge_enhance (x, y) is also used as the guidance image of the guided filter. When the guidance image is the input image itself, the guided filter becomes an edge-preserving filtering operation. The specific expression of the guided filtering operation in the case where the guidance image is the input image is as follows:

[0036]

[0037] f cov (x, y) = f corr (x, y) - f mean (x, y).*f mean (x, y)

[0038] f a (x, y) = f cov (x, y). / (f cov (x, y) + ∈)

[0039] f b (x, y) = f mean (x, y) - f a (x, y).*f mean (x, y)

[0040]

[0041] f restore (x, y) = f mean_a (x, y).*f edge_engance +f mean_b (x, y)

[0042] In the above formula, f edge_enhance (x, y) is the input image of this step, and f restore (x, y) is the final output image, where:

[0043] represents the convolution operation symbol,.* represents the matrix dot multiplication operation symbol,. / represents the matrix dot division operation symbol, m(x, y) is a 3*3 mean filter operator, and f mean (x, y) is the image after mean filtering of the input image / guidance image using the mean filter operator, and f corr (x, y) is the mean filtered image of the image after the dot multiplication of the input image and the guidance image, and f cov (x, y) is the covariance image of the input image and the guidance image, and f a (x, y), f b (x, y) is the local linear transformation coefficient image, is the image after mean filtering of f a (x, y), and f mean_b (x, y) is f b (x, y) is the image after mean filtering of f(x, y), ∈ is an adjustable parameter, and the value of ∈ controls the strength of the guidance filtering smoothing.

[0044] -6 ~10 -5between

[0045] Advantages of the present invention:

[0046] The image restoration process of the present invention is divided into three steps: deblurring, edge enhancement, and denoising. First, the constrained least squares filtering method is used for deblurring. During this process, a strong smoothing constraint strategy is adopted to prevent ringing in the deblurred image. However, the edges will be smoothed to a large extent. Then, the image output from the previous step is subjected to edge enhancement to enhance the smoothed edges in the previous step. It should be noted that while enhancing the edges, the noise in the flat areas of the image will also increase, resulting in a deterioration of the overall signal-to-noise ratio. Finally, the guided filtering method is used for denoising. While retaining the enhanced edge details from the previous step, the noise is also reduced. After processing through the above steps, the restored image has no ringing phenomenon, and the edge details of the image are improved while maintaining a certain signal-to-noise ratio.

[0047] The present invention makes full use of the advantages of the constrained least squares filtering in solving the problem of the sensitivity of the degradation function to noise, and the advantages of the guided filtering in maintaining edge and detail information, taking into account noise reduction and edge detail preservation while restoring image sharpness. The present invention can maintain a balance between edge preservation and noise reduction, making the restoration effect more prominent in edge details, improving edge strength, and not generating ringing phenomenon while meeting a certain signal-to-noise ratio. The present invention has strong practicability and can be extended to multi-spectral remote sensing images for image restoration. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flowchart of the present invention;

[0049] Figure 2 is the input degraded image to be restored;

[0050] Figure 3 is the image after deblurring by the constrained least squares filtering;

[0051] Figure 4 is the output image after edge enhancement using high-pass filtering on the basis of deblurring;

[0052] Figure 5 is the final restored image after edge-preserving denoising using guided filtering on the basis of edge enhancement. DETAILED DESCRIPTION OF THE INVENTION

[0053] The present invention provides a high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering. The process is as Figure 1 shown, including the following steps:

[0054] Step 1, perform deblurring on the input degraded image g(x,y) to be restored using constrained least squares filtering;

[0055] Adopt a general linear and spatially invariant degradation model to characterize the degradation process, that is, the original image f(x,y) is affected by a degradation function h(x,y) and superimposed with noise n(x,y) to form the degraded image g(x,y). Assuming the operator or system is linear and spatially shift-invariant, the relationship between the degraded image g(x,y) and the original image f(x,y) is expressed as follows:

[0056]

[0057] represents the convolution operation symbol;

[0058] The convolution operation of two functions in the spatial domain is equal to the product of their Fourier transforms in the frequency domain. Therefore, the above relationship in the frequency domain is expressed as:

[0059] G(u,v) = H(u,v)F(u,v) + N(u,v)

[0060] G(u,v) is the Fourier transform of the degraded image g(x,y), H(u,v) is the Fourier transform of the degradation function h(x,y), and N(u,v) is the Fourier transform of the noise n(x,y). Based on this degradation process, if the degraded image g(x,y), the noise n(x,y), and the system's degradation function h(x,y) are known, the original input image f(x,y) can be accurately obtained. However, in actual situations, the degradation function and the noise cannot be completely and accurately described. Therefore, only an approximate estimate of the original image can be obtained. Currently, there are a large number of studies on the acquisition and representation of the degradation function. This invention focuses on the research of the restoration method and does not elaborate too much on the accurate acquisition of the degradation function;

[0061] In this step, the input image of this step is the degraded image g(x,y), and the output image f deblur (x,y) after deblurring is obtained through constrained least squares filtering;

[0062] The expression of the constrained least squares filter in the frequency domain is as follows:

[0063]

[0064] where is the Fourier transform of the output image f deblur (x,y) of this step's deblurring process, and IFFT represents the inverse Fourier transform. The output image f deblur(x, y), H * (u, v) is the complex conjugate of the degenerate function G(u, v), γ is an adjustable regularization parameter, and the value of γ controls the strength of the smoothing constraint; O(u, v) is called the smoothing matrix, and its shape determines the degree of influence of different frequency components on the smoothness. O(u, v) is the Fourier transform of the Laplacian operator p(x, y), and p(x, y) is expressed as the following 3*3 matrix:

[0065]

[0066] In the present invention, through a large number of experimental explorations, it is found that the value of γ between 0.7 and 0.9 has better effects;

[0067] Step 2: Perform edge enhancement processing on the deblurred image f deblur (x, y).

[0068] The input image of Step 2 is the deblurred image f deblur (x, y) obtained in Step 1. In this step, edge enhancement processing is performed to enhance the high-frequency detail information in the image. The output of Step 2 is the edge-enhanced image f edge_enhance (x, y), which is used as the input image for Step 3;

[0069] In the present invention, edge enhancement consists of two parts, namely edge extraction and edge superposition. Select a 5*5 edge extraction operator r(x, y) to perform a convolution operation on the image f deblur (x, y) to obtain the edge image f edge (x, y). Then, superimpose the edge image f edge (x, y) and the input image f deblur (x, y) to obtain the edge-enhanced image f edge_enhance (x, y). The specific expression is as follows:

[0070]

[0071] f edge_enhance (x, y) = f deblur (x, y) + δf edge (x, y)

[0072] In the above formula, represents the convolution operation symbol, δ is an adjustable edge superposition parameter, and the value of δ controls the strength of the edge detail superposition;

[0073] Through a large number of experimental explorations, it is found that the value of δ between 0.1 and 0.2 has better effects;

[0074] Step 3: Use guided filtering on the edge-enhanced image f obtained in Step 2 edge_enhancePerform denoising processing with edge characteristics on (x, y);

[0075] The input image of step 3 is the edge-enhanced image f obtained in step 2 edge_enhance (x, y), and the output image of step 3 is the final restored image f restore (x, y);

[0076] In the present invention, the edge-enhanced image f edge_enhance (x, y) obtained in step 2 is used as the input image of guided filtering, and at the same time f edge_enhance (x, y) is used as the guiding image of guided filtering. When the guiding image is the input image itself, guided filtering becomes an edge-preserving filtering operation. The specific expression of the guided filtering operation in the case where the guiding image is the input image is as follows:

[0077]

[0078] f cov (x, y) = f corr (x, y) - f mean (x, y).* f mean (x, y)

[0079] f a (x, y) = f cov (x, y). / (f cov (x, y) + ∈)

[0080] f b (x, y) = f mean (x, y) - f a (x, y).* f mean (x, y)

[0081]

[0082] f restore (x, y) = f mean_a (x, y).* f edge_engance + f mean_b (x, y)

[0083] In the above formula, f edge_enhance (x, y) is the input image of this step, and f restore (x, y) is the output image of this step and also the final output image of this method; where:

[0084] represents the convolution operation symbol,.* represents the matrix dot multiplication operation symbol,. / represents the matrix dot division operation symbol, m(x, y) is a 3*3 mean filtering operator, and f mean(x, y) is the image after mean filtering the input image / guide image using the mean filtering operator, f corr (x, y) is the mean filtered image of the image obtained by multiplying the input image and the guide image, f cov (x, y) is the covariance image of the input image and the guide image, f a (x, y), f b (x, y) is the local linear transformation coefficient image, is f a (x, y) is the image after mean filtering of f mean_b (x, y) is f b (x, y) is the image after mean filtering of f. ∈ is an adjustable parameter, and the value of ∈ controls the intensity of the guidance filtering smoothing;

[0085] In the present invention, through a large number of experimental explorations, the value of ∈ ranges between 10 -6 ~10 -5 and has better effects.

[0086] The following further illustrates the present invention in conjunction with experimental examples.

[0087] Guided filtering is an image filtering method based on a local linear model proposed by He Kaiming et al. in 2010. It believes that any pixel point in the image has a linear relationship with its adjacent pixel points, uses a guide image to guide the filtering process of the target image, makes the gradient of the output image as similar as possible to the guide image, and at the same time makes the gray level of the output image similar to the input image, so as to preserve edges and weaken noise. The guide image can be the image to be processed itself or other images. When the guide image is the input image itself, guided filtering becomes an edge-preserving filtering operation.

[0088] First, the constrained least squares filtering method is used to deblur the input degraded image to be restored. The regularization parameter γ in this step takes the value of 0.8; the input degraded image to be restored is shown in Figure 2 , and the image after deblurring is shown in Figure 3 . By comparing Figure 2 and Figure 3 , it can be intuitively and obviously found that Figure 3 the image in Figure 2 has improved clarity compared to the image in

[0089] . Moreover, there is no ringing phenomenon, but the contrast of the edges and flat areas of the image has not been significantly enhanced; Figure 4 Subsequently, the deblurred image is subjected to edge enhancement processing. The superposition parameter δ in this step takes the value of 0.15. The image after edge enhancement is shown in Figure 3 . By comparing the image in Figure 4 with the image in Figure 4The contrast between the edges and the flat areas in the middle image has been significantly enhanced, but there is also a lot of noise in the flat areas, and the overall signal-to-noise ratio deteriorates;

[0090] Finally, guided filtering is used to denoise the edge-enhanced image to obtain the final restored output image. The regularization parameter ∈ in this step is set to 0.000005. The final restored output image is shown in Figure 5 , and compared with Figure 4 the middle image and Figure 5 the middle image, Figure 5 while maintaining the enhanced edges in the middle image, the noise in the flat areas has been reduced.

Claims

1. A high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering, characterized in that: Including the following steps: Step 1: Perform deblurring processing on the input degraded image g(x, y) to be restored using constrained least squares filtering; Step 2: Perform edge enhancement on the deblurred image f deblur (x, y) obtained in Step 1, and output the edge-enhanced image f edge_enhance (x, y); Step 3: Perform denoising processing with edge characteristics on the edge-enhanced image f edge_enhance (x, y) obtained in Step 2 to obtain the restored image f restore (x, y).

2. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 1, wherein: The input degraded image g(x, y) to be restored adopts a general linear and spatially shift-invariant degradation model to characterize the degradation process, that is, the original image f(x, y) is affected by a degradation function h(x, y) and superimposed with noise n(x, y) to form the degraded image g(x, y). Assuming that the operator or system is linear and spatially shift-invariant, the relationship between the degraded image g(x, y) and the original image f(x, y) is expressed as follows: represents the convolution operation symbol; The convolution operation of two functions in the spatial domain is equal to the product of their Fourier transforms in the frequency domain. Therefore, the above relationship in the frequency domain is expressed as: G(u, v) = H(u, v)F(u, v) + N(u, v) G(u, v) is the Fourier transform of the degraded image g(x, y), H(u, v) is the Fourier transform of the degradation function h(x, y), and N(u, v) is the Fourier transform of the noise n(x, y).

3. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 2, characterized in that: The input image in this step is the degraded image g(x, y), and the output image f deblur (x, y) is obtained through constrained least squares filtering for deblurring; The expression of the constrained least squares filter in the frequency domain is as follows: Among them is the output image f of the deblurring process in this step deblur (x,y) is the Fourier transform, and IFFT represents the inverse Fourier transform The output image f of the deblurring process in this step is obtained through the inverse Fourier transform deblur (x,y), H * (u,v) is the complex conjugate of the degradation function H(u,v), γ is an adjustable regularization parameter, and the value of γ controls the strength of the smoothing constraint; P(u,v) is called the smoothing matrix, and its shape determines the degree of influence of different frequency components on smoothness. P(u,v) is the Fourier transform of the Laplacian operator p(x,y), and p(x,y) is expressed as the following 3*3 matrix:

4. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 3, wherein: The value of γ ranges between 0.7 and 0.

9.

5. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 1, characterized in that: The input image of step 2 is the deblurred image f deblur (x, y) obtained in step 1.

6. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 5, characterized in that: In step 2, the edge enhancement consists of two parts, namely edge extraction and edge superposition. A 5*5 edge extraction operator r(x,y) is selected to convolve the image f deblur (x,y) to obtain the edge image f edge (x,y). The edge image f edge (x,y) and the input image f deblur (x,y) are superposed to obtain the edge-enhanced image f edge_enhance (x,y). The specific expression is as follows: f edge_enhance (x,y) = f deblur (x,y) + δf edge (x,y) In the above formula, represents the convolution operation symbol, δ is an adjustable edge superposition parameter, and the value of δ controls the intensity of edge detail superposition.

7. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 6, characterized in that: The value of δ ranges between 0.1 and 0.

2.

8. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 1, characterized in that: In step 3, the edge-enhanced image f edge_enhance (x, y) obtained in step 2 is used as the input image for guided filtering.

9. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 8, wherein: In step 3, f edge_enhance (x, y) is used as the guiding image for guided filtering. When the guiding image is the input image itself, guided filtering becomes an edge-preserving filtering operation. The specific expression of the guided filtering operation in the case where the guiding image is the input image is as follows: f cov (x,y) = f corr (x,y) - f mean (x,y).*f mean (x,y) f a (x,y) = f cov (x,y) / (f cov (x,y) + ∈) f b (x,y) = f mean (x,y) - f a (x,y).*f mean (x,y) f restore (x,y) = f mean_a (x,y).*f edge_enhance +f mean_b (x,y) In the above formula, f edge_enhance (x, y) is the input image of this step, and f restore (x, y) is the final output image, where: represents the convolution operation symbol,.* represents the matrix dot multiplication operation symbol,. / represents the matrix division operation symbol, m(x,y) is a 3*3 mean filter operator, f mean (x,y) is the image after mean filtering of the input image / guide image using the mean filter operator, f corr (x,y) is the mean filtered image of the image after the dot multiplication of the input image and the guide image, f cov (x,y) is the covariance image of the input image and the guide image, f a (x,y), f b (x,y) is the local linear transformation coefficient image, is the mean filtered image of f a (x,y), f mean_b (x,y) is the mean filtered image of f b (x,y) is the mean filtered image of f (x,y), ∈ is an adjustable parameter, and the value of ∈ controls the intensity of the guidance filtering smoothing.

10. The high-resolution remote sensing satellite image restoration method combining constrained least squares filtering and guided filtering according to claim 9, wherein: The value range of ∈ is between 10 -6 and 10 -5 .

Images