A hybrid method for automatic enhancement of high dynamic range industrial X-ray images
By decomposing the X-ray image into a basic layer and a detail layer, the contrast is reduced and combined, and combined with high-frequency emphasis filtering and sub-step processing, the problem of low contrast and no outstanding details of the X-ray image is solved, efficient enhancement of the image and outstanding details are achieved, and the detection effect of industrial detection is significantly improved.
Patent Information
- Application Number
- CN202411021658.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-29
- Publication Date
- 2025-03-11
- Estimated Expiration
- 2044-07-29
AI Technical Summary
The existing X-ray images have problems in industrial detection with low contrast and no outstanding details, which cannot meet the actual detection needs, which is not conducive to the detection and judgment of product defects.
The high dynamic range industrial X-ray image automatic enhancement mixing method is adopted to decompose the image into a base layer and a detail layer, reduce the contrast of the base layer, and combine it with the detail layer for compression to eliminate image noise. Then, high frequency emphasis filtering is used to highlight the image details and the contrast of the image is increased by the processing of substeps 1 to 6.
It effectively improves the contrast and detailed information of X-ray images, significantly improves the detection effect of the image, enhances the detection ability of automobile casting defects, and has higher contrast and detail enhancement effects.
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Figure CN118864330B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of nondestructive testing, and in particular to a high dynamic range industrial X-ray image automatic enhancement hybrid method. Background Art
[0002] X-ray inspection technology is a non-contact, non-destructive optical inspection method, which is widely used in medical diagnosis, aerospace, safety inspection, industrial inspection and other fields.
[0003] X-ray imaging technology has developed from film radiography to computer radiography (CR) and digital imaging (DR). Among them, DR technology is the most widely used X-ray detection technology today and is also the main development direction in the future. However, in the process of X-ray imaging, the X-ray image contains a lot of noise due to factors such as X-ray quantum noise and scattering. At the same time, due to the power limitation of the light source, the difference in the absorption of X-rays by different materials, and the structural complexity of the workpiece being measured, the spatial contrast and detail contrast of the X-ray image are low.
[0004] In the process of implementing the technical method of the embodiment of the present invention, the inventor of this patent found at least the following technical problems in the prior art:
[0005] Traditional X-ray images use mean filtering to filter out Gaussian noise and median filtering to filter out salt and pepper noise. This method will cause the loss of some image detail information. In industrial inspection, the edge details of the image contain important defects and damage information of the workpiece.
[0006] Recently, least squares-based filtering algorithms have been widely used to filter Gaussian noise, such as anisotropic diffusion and total variation (TV). Among them, the anisotropic diffusion method enhances image details by stopping diffusion at the edge, but blurs the noise edge; the TV method can well unify the noise, but it is easy to cause staircase artifacts.
[0007] Recently, bilateral filtering and non-local means filtering (NLM) have been widely used because of their advantages of effectively protecting the edge details of the image while filtering out noise. Among them, bilateral filtering is a nonlinear filtering that achieves filtering effects by replacing the current pixel value with the weighted neighborhood value of each pixel, but the efficiency of bilateral filtering is relatively low. NLM filtering uses the weighted average of the pixels judged to be the most similar to update the pixel, but the effect of NLM filtering is poor.
[0008] In addition, since industrial X-ray inspection images are usually 14 or 16-bit images, which are high dynamic range (HDR) images, they are usually displayed as low-light images when displayed directly on a computer monitor, which will present a darker image, making it inconvenient for inspectors to detect and identify product defects. Therefore, they need to be compressed into low dynamic range images (LDR) when displayed on the terminal. This process is called tone mapping. The existing tone mapping method is a global tone mapping method, which uses a single spatially invariant mapping function to transform all pixels. This method is relatively simple, but it is easy to cause the loss of image details.
[0009] In summary, the existing X-ray images of the workpieces under test have the disadvantages of low contrast and unclear details, which cannot meet the actual detection needs and are not conducive to the detection and identification of product defects. Summary of the invention
[0010] The embodiment of the present invention provides a hybrid method for automatic enhancement of high dynamic range industrial X-ray images, which solves the problem that the existing X-ray images of the workpiece under test have low contrast and unclear details, cannot meet actual detection needs, and are not conducive to the detection and identification of product defects.
[0011] An embodiment of the present invention provides a hybrid method for automatically enhancing high dynamic range industrial X-ray images, comprising:
[0012] Step S1: decomposing a high dynamic range industrial X-ray image of an automobile casting into a base layer and a detail layer; reducing the contrast of the base layer; merging the base layer and the detail layer after the contrast reduction for compression to obtain a compressed X-ray image to eliminate image noise;
[0013] Step S2: The compressed X-ray image is filtered through a high-frequency emphasis filter to highlight the details of the defects of the automobile castings in the image. The expression of the high-frequency emphasis filter is:
[0014] ;
[0015] In the formula, and represents Fourier transform and inverse Fourier transform, F(u,v) is the compressed X-ray image above J Fourier transform, k represents the enhancement coefficient, and the value of k controls the degree of detail enhancement. is a frequency domain high-pass filter, I out2 (x,y) Represents the output image after high-frequency emphasis filtering;
[0016] When using a Gaussian high-pass filter, The expression is as follows:
[0017] ;
[0018] In the formula, D 0 means the cutoff frequency is at the distance from the center of the frequency rectangle, and D means the frequency of the filter;
[0019] Step S3: Process the filtered X-ray image in sub-steps 1 to 6 to obtain a final high-contrast image;
[0020] Sub-step 1: Divide the input image into sub-blocks of size M rows and N columns;
[0021] Sub-step 2: Calculate the histogram of each sub-block;
[0022] Sub-step 3: Calculate the clipping threshold T, the formula is as follows:
[0023] ;
[0024] in, is the crop factor; and are the number of pixels in the x-direction and y-direction of each sub-block, and L is the number of gray levels of each sub-block;
[0025] Sub-step 4: crop the grayscale histogram of each sub-block and redistribute the pixels of the cropped part;
[0026] Assuming that the total number of pixels in the original histogram that exceed the clipping threshold T is S, we get:
[0027] ;
[0028] in, h(x) Represents the original histogram of the processed image;
[0029] Therefore, the converted histogram h'(x) is expressed as:
[0030] ;
[0031] ;
[0032] in, A Indicates the conversion factor;
[0033] Sub-step 5: performing a histogram equalization operation on the sub-blocks after the pixels are reallocated in sub-step 4;
[0034] Sub-step 6: To overcome the discontinuity problem at the junctions of the sub-blocks, bilinear interpolation is used to reconstruct the grayscale level of the pixels.
[0035] Optionally, decomposing the high dynamic range industrial X-ray image into a base layer and a detail layer specifically includes:
[0036] The high dynamic range industrial X-ray image is decomposed into a base layer and a detail layer, wherein the base layer is obtained by performing guided filtering on the logarithm of the original HDR image, and is expressed as follows:
[0037] ;
[0038] In the formula, p i Represents the logarithmic image of the original image; I i Represents the input raw HDR image I The intensity of each pixel;
[0039] According to the linear model of the guided filter, each pixel of the base layer is Base i It is expressed as:
[0040] ;
[0041] In the formula, and Respectively indicated in the window The scale factor for transferring details and the bias factor for adjusting intensity in the logarithmic image p i As a guiding image, and It can be given by the following formula:
[0042] ;
[0043] ;
[0044] In the formula, and The input image is in the window The mean and variance of Display Window In p i The mean of is the number of pixels in the filter window, is the regularization parameter;
[0045] Get the detail layer Detail i :
[0046] .
[0047] Optionally, reducing the contrast of the base layer specifically includes:
[0048] To adjust the contrast of the base layer, the compression factor needs to be calculated :
[0049] ;
[0050] Among them, C contrast Represents the contrast coefficient, and Base is the base image.
[0051] Optionally, the step of merging the contrast-reduced base layer and the detail layer for compression to obtain a compressed X-ray image is as follows:
[0052] Set the contrast factor , then the final compressed image can be obtained J i :
[0053] .
[0054] Optionally, the window radius r=3, the regularization parameter .
[0055] Optionally, the cutoff frequency is at a distance from the center of the frequency rectangle , enhancement coefficient k=1.5.
[0056] Optionally, the crop factor , the number of rows M=4, and the number of columns N=4.
[0057] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:
[0058] The X-ray images of typical automobile castings are processed and analyzed by a hybrid method of automatic enhancement of high dynamic range industrial X-ray images of the present invention. First, the high dynamic range industrial X-ray images of automobile castings are compressed according to step S1, which has more complex calculations, can retain more image details, can denoise and enhance details. Compared with the bilateral filtering method, it not only has a more efficient filtering efficiency, but also can well maintain the image gradient information; then, according to step S2, the compressed X-ray image is filtered, and the frequency domain filtering method can be used to enhance the image, which can effectively enhance the main edge information of the image and facilitate the detection of automobile casting defects; finally, sub-steps S1 to S6 are used to widen the grayscale range of the image, which can improve the image contrast. The experimental results show that the present invention can effectively highlight the details of automobile casting defects in the image while improving the contrast of the X-ray image. Compared with the processing results of the existing VI3 software, it has higher contrast and detail enhancement effects, which is conducive to industrial defect detection and discrimination. BRIEF DESCRIPTION OF THE DRAWINGS
[0059] Figure 1 A flow chart of a hybrid method for automatic enhancement of high dynamic range industrial X-ray images in one embodiment of the present invention;
[0060] Figure 2 This is a schematic diagram of a specific implementation of step S1 in one embodiment of the present invention;
[0061] Figure 3 A simplified flow chart of sub-steps 1 to 6 in one embodiment of the present invention;
[0062] Figure 4 A schematic diagram of sub-block histogram clipping and pixel reallocation in one embodiment of the present invention;
[0063] Figure 5 A diagram of an X-ray device for performing an X-ray nondestructive testing test on an automotive aluminum casting in one embodiment of the present invention;
[0064] Figure 6 This is a comparison chart of the test results of image enhancement test 1 of the present invention and VI3 software in one embodiment of the present invention;
[0065] Figure 7 This is a comparison chart of the test results of image enhancement test 2 of the present invention and VI3 software in one embodiment of the present invention. DETAILED DESCRIPTION
[0066] The embodiment of the present invention provides a hybrid method for automatic enhancement of high dynamic range industrial X-ray images, which solves the problem that the existing X-ray images of the workpiece under test have low contrast and unclear details, cannot meet actual detection needs, and are not conducive to the detection and identification of product defects.
[0067] In order to better understand the above-mentioned high dynamic range industrial X-ray image automatic enhancement hybrid method, the following will be described in detail in conjunction with the drawings and specific implementation methods of the specification. Obviously, the embodiments described in the present invention are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.
[0068] Please refer to the following Figure 1 , a hybrid method for automatic enhancement of high dynamic range industrial X-ray images, comprising:
[0069] Step S1: decomposing a high dynamic range industrial X-ray image of an automobile casting into a base layer and a detail layer; reducing the contrast of the base layer; merging the base layer and the detail layer after the contrast reduction for compression to obtain a compressed X-ray image to eliminate image noise.
[0070] Since the high dynamic range industrial X-ray image of automobile castings is a HDR (High Dynamic Range) image, it is usually displayed as a low-light image when displayed directly on a computer monitor. It will present a darker image, which is not convenient for inspectors to detect and identify product defects. During the display process, the HDR image needs to be compressed into an LDR (Low Dynamic Range) image.
[0071] like Figure 2 As shown, step S1, its basic principle is to decompose the original HDR image into a base layer and a detail layer, reduce the contrast of the base layer, keep the detail layer unchanged, and finally merge the two layers of data to achieve compression. The specific implementation process is as follows.
[0072] First, the original HDR image is decomposed into a base layer and a detail layer, where the base layer is obtained by guiding the logarithm of the original HDR image, and its expression is as follows:
[0073] ;
[0074] In the formula, p i Represents the logarithmic image of the original image; I i Represents the input raw HDR image I The intensity of each pixel.
[0075] According to the linear model of the guided filter, each pixel of the base layer is Base i It is expressed as:
[0076] ;
[0077] In the formula, and Respectively indicated in the window The scale factor of the transmitted details and the bias factor of the adjusted intensity in , if the window radius is a rectangular window of r, then The size of is (2r+1)×(2r+1). The present invention utilizes logarithmic images p i As a guiding image, and It can be given by the following formula:
[0078] ;
[0079] ;
[0080] In the formula, and The input image is in the window The mean and variance of Display Window In p i The mean of is the number of pixels in the filter window, is the regularization parameter. Preferably, the parameters of the present invention are set as follows: the window radius r=3, the regularization parameter The parameters recommended by the method of the present invention are the results obtained through a large number of experimental verifications and summaries, and are applicable to most low-illuminance and high-dynamic industrial X-ray images.
[0081] After the above filtering, the detail layer is further obtained Detail i :
[0082] ;
[0083] Next, adjust the contrast of the base layer and calculate the compression factor :
[0084] ;
[0085] Among them, C contrast Represents the contrast coefficient, and Base is the base image.
[0086] For most X-ray images, , then the final compressed image can be obtained J i :
[0087] ;
[0088] Through the steps described above, an LDR image retaining image details, that is, a compressed X-ray image, can be obtained.
[0089] Step S2: The compressed X-ray image is filtered through a high-frequency emphasis filter to highlight the details of the defects of the automobile casting in the image. The high-frequency emphasis filter adopts a Gaussian high-pass filter.
[0090] Since X-rays cannot be focused using optical lenses, high dynamic range industrial X-ray images of automotive castings are usually blurred. Although the display effect is improved to a certain extent after the HDR image fast compression method using guided filtering, the edge details are still not clear enough. In non-destructive testing applications, the intuitive display of tiny details is particularly important, so the details of the image need to be further improved. The present invention filters the compressed X-ray image through high-frequency emphasis to highlight the details of the defects of the automotive castings in the image. The expression of high-frequency emphasis filtering is:
[0091] ;
[0092] In the formula, and represents Fourier transform and inverse Fourier transform, F(u,v) is the compressed X-ray image above J Fourier transform, k is the enhancement coefficient, and the value of k controls the degree of detail enhancement. is a frequency domain high-pass filter, I out2 (x,y) Represents the output image after high-frequency emphasis filtering.
[0093] is a frequency domain high-pass filter. When the present invention adopts a Gaussian high-pass filter, its expression is as follows:
[0094] ;
[0095] In the formula, D 0 means the cut-off frequency is at the distance from the center of the frequency rectangle, and D means the frequency of the filter. J i The image with enhanced details is obtained by filtering with high frequency emphasis Preferably, the parameters of the present invention are set as follows: the cut-off frequency is at a distance from the center of the frequency rectangle , enhancement coefficient k = 1.5. The parameters recommended by the method of the present invention are the results obtained through a large number of experimental verifications and summaries, and are applicable to most low-illuminance and high-dynamic industrial X-ray images.
[0096] Step S3: Perform sub-steps 1 to 6 on the filtered X-ray image to obtain a final high-contrast image.
[0097] Through the image processing of step S1 and step S2, although the details of the original image are enhanced, the contrast between its background and the object under test is still not high. In order to make the image more suitable for human observation, this article adopts sub-steps 1 to 6 to improve the contrast of the image. Compared with the traditional HE (Histogram Equalization) method, this method can suppress the amplification of noise while enhancing the contrast. The contrast amplification near a given pixel value is given by the slope of the transfer function CDF (Cumulative Distribution Function). The amplification is limited by clipping the histogram to a predetermined value before calculating the transfer function CDF, thereby limiting the slope of the transfer function CDF, thereby achieving the purpose of preventing over-enhancement and limiting noise. As Figure 3 As shown, sub-steps 1 to 6 are respectively as follows.
[0098] Sub-step 1: Divide the input image into sub-blocks of size M rows and N columns. The more pixels a sub-block contains, the higher the local contrast, but the more serious the loss of image details.
[0099] Sub-step 2: Calculate the histogram of each sub-block and denote the obtained histogram by h(x).
[0100] Sub-step 3: Calculate the clipping threshold T, which can be calculated using the following formula:
[0101] ;
[0102] in, is the crop factor; and are the number of pixels in the x and y directions of each sub-block, and L is the number of gray levels of each sub-block.
[0103] Sub-step 4: Crop the grayscale histogram of each sub-block. The cropping process is as follows: Figure 4 (a). Then, the pixels of the cropped part are redistributed, as shown in Figure 4 (b) as shown.
[0104] Assuming that the total number of pixels in the original histogram that exceed the clipping threshold T is S, we can get:
[0105] ;
[0106] in, h(x) Represents the original histogram of the processed image.
[0107] Therefore, the converted histogram h'(x) is expressed as:
[0108] ;
[0109] ;
[0110] in, A Indicates the conversion factor.
[0111] Sub-step 5: Perform a histogram equalization operation on the sub-blocks after the pixels are reallocated in sub-step 4.
[0112] Sub-step 6: To overcome the discontinuity problem at the junctions of the sub-blocks, bilinear interpolation is used to reconstruct the grayscale values of the pixels.
[0113] Preferably, the parameter is set to the crop factor , the number of rows M=4, the number of columns N=4. The parameters recommended by the method of the present invention are the results of a large number of experimental verifications and summaries, and are applicable to most low-illumination and high-dynamic industrial X-ray images. After CLAHE processing, the contrast of the X-ray image will be further improved, and it is also beneficial to improve the contrast of tiny details and edges.
[0114] In order to verify the effectiveness of the hybrid method for automatic enhancement of high dynamic range industrial X-ray images proposed in this paper, X-ray nondestructive testing of automotive aluminum castings was carried out using X-ray equipment from VJ Technology in the United States. Figure 5 As shown, the original image obtained is a 16-bit HDR image. Figure 6 (a) and Figure 7 (a) shown.
[0115] Figure 6 In the figure, (a) is the original image of experiment 1, (b) is the enhancement result of VI3 software of experiment 1, (c) is the enhancement result of the present invention of experiment 1, (d) is the histogram of the original image of experiment 1, (e) is the histogram of the enhancement result of VI3 software of experiment 1, and (f) is the histogram of the enhancement result of the present invention of experiment 1.
[0116] Figure 7 In the figure, (a) is the original image of Experiment 2, (b) is the enhancement result of VI3 software of Experiment 2, (c) is the enhancement result of the present invention of Experiment 2, (d) is the histogram of the original image of Experiment 2, (e) is the histogram of the enhancement result of VI3 software of Experiment 2, and (f) is the histogram of the enhancement result of the present invention of Experiment 2.
[0117] Next, the collected X-ray original images of automobile aluminum castings were processed and compared using the method of the present invention and the American VJ Technology Imaging Software (VI3 Software for short). The image enhancement results of the present invention are shown in the figure. Figure 6 (c) and Figure 7 (c) shows the image enhancement results of VI3 software. Figure 6 (b) and Figure 7 (b) shown.
[0118] On the other hand, for the objective evaluation of enhanced images, the present invention uses information entropy, peak signal-to-noise ratio, Tenengrad criterion value and contrast improvement index to evaluate the image enhancement effect. Among them, information entropy expresses the richness of image information. The larger the entropy value, the richer the image details; the larger the peak signal-to-noise ratio, the lower the noise level of the image; the Tenengrad criterion value is based on the gradient to evaluate the image quality. The larger the Tenengrad criterion value, the better the sharpness of the image; the larger the contrast improvement index, the better the contrast of the enhanced image.
[0119] The evaluation indicators corresponding to the above test data are shown in the following table, where the peak signal-to-noise ratio is calculated and the reference image is obtained by low-pass filtering the original image.
[0120]
[0121] from Figure 6 and Figure 7 It can be seen intuitively from the test results that the method of the present invention has significantly improved the contrast and clarity of low-illuminance industrial X-ray images, and its enhancement effect is greater than that of the American VJ Technology Imaging Software, especially for the details at low illumination. It is very important for the non-destructive detection of industrial product defects. In addition, it can be seen from the evaluation indicators in the above table that the information entropy, Tenengrad criterion and contrast improvement index of the images processed by the method of the present invention are higher than those of the American VJ Technology Imaging Software, among which the sharpness Tenengrad criterion has been greatly improved. This shows that the images processed by the method of the present invention have richer image details, higher sharpness and higher contrast. In addition, the peak signal-to-noise ratio is slightly lower than the indicator of the American VJ Technology Imaging Software. This is because high-frequency enhancement leads to a certain degree of noise amplification while enhancing details. Therefore, in the high-frequency enhancement process, the value of the enhancement coefficient k should not be too large. The present invention recommends using k=1.5. The parameters recommended by the method of the present invention are the results obtained through a large number of experimental verifications and summaries, and are applicable to most low-illuminance and high-dynamic industrial X-ray images. Although the peak signal-to-noise ratio is lower than the indicator of the VI3 software, from Figure 6 and Figure 7 It can be seen that this does not affect the final human eye observation effect.
[0122] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.
Claims
1. A hybrid method for automatic enhancement of high dynamic range industrial X-ray images, characterized in that: include: Step S1: decomposing a high dynamic range industrial X-ray image of an automobile casting into a base layer and a detail layer; reducing the contrast of the base layer; The base layer after contrast reduction and the detail layer are combined for compression to obtain a compressed X-ray image to eliminate image noise; Step S2: The compressed X-ray image is filtered through a high-frequency emphasis filter to highlight the details of the defects of the automobile castings in the image. The expression of the high-frequency emphasis filter is: ; In the formula, and represents Fourier transform and inverse Fourier transform, F(u,v) is the compressed X-ray image above J Fourier transform, k represents the enhancement coefficient, and the value of k controls the degree of detail enhancement. is a frequency domain high-pass filter, I out2 (x,y) Represents the output image after high-frequency emphasis filtering; When using a Gaussian high-pass filter, The expression is as follows: ; In the formula, D 0 means the cutoff frequency is at the distance from the center of the frequency rectangle, and D means the frequency of the filter; Step S3: Process the filtered X-ray image in sub-steps 1 to 6 to obtain a final high-contrast image; Sub-step 1: Divide the input image into sub-blocks of size M rows and N columns; Sub-step 2: Calculate the histogram of each sub-block; Sub-step 3: Calculate the clipping threshold T, the formula is as follows: ; in, is the crop factor; and are the number of pixels in the x-direction and y-direction of each sub-block, and L is the number of gray levels of each sub-block; Sub-step 4: crop the grayscale histogram of each sub-block and redistribute the pixels of the cropped part; Assuming that the total number of pixels in the original histogram that exceed the clipping threshold T is S, we get: ; in, h(x) Represents the original histogram of the processed image; Therefore, the converted histogram h'(x) is expressed as: ; ; in, A Indicates the conversion factor; Sub-step 5: performing a histogram equalization operation on the sub-blocks after the pixels are reallocated in sub-step 4; Sub-step 6: To overcome the discontinuity problem at the junctions of the sub-blocks, bilinear interpolation is used to reconstruct the grayscale levels of the pixels.
2. The method according to claim 1, characterized in that Decomposing the high dynamic range industrial X-ray image into a base layer and a detail layer specifically includes: The high dynamic range industrial X-ray image is decomposed into a base layer and a detail layer, wherein the base layer is obtained by performing guided filtering on the logarithm of the original HDR image, and is expressed as follows: ; In the formula, p i Represents the logarithmic image of the original image; I i Represents the input raw HDR image I The intensity of each pixel; According to the linear model of the guided filter, each pixel of the base layer is Base i It is expressed as: ; In the formula, and Respectively indicated in the window The scale factor for transferring details and the bias factor for adjusting intensity in the logarithmic image p i As a guiding image, and It can be given by the following formula: ; ; In the formula, and The input image is in the window The mean and variance of Display Window In p i The mean of is the number of pixels in the filter window, is the regularization parameter; Get the detail layer Detail i : 。 3. The method according to claim 2, characterized in that The reducing the contrast of the base layer specifically includes: To adjust the contrast of the base layer, the compression factor needs to be calculated : ; Among them, C contrast Represents the contrast coefficient, and Base is the base image.
4. The method according to claim 3, characterized in that The base layer after reducing contrast and the detail layer are combined for compression to obtain a compressed X-ray image, specifically: Set the contrast factor , then the final compressed image can be obtained J i : 。 5. The method according to claim 2, characterized in that The window radius r=3, the regularization parameter .
6. The method according to claim 1, characterized in that The cut-off frequency is at a distance from the center of the frequency rectangle , enhancement coefficient k=1.
5.
7. The method according to claim 1, characterized in that The crop factor , the number of rows M=4, and the number of columns N=4.
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