A fan-shaped cross-polarization SAR image scallop noise correction method

Abstract

The application discloses a kind of wide cross-polarization SAR image scallop noise correction methods, comprising the following steps: obtaining wide dual-polarization SAR image containing co-polarization and cross-polarization, and obtaining 1km spatial resolution co-polarization and cross-polarization backscatter coefficient image after preprocessing;Cross-polarization backscatter coefficient image is corrected to thermal noise in range direction;Co-polarization backscatter coefficient image is carried out sea surface wind speed inversion using geophysical model function, and co-polarization image inversion wind speed field is obtained;Based on co-polarization image inversion wind speed field, select calm and uniform sea surface;Cross-polarization image of calm and uniform sea surface is divided into sub-swath, and scallop noise of each sub-swath is extracted;The function model of each sub-swath scallop noise is established respectively, and the function model coefficient of each sub-swath is determined by fitting calculation using scallop noise and azimuth distance.The application can correct the influence of scallop noise on cross-polarization radar image product.

Description

Technical Field

[0001] This invention relates to the field of radar data processing technology, and in particular to a method for correcting scallop noise in wide-swath cross-polarization SAR images. Background Technology

[0002] Spaceborne Synthetic Aperture Radar (SAR) features multi-polarization, multi-mode, all-day, and all-weather operation, and can acquire remote sensing images with spatial resolution higher than 1 km and swath width up to 500 km. It has important applications in areas such as maritime vessel detection, marine oil spill monitoring, sea ice detection, and remote sensing inversion of sea surface wind fields. Based on the differences in the polarization of the transmitted and received electric field vectors of the radar antenna, existing spaceborne SARs can acquire radar images through four different polarization modes: HH (Horizontal Transmitting and Horizontal Receiving), VV (Vertical Transmitting and Vertical Receiving), and VH (Vertical Transmitting and Horizontal Receiving). VV and HH are collectively referred to as co-polarization, while VH and HV are collectively referred to as cross-polarization.

[0003] For different polarization modes, scholars at home and abroad have carried out a lot of research on wind field inversion. Among them, the sea surface wind field inversion method of co-polarized C-band SAR image has been operationally used for sea surface wind field inversion after many years of development. However, the radar backscatter signal of VV polarized SAR will saturate under high wind speed conditions, and is not suitable for sea surface wind field inversion under extreme weather conditions.

[0004] In recent years, scholars have discovered through research on C-band cross-polarization SAR that, under high wind speed conditions, wind speeds retrieved using cross-polarization SAR have higher accuracy than those retrieved using homopolarization SAR. This is mainly due to the fact that the cross-polarization backscattering coefficient is not affected by saturation effects under very high wind speeds. Currently, satellites equipped with C-band synthetic aperture radar, such as RADARSAT-2, Sentinel-1A / B, and Gaofen-3, are capable of providing wide-swath cross-polarization imagery, providing crucial data support for remote sensing inversion of sea surface wind fields under high sea states.

[0005] However, due to the high platform noise of wide-swath C-band SAR and the weak cross-polarization backscattered signal, the cross-polarization backscattered signal is easily affected by platform noise under low sea states. Although some SAR image products currently offer thermal noise correction methods, these methods mainly target range-direction thermal noise correction, while residual scallop noise in the azimuth direction still significantly impacts wide-swath cross-polarization images. Therefore, further development of scallop noise correction methods for cross-polarization images is needed to effectively suppress the impact of scallop noise on the image, improve the radiation uniformity of the impact, and enable cross-polarization images to have better applications. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a method for correcting scallop noise in wide-swath cross-polarization SAR images, which can effectively suppress the interference of scallop noise on images and is applicable to wide-swath cross-polarization SAR image products that do not provide scallop noise information or whose provided information is inaccurate.

[0007] Technical solution: The present invention provides a method for correcting scallop noise in wide-swath cross-polarization SAR images, comprising the following steps:

[0008] S1, acquire wide-swath dual-polarization SAR images containing co-polarization and cross-polarization, and after preprocessing, obtain co-polarization backscattering coefficient images and cross-polarization backscattering coefficient images with a spatial resolution of 1km.

[0009] S2, perform range-direction thermal noise correction on the cross-polarized backscattering coefficient image;

[0010] S3, using geophysical model functions to invert sea surface wind speed from the same polarization backscattering coefficient image, to obtain the wind speed field inverted from the same polarization image;

[0011] S4, based on the wind speed field retrieved from the same polarization image, the area with sea surface wind speed less than 5 m / s and wind speed spatial variation less than 1 m / s is extracted as a calm and uniform sea surface.

[0012] S5 uses a calm and uniform sea surface as the region of interest, divides the cross-polarized image within the region of interest into sub-cutting frames, and extracts the scallop noise of each sub-cutting frame using the lower envelope method.

[0013] S6. Establish a 4th-order Fourier series model of scallop noise for each sub-cutting area, use scallop noise and azimuth distance to fit the model parameters, solve the fitting coefficients, and thus determine the scallop noise model coefficients for each sub-cutting area.

[0014] S7 was used to verify the effectiveness of the cross-polarization image scallop noise extraction model.

[0015] Furthermore, in step S1, the acquired SAR image is radiometrically calibrated, land masked, and ship filtered out. Then, the preprocessed image is resampled to 1km to eliminate the interference of speckle noise on the image, resulting in a 1km spatial resolution image of co-polarized and cross-polarized backscattering coefficients.

[0016] Furthermore, in step S2, the formula for calculating the cross-polarized backscattering coefficient to remove product thermal noise is as follows:

[0017]

[0018]

[0019] in, It is the cross-polarized backscattering coefficient in dB for removing product thermal noise, σ° observation It is the cross-polarized backscattering coefficient in linear power form, η is the thermal noise calibration parameter provided by the imaging product, and A is the backscattering coefficient calibration factor; The product thermal noise is in linear power form.

[0020] Furthermore, in step S3, the sea surface wind speed is inverted using the same polarization backscattering coefficient image of the geophysical model function. The specific steps for obtaining the wind speed field inverted from the same polarization image are as follows:

[0021] S31, using external wind direction data as the external wind direction information of the same polarization mode function, and performing spatial interpolation to obtain an external wind direction layer with the same spatial resolution as the same polarization backscattering coefficient image.

[0022] S32 inputs the external wind direction layer, the same polarization backscattering coefficient image, and the radar incident angle information into the same polarization geophysical model function for inversion calculation to obtain a wind speed image with a spatial resolution of 1km.

[0023] Further, in step S4, based on the same polarization wind speed image, areas with wind speeds less than 5 m / s are extracted as calm sea surfaces, and the mean value of the calm sea surface is calculated; then, the deviation of each wind speed point within the calm sea surface from the mean value is calculated, and areas with a wind speed deviation of less than 1 m / s are taken as uniform sea surfaces. Through mask calculation, calm uniform sea surfaces with wind speeds less than 5 m / s and spatial variations of less than 1 m / s are extracted.

[0024] Furthermore, in step S5, the implementation steps for extracting the scallop noise of each sub-cutting amplitude using the lower envelope method are as follows:

[0025] S51, using a calm and uniform sea surface as a reference, the cross-polarization backscattering coefficient layer corresponding to the calm and uniform sea surface is divided into sub-spans of the wide-span image to obtain the backscattering coefficients of the calm and uniform sea surface in different sub-spans.

[0026] S52, the backscattering coefficient of a calm, uniform sea surface within different sub-areas is calculated by averaging the values ​​row by row, resulting in a curve showing the variation of the backscattering coefficient of the calm, uniform sea surface within different sub-areas with the azimuth direction. This curve is σ°. range_noise_correction The mean curve in the distance direction;

[0027] S53, using a preset distance as the step size, calculates the lower envelope of the backscattering coefficient of a calm, uniform sea surface within different sub-areas as a function of the azimuth direction. This lower envelope is then σ°. signal The mean curve in the distance direction.

[0028] S54, via σ° range_noise_correction The mean curve minus σ° signal The mean curve is used to obtain the scallop noise information for each sub-cutting amplitude.

[0029] Further, in step S6, for each sub-cutting amplitude, a fourth-order Fourier series model with respect to the azimuth distance is established based on the cross-polarization backscattering coefficients of each sub-cutting amplitude. Then, the coefficients of the fourth-order Fourier series model are fitted using the least squares method, resulting in the scallop noise extraction model for each sub-cutting amplitude as follows:

[0030] σ° scalloping =a0+a1*cos(x*w)+b1*sin(x*w)+a2*cos(2*x*w)+b2

[0031] *sin(2*x*w)+a3*cos(3*x*w)+b3*sin(3*x*w)+a4

[0032] *cos(4*x*w)+b4*sin(4*x*w)

[0033] Where, σ° scalloping denoted as scallop noise in linear power form simulated by the model; x represents the azimuth distance in km; a0, a1, b1, a2, b2, a3, b3, a4, b4, and w are the fitted coefficients.

[0034] Compared with the prior art, the significant advantages of this invention are as follows:

[0035] 1. This invention directly utilizes dual-polarization SAR image data to extract cross-polarization scallop noise without relying on ground observation data, thus effectively reducing observation costs and saving time and resources.

[0036] 2. Since there is basically no time difference between the co-polarized image and the cross-polarized image of dual-polarized data in terms of imaging time, this invention directly uses the calm and uniform sea surface extracted from the co-polarized image as the region of interest to extract cross-polarized scallop noise, which can reduce the error caused by the time difference of external reference data, thereby improving the accuracy and consistency of the data.

[0037] 3. This invention can automatically establish a scallop noise correction model for cross-polarization SAR images without relying on known scallop noise calibration information, thus achieving automated processing. It is applicable to cross-polarization SAR image products that do not provide scallop noise information or whose provided scallop noise information is inaccurate. Therefore, this invention has wider applicability and practicality. Attached Figure Description

[0038] Figure 1 This is a flowchart of the present invention;

[0039] Figure 2 This is a schematic diagram of the preprocessed Sentinel-1 interferometric wide-swath cross-polarization image;

[0040] Figure 3 This is a schematic diagram of the cross-polarization image after distance-directed thermal noise correction.

[0041] Figure 4 This is a schematic diagram of scallop noise extraction.

[0042] Figure 5 A schematic diagram illustrating scallop noise simulation and correction;

[0043] Figure 6 This is a schematic diagram of the cross-polarized image after azimuth scallop noise correction. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0045] This invention proposes a method for effectively suppressing scallop noise in wide-swath cross-polarization SAR imagery, resulting in clearer and more accurate image data and improving the quality and precision of image processing. Simultaneously, this provides a more reliable data foundation for a wide range of applications, such as environmental monitoring, geological exploration, and disaster management. Overall, this invention plays a significant role in promoting the development of wide-swath cross-polarization SAR imagery technology and further expanding its application areas.

[0046] This embodiment provides a method for correcting scallop noise in wide-swath cross-polarization SAR images. The specific process is as follows: Figure 1 As shown, it includes the following steps:

[0047] Step 1: Acquire wide-swath dual-polarization SAR images containing co-polarization and cross-polarization, and after preprocessing, obtain co-polarization and cross-polarization backscattering coefficient images with a spatial resolution of 1km.

[0048] Specifically, this embodiment uses interferometric wide-swath SAR images from the ESA's recently launched Sentinel-1 satellite as an example to acquire a large number of Sentinel-1 satellite interferometric wide-swath images with VV+VH or HH+HV polarization. After acquiring the SAR images, preprocessing such as radiometric calibration, land masking, and ship filtering is performed. Then, the preprocessed images are resampled to 1km to eliminate speckle noise interference, resulting in backscattering coefficient images with co-polarization and cross-polarization at 1km spatial resolution. The preprocessed cross-polarization backscattering coefficient image is shown below. Figure 2 As shown.

[0049] Step 2: Perform range-direction thermal noise correction on the cross-polarized backscattering coefficient image obtained in Step 1.

[0050] Specifically, the thermal noise of the product is calculated based on the thermal noise calculation model provided in the radar image product manual. Then, the product thermal noise is subtracted from the cross-polarization backscattering coefficient image obtained in step 1 to obtain the cross-polarization backscattering coefficient after removing range-direction thermal noise. Taking Sentinel-1 data product as an example, the formula for calculating the cross-polarization backscattering coefficient after removing product thermal noise is as follows:

[0051]

[0052]

[0053] in, It is the cross-polarized backscattering coefficient in dB for removing product thermal noise, σ° observation The cross-polarized backscattering coefficient is obtained in linear power form from step 1, where η is the thermal noise calibration parameter provided by the image product, and A is the backscattering coefficient calibration factor. For product thermal noise in linear power form, both η and A can be extracted from the image product's annotation file. The image of cross-polarized backscattering coefficients after range-directed thermal noise correction is shown below. Figure 2 As shown in the image, the residual scallop noise still significantly affects the image, appearing as alternating bright and dark stripes. Therefore, further correction of the scallop noise is needed.

[0054] Step 3: Use geophysical model functions to invert sea surface wind speed in the same polarization backscattering coefficient image obtained in Step 1 to obtain the wind speed field inverted from the same polarization image.

[0055] In this invention, external wind direction data is used as the external wind direction information for the same polarization model function, and spatial interpolation is performed to obtain an external wind direction layer with the same spatial resolution as the same polarization backscattering coefficient image in step 1. Next, the external wind direction layer, the same polarization backscattering coefficient image, and the radar incident angle information are input together into the same polarization geophysical model function, and then inversion calculations are performed to obtain a wind speed image with a spatial resolution of 1 km.

[0056] For C-band VV polarimetric SAR data, the C-band VV polarimetric geophysical model function CMOD5.n is used as the model function for wind field inversion. The CMOD5.n model is shown in the following equation:

[0057]

[0058] Where, σ° VV The backscattering coefficient of VV polarization radar. Let θ be the horizontal angle between the wind direction and the incident wind direction of the radar, v be the wind speed, θ be the incident angle of the radar, and A0, A1, A2 and A3 be functions of wind speed (v) and incident angle (θ).

[0059] For C-band HH polarimetric SAR data, the C-band HH polarimetric geophysical model function CMODH is used as the model function for wind field inversion. The CMODH model is shown in the following equation:

[0060]

[0061] Where, σ° HH The backscattering coefficient of the HH polarization radar. Let θ be the horizontal angle between the wind direction and the incident wind direction of the radar, v be the wind speed, θ be the incident angle of the radar, and B0, B1, and B2 be functions of wind speed (v) and incident angle (θ).

[0062] Step 4: Based on the wind speed field obtained from the same polarization image inversion in Step 3, the area with sea surface wind speed less than 5 m / s and wind speed spatial variation less than 1 m / s is extracted as a calm and uniform sea surface.

[0063] Specifically, based on the same polarization wind speed image obtained in step 3, areas with wind speeds less than 5 m / s are extracted as calm sea surfaces, and the mean value of the calm sea surface is calculated. Then, the deviation of each wind speed point within the calm sea surface from the mean value is calculated, and areas with a wind speed deviation of less than 1 m / s are taken as uniform sea surfaces. Through mask calculation, calm uniform sea surfaces with wind speeds less than 5 m / s and spatial variations of less than 1 m / s are extracted.

[0064] Step 5: Using the calm and uniform sea surface obtained in Step 4 as the region of interest, the cross-polarization image within the region of interest is divided into sub-cutting frames, and the scallop noise of each sub-cutting frame is extracted by the lower envelope method.

[0065] Even after step 2, range-direction thermal noise correction, the image still failed to effectively remove scallop noise. Therefore, the radar backscattering coefficient (σ°) after range-direction thermal noise correction... range_noise_correction ) contains the echo signal from the sea surface (σ°) signal ) and periodic scallop noise (σ° scalloping As shown in Formula 5.

[0066] σ° range_noise_correction =σ° signal +σ° scalloping (5) Specifically, in order to obtain σ° range_noise_correction The periodic scallop noise was extracted, and the detailed steps are as follows:

[0067] Step 51: Using the calm and uniform sea surface obtained in Step 4 as a reference, divide the cross-polarization backscattering coefficient layer corresponding to the calm and uniform sea surface into sub-spans of the wide-span image to obtain the backscattering coefficients of the calm and uniform sea surface in different sub-spans.

[0068] Step 52: Calculate the mean value of the backscattering coefficient of the calm, uniform sea surface within different sub-areas, row by row, to obtain the curve of the backscattering coefficient of the calm, uniform sea surface within different sub-areas as a function of the azimuth direction. This curve is σ°. range_noise_correction The mean curve in the distance direction.

[0069] Step 53: In this embodiment, using a step size of 10 km, the lower envelope of the backscattering coefficient of a calm, uniform sea surface within different sub-cutting widths as a function of the azimuth direction is calculated. This envelope is σ°. signal The mean curve in the distance direction.

[0070] Step 54, via σ° range_noise_correction The mean curve minus σ° signal By analyzing the mean curve, the scallop noise information for each sub-cutting amplitude can be obtained.

[0071] Figure 4 The results demonstrate the effectiveness of scallop noise extraction. It can be seen that scallop noise information can be extracted well from images on calm, uniform sea surfaces. However, on sea surfaces with high wind speeds, the extracted scallop noise becomes chaotic and disordered. Therefore, this embodiment utilizes the scallop noise information extracted well from images on calm, uniform sea surfaces as modeling data for the scallop noise model.

[0072] Step 6: Establish a 4th-order Fourier series model of scallop noise for each sub-cutting area. Use the scallop noise and azimuth distance extracted in Step 5 to perform model parameter fitting calculation, solve for the fitting coefficients, and thus determine the scallop noise model coefficients for each sub-cutting area.

[0073] Specifically, the fitting parameters of the Fourier series model are obtained by fitting the scallop noise and azimuth distance within each sub-swastika. Taking the Sentinel-1 interferometric wide-swath image as an example, which is composed of three different sub-swastikas, a fourth-order Fourier series model of the cross-polarization backscattering coefficient with respect to the azimuth distance based on different sub-swastikas is established. Then, the coefficients of the fourth-order Fourier series model are fitted using the least squares method, resulting in the scallop noise extraction model established based on Sentinel-1 interferometric wide-swath SAR data as follows:

[0074] σ° scalloping =a0+a1*cos(x*w)+b1*sin(x*w)+a2*cos(2*x*w)+b2*sin(2*x*w)

[0075] +a3*cos(3*x*w)+b3*sin(3*x*w)+a4*cos(4*x*w)+b4

[0076] *sin(4*x*w) (6)

[0077] Where, σ° scalloping denoted as scallop noise in linear power form simulated by the model; x represents the azimuth distance in km; a0, a1, b1, a2, b2, a3, b3, a4, b4, and w are the fitted coefficients.

[0078] Step 7: Verify the effectiveness of the cross-polarization image scallop noise extraction model.

[0079] The original cross-polarized image and the cross-polarized image corrected by the scallop noise correction method of the present invention are plotted to evaluate the effect of the scallop noise correction method of the present invention.

[0080] Specifically, the sea surface backscattering signal σ° is obtained by subtracting the scallop noise simulated by the scallop noise model obtained in this invention from the cross-polarized backscattering coefficient image obtained in step 2 after range-direction thermal noise correction. signal Then draw σ° signal The two-dimensional image is compared and analyzed with the original image to evaluate the scallop noise correction effect of the present invention. The specific formula for scallop noise correction is as follows:

[0081] σ° signal =σ° range_noise_correction -σ° scalloping_simulated (7)

[0082]

[0083] Figure 5 This demonstrates a linear power form of the scallop noise model and the effect of using the scallop noise model for scallop noise correction in cross-polarization images. Figure 5 As can be seen, after the cross-polarization backscattering coefficient is corrected for scallop noise, the periodic scallop noise in the azimuth direction can be well suppressed.

[0084] To more intuitively demonstrate the effect of scallop noise correction on the image, Figure 6 This image shows the cross-polarization backscattering coefficients in dB form after scallop noise correction. From Figure 6 As can be seen, after scallop noise correction, the periodic scallop noise stripes of the image can be significantly eliminated, and the image maintains good radiation uniformity, indicating that the scallop noise correction method for cross-polarized images proposed in this invention is feasible.

Claims

1. A method for correcting scallop noise in wide-swath cross-polarization SAR images, characterized in that, The steps include the following: S1, acquire wide-swath dual-polarization SAR images containing co-polarization and cross-polarization, and after preprocessing, obtain co-polarization backscattering coefficient images and cross-polarization backscattering coefficient images with a spatial resolution of 1km. S2, perform range-direction thermal noise correction on the cross-polarized backscattering coefficient image; S3, using geophysical model functions to invert sea surface wind speed from the same polarization backscattering coefficient image, to obtain the wind speed field inverted from the same polarization image; S4, based on the wind speed field retrieved from the same polarization image, the area with sea surface wind speed less than 5 m / s and wind speed spatial variation less than 1 m / s is extracted as a calm and uniform sea surface. S5 uses a calm and uniform sea surface as the region of interest, divides the cross-polarized image within the region of interest into sub-cutting frames, and extracts the scallop noise of each sub-cutting frame using the lower envelope method. S6. Establish a 4th-order Fourier series model of scallop noise for each sub-cutting area, use scallop noise and azimuth distance to fit the model parameters, solve the fitting coefficients, and thus determine the scallop noise model coefficients for each sub-cutting area. S7 was used to verify the effectiveness of the cross-polarization image scallop noise extraction model.

2. The method for correcting scallop noise in wide-swath cross-polarization SAR images according to claim 1, characterized in that, In step S1, the acquired SAR image is radiometrically calibrated, land masked, and ship filtered. Then, the preprocessed image is resampled to 1km to eliminate speckle noise interference and obtain a 1km spatial resolution image of co-polarized and cross-polarized backscattering coefficients.

3. The method for correcting scallop noise in wide-swath cross-polarization SAR images according to claim 1, characterized in that, In step S2, the formula for calculating the cross-polarized backscattering coefficient to remove product thermal noise is as follows: ， ， in, It is the cross-polarized backscattering coefficient in dB for removing product thermal noise. It is the cross-polarized backscattering coefficient in linear power form. Thermal noise calibration parameters provided for imaging products, where A is the backscattering coefficient calibration factor; The product thermal noise is in linear power form.

4. The method for correcting scallop noise in wide-swath cross-polarization SAR images according to claim 1, characterized in that, In step S3, the sea surface wind speed is inverted using the same polarization backscattering coefficient image of the geophysical model function. The specific steps for obtaining the wind speed field inverted from the same polarization image are as follows: S31, using external wind direction data as the external wind direction information of the same polarization mode function, and performing spatial interpolation to obtain an external wind direction layer with the same spatial resolution as the same polarization backscattering coefficient image. S32 inputs the external wind direction layer, the same polarization backscattering coefficient image, and the radar incident angle information into the same polarization geophysical model function for inversion calculation to obtain a wind speed image with a spatial resolution of 1km.

5. The method for correcting scallop noise in wide-swath cross-polarization SAR images according to claim 1, characterized in that, In step S4, based on the same polarization wind speed image, areas with wind speeds less than 5 m / s are extracted as calm sea surfaces, and the mean value of the calm sea surface is calculated. Then, the deviation of each wind speed point within the calm sea surface from the mean value is calculated, and areas with a wind speed deviation of less than 1 m / s are taken as uniform sea surfaces. Through mask calculation, calm uniform sea surfaces with wind speeds less than 5 m / s and spatial variations of less than 1 m / s are extracted.

6. The method for correcting scallop noise in wide-swath cross-polarization SAR images according to claim 1, characterized in that, In step S5, the steps for extracting the scallop noise of each sub-cutting amplitude using the lower envelope method are as follows: S51, using a calm and uniform sea surface as a reference, the cross-polarization backscattering coefficient layer corresponding to the calm and uniform sea surface is divided into sub-spans of the wide-span image to obtain the backscattering coefficients of the calm and uniform sea surface in different sub-spans. S52, the backscattering coefficient of a calm, uniform sea surface within different sub-areas is calculated by averaging the values ​​row by row, resulting in curves showing the variation of the backscattering coefficient of a calm, uniform sea surface within different sub-areas with the azimuth direction. These curves are... In the mean curve of the distance direction, This represents the cross-polarization backscattering coefficient used to remove thermal noise from a product. S53, using a preset distance as the step size, calculates the lower envelope of the backscattering coefficient of a calm, uniform sea surface within different sub-cutting widths as a function of the azimuth direction. This lower envelope is then... In the mean curve of the distance direction, This represents the backscattering coefficient of the sea surface; S54, via The mean curve minus The mean curve is used to obtain the scallop noise information for each sub-cutting amplitude.

7. The method for correcting scallop noise in wide-swath cross-polarization SAR images according to claim 1, characterized in that, In step S6, for each sub-cutting amplitude, a fourth-order Fourier series model with respect to the azimuth distance is established based on the cross-polarization backscattering coefficients of each sub-cutting amplitude. Then, the coefficients of the fourth-order Fourier series model are fitted using the least squares method, resulting in the scallop noise extraction model for each sub-cutting amplitude: ， in, denoted as scallop noise in linear power form simulated by the model; x represents the azimuth distance in km; a0, a1, b1, a2, b2, a3, b3, a4, b4, and w are the fitted coefficients.

Images