Nonlinear iteration radar image data reconstruction method and system based on MART

Abstract

The invention provides a non-linear iteration radar image data reconstruction method and system based on MART. The method comprises the following steps: performing high-resolution grid segmentation on a measured value of a radar observation area; according to a measured value grid segmentation condition, defining a measured value Z, a distribution parameter S to be solved and a weighting matrix H, and establishing a system equation set; based on an MART method, determining a non-linearly updated correction factor; and an initial value S0 is reasonably selected, the precision of an iteration result is determined, and solving is completed according to an iteration equation. The predicted value is made close to the measured value by comparing each measured value with a predicted value calculated from the current estimated image and then applying an optimized non-linear correction factor to each pixel covered by the measurement. Subsequent measurements further change pixel values. In multiple iterations, the correction factor ideally converges to unit 1, and all forward estimates match the measured values.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite remote sensing image processing, and in particular to a MART-based nonlinear iterative radar image data reconstruction method and system. Background Art

[0002] As a non-imaging active microwave radar sensor, radar scatterometers possess unique and irreplaceable advantages in the field of remote sensing. They obtain surface microwave backscatter coefficients through multi-angle, multi-polarization observation modes and employ radar scatterometer image reconstruction (Scatterometer Image Reconstruction, SIR) to quantitatively invert surface and atmospheric parameters. This technology has become a core component of modern remote sensing data processing systems. Compared to traditional optical remote sensing, SIR technology's breakthrough lies in its ability to fuse multi-source observation data through mathematical and physical models, reconstructing sparse low-spatial-resolution observations into high-resolution parameter distribution maps. This technology is particularly suitable for spatial reconstruction of geophysical parameters such as sea surface wind field inversion and soil moisture monitoring. Its technical principle is based on the high temporal resolution of radar scatterometers and the spatiotemporal correlation between the scattering characteristics of ground objects. An optimal estimation algorithm is used to establish a mapping between observation data and surface parameters.

[0003] The current spaceborne radar scatterometer system uses a side-looking radar working mechanism, which transmits microwave pulses and receives the backscattered power from the surface, and obtains the normalized radar cross section σ by solving the radar equation. 0 . This all-day and all-weather observation capability gives it the advantage of global coverage. Traditional radar image data reconstruction technologies mainly include the following categories. The first is the algebraic reconstruction technique (ART), which introduces a relaxation factor and iteratively adjusts the system matrix value to gradually minimize the error between the observed data and the model prediction. This method is simple and intuitive and suitable for sparse data. However, it will produce inversion errors when dealing with nonlinear relationships; filtered back projection (FBP), whose main idea is to back-project the observed data into the image domain along different projection directions and suppress artifacts through filtering. It is often used in medical CT imaging and is not suitable for sparse and noisy data; the Bayesian method, by introducing prior information (such as wind speed smoothness), optimizes the inversion results through the posterior distribution, but this method is extremely dependent on the accuracy of the prior model; the empirical model method, which directly inverts parameters based on empirical relationships (such as the geophysical model function CMOD), is simple to calculate but depends on the accuracy of the physical model, and is unable to invert scenes not covered by the model. In addition, the model parameters need to be adjusted frequently, and the maintenance cost is high.

[0004] Patent document CN102367890B discloses a scatterometer image reconstruction method based on algebraic reconstruction technology. It uses algebraic reconstruction technology (ART) to gradually minimize the error between observed data and model predictions by iteratively adjusting the system matrix values. This method has limited tolerance to noise and large inversion errors.

[0005] Patent document CN104567890B discloses a scatterometer image reconstruction method based on the Bayesian method, which introduces prior information and optimizes the inversion result through the posterior distribution. The result depends on the accuracy of the prior model, and the effect is poor when the model is inaccurate.

[0006] Patent document CN105678901B discloses a scatterometer image reconstruction method based on an empirical model. It directly inverts parameters based on empirical relationships. The calculation is simple and depends on the accuracy of the physical model. It is unable to invert scenes not covered by the model.

[0007] Patent document CN106789012B discloses a scatterometer image reconstruction method based on multi-scale analysis. The method uses multi-scale analysis technology to improve accuracy by reconstructing images with different resolutions. However, the method has high computational complexity and is not suitable for scenarios with high real-time requirements.

[0008] The traditional MART (Multiplicative Algebraic Reconstruction Technique) algorithm can ideally converge the equations as the number of iterations increases. However, due to the introduction of high noise disturbances in actual measurements, the iterative results may lose convergence or obtain unsatisfactory solutions. Summary of the Invention

[0009] In view of the defects in the prior art, the object of the present invention is to provide a nonlinear iterative radar image data reconstruction method and system based on MART.

[0010] The nonlinear iterative radar image data reconstruction method based on MART provided by the present invention includes:

[0011] Step S1: Divide the earth's surface into layers with a resolution of S c ×S a The radar ground measurement footprint is projected onto the linear grid, where the subscript c represents the scanning direction and the subscript a represents the flight direction;

[0012] Step S2: The grids σ covered by the footprint 0 The weighted average of is taken as the radar measurement value;

[0013] Step S3: Select a c ×N a The area of ​​the grid cells is collected, and all radar measurements z are collected for which the footprint boundary is completely contained in the area k, where k is the number of measurements, and the measured value is defined as 0 The matrix equation is:

[0014] Z=HS

[0015] Where Z is the measurement value z k N-dimensional vector; H is an N×M matrix containing h(c,a,k), M=N c ×N a ; S is a σ 0 (c, a, k) are M-dimensional vectors arranged in order;

[0016] Convert the problem into solving the S matrix in the matrix equation;

[0017] Step S4: Select an initial value image S after solving the S matrix 0 , in the kth iteration, for image S k Each pixel to update.

[0018] Preferably, the radar measurement values ​​and the respective grids σ 0 The relationship between the values ​​is expressed as:

[0019]

[0020] Among them, L k 、R k 、B k and T k is the footprint boundary of the kth measurement; h(c,a,k) is the weight function of the (c,a)th grid resolution unit, 0≤h(c,a,k)≤1; σ 0 (c,a,k) is the σ of the (c,a)th grid resolution unit 0 value.

[0021] Preferably, the weight function h(c,a,k) is calculated based on the intersection area of ​​the footprint and the grid cell. For grid cells completely covered by the footprint, the weight function value is 1; for partially covered grid cells, the weight function value is determined based on the intersection area ratio.

[0022] Preferably, the matrix equation is solved by an iterative optimization algorithm, and in each iteration, each pixel of the image is nonlinearly updated to gradually approximate the measured value;

[0023] For image S k Each pixel The rules for updating are as follows:

[0024]

[0025] in:

[0026]

[0027] in, is the updated pixel, is the forward estimate; p i is the number of measurements covering the pixel i, q j is the number of pixels covered by the jth measurement; l∈M; j∈N; h ji is the weight value of pixel i in the jth measurement; It is the intermediate parameter for iterating the image S; It is an intermediate variable of the iterative strategy, which indicates the degree of deviation between the forward estimate and the measured value after being controlled by the nonlinear weighting factor w; j is the grids σ covered by the footprint obtained by the jth measurement 0 The weighted average of is the image S obtained at the kth iteration k The lth element of h li Indicates h ji The expression for summing the subscript j, the p obtained after summing i represents the number of measurements of the footprint covering the i-th pixel; h jl Indicates h ji The expression for summing the subscript i, and the q obtained after summing j represents the number of pixels covered by the jth measurement footprint; w is a nonlinear weighting factor that limits the update step size when the deviation between the forward estimate and the measured value exceeds a preset range, thereby improving noise tolerance.

[0028] Preferably, the method further includes post-processing the reconstructed image, including filtering and smoothing operations, to further improve the image quality.

[0029] The nonlinear iterative radar image data reconstruction system based on MART provided by the present invention includes:

[0030] Module M1: Divide the Earth's surface into layers with a resolution of S c ×S a The radar ground measurement footprint is projected onto the linear grid, where the subscript c represents the scanning direction and the subscript a represents the flight direction;

[0031] Module M2: Each grid covered by the footprint σ 0 The weighted average of is taken as the radar measurement value;

[0032] Module M3: Select a program containing N c ×N a The area of ​​the grid cells is collected, and all radar measurements z are collected for which the footprint boundary is completely contained in the areak , where k is the number of measurements, and the measured value is defined as 0 The matrix equation is:

[0033] Z=HS

[0034] Where Z is the measurement value z k N-dimensional vector; H is an N×M matrix containing h(c,a,k), M=N c ×N a ; S is a σ 0 (c, a, k) are M-dimensional vectors arranged in sequence;

[0035] Convert the problem into solving the S matrix in the matrix equation;

[0036] Module M4: Select an initial value image S after solving the S matrix 0 , in the kth iteration, for image S k Each pixel to update.

[0037] Preferably, the radar measurement values ​​and the respective grids σ 0 The relationship between the values ​​is expressed as:

[0038]

[0039] Among them, L k 、R k 、B k and T k is the footprint boundary of the kth measurement; h(c,a,k) is the weight function of the (c,a)th grid resolution unit, 0≤h(c,a,k)≤1; σ 0 (c,a,k) is the σ of the (c,a)th grid resolution unit 0 value.

[0040] Preferably, the weight function h(c,a,k) is calculated based on the intersection area of ​​the footprint and the grid cell. For grid cells completely covered by the footprint, the weight function value is 1; for partially covered grid cells, the weight function value is determined based on the intersection area ratio.

[0041] Preferably, the matrix equation is solved by an iterative optimization algorithm, and in each iteration, each pixel of the image is nonlinearly updated to gradually approximate the measured value;

[0042] For image S k Each pixel The rules for updating are as follows:

[0043]

[0044] in:

[0045]

[0046] in, is the updated pixel, is the forward estimate; p i is the number of measurements covering the pixel i, q j is the number of pixels covered by the jth measurement; l∈M; j∈N; h ji is the weight value of pixel i in the jth measurement; It is the intermediate parameter for iterating the image S; It is an intermediate variable of the iterative strategy, which indicates the degree of deviation between the forward estimate and the measured value after being controlled by the nonlinear weighting factor w; j is the grids σ covered by the footprint obtained by the jth measurement 0 The weighted average of is the image S obtained at the kth iteration k The lth element of h li Indicates h ji The expression for summing the subscript j, the p obtained after summing i represents the number of measurements of the footprint covering the i-th pixel; h jl Indicates h ji The expression for summing the subscript i, and the q obtained after summing j represents the number of pixels covered by the jth measurement footprint; w is a nonlinear weighting factor that limits the update step size when the deviation between the forward estimate and the measured value exceeds a preset range, thereby improving noise tolerance.

[0047] Preferably, the method further includes post-processing the reconstructed image, including filtering and smoothing operations, to further improve the image quality.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] (1) This invention proposes a nonlinear iterative scatterometer image data reconstruction method based on MART, which can improve the noise tolerance of the image and the inversion accuracy. It plays a decisive role in the use efficiency of spaceborne scatterometers. The key technologies solved and the technical platform established not only fill the technical gap, but also support the high-precision inversion of spaceborne scatterometer images.

[0050] (2) The present invention performs nonlinear iterative calculation on the S vector, limiting the iterative step size of the large deviation between the forward estimate and the measured value. Compared with the traditional MART algorithm, it can effectively improve the noise tolerance, effectively reduce the impact of noise, and help convergence. The present invention also performs post-processing on the reconstructed image, including filtering, smoothing and other operations, to further improve the image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0052] Figure 1 This is a processing flow chart of the nonlinear iterative radar image data reconstruction method based on MART;

[0053] Figure 2 Schematic diagram of the radar footprint projection method on the high-resolution grid. DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0055] Example

[0056] See also Figure 1 The present invention provides a nonlinear iterative radar image data reconstruction method based on MART, comprising the following steps:

[0057] Step S1: Divide the earth's surface into c ×S a The radar ground measurement footprint is projected onto this grid, where the subscript c represents the scanning direction and the subscript a represents the flight direction.

[0058] Specifically, if Figure 2 Shown is how the radar footprint is projected onto a high-resolution grid.

[0059] Step S2: radar measurement value z k Represented as the grids σ covered by the footprint 0 The weighted average of is expressed as:

[0060]

[0061] Where k is the number of measurements, L k 、R k 、B k and T k is the footprint boundary of the kth measurement; h(c,a,k) is the weight function of the (c,a)th grid resolution unit, 0≤h(c,a,k)≤1; σ 0 (c,a,k) is the σ of the (c,a)th grid resolution unit0 value.

[0062] Step S3: Select a c ×N a The area of ​​the grid cells is collected, and all radar measurements z are collected for which the footprint boundary is completely contained in the area k , define the measured value and σ 0 The matrix equation is:

[0063] Z=HS

[0064] Where Z is the measurement value z k N-dimensional vector; H is an N×M matrix containing h(c,a,k), M=N c ×N a ; S is a σ 0 (c, a, k) is an M-dimensional vector arranged in sequence.

[0065] Specifically, the weight function h(c,a,k) is calculated based on the intersection area of ​​the footprint and the grid cell. For the grid cell completely covered by the footprint, the weight function value is 1. For the grid cell partially covered, the weight function value is determined according to the intersection area ratio. The resulting H matrix will be very sparse. The arrangement of the elements in S is not unique, and you can use, for example, s n =σ 0 (c,a,k),n=c+aN c This is a simple arrangement.

[0066] Step S4: Select an initial value image S 0 (usually a uniform constant), in the kth iteration, for the image S k Each pixel To update:

[0067]

[0068] in:

[0069]

[0070] in, is the updated pixel, is the forward estimate; p i is the number of measurements covering the pixel i, q j is the number of pixels covered by the jth measurement; l∈M; j∈N; h ji is the weight value of pixel i in the jth measurement; It is the intermediate parameter for iterating the image S; It is an intermediate variable of the iterative strategy, which indicates the degree of deviation between the forward estimate and the measured value after being controlled by the nonlinear weighting factor w; j is the grids σ covered by the footprint obtained by the jth measurement 0 The weighted average of is the image S obtained at the kth iteration k The lth element of h li Indicates h ji The expression for summing the subscript j, the p obtained after summing i represents the number of measurements of the footprint covering the i-th pixel; h jl Indicates h ji The expression for summing the subscript i, and the q obtained after summing j represents the number of pixels covered by the jth measurement footprint; w is a nonlinear weighting factor that limits the update step size when the deviation between the forward estimate and the measured value exceeds a preset range, thereby improving noise tolerance.

[0071] Where w is an adjustable parameter. For radar data, w = 1 / 2 can provide better reconstruction results. When w = 1, it is unweighted MART, and when w ≠ 1, it is called weighted MART.

[0072] Specifically, to improve noise tolerance and convergence, SIR uses an update scheme that nonlinearly weights the measured values ​​and forward estimates. This nonlinear update calculation limits the update step size for large deviations between the forward estimate and the measured values, reducing the impact of noise and facilitating convergence. The SIR algorithm is an iterative algorithm with nonlinear updates.

[0073] If we follow the traditional MART algorithm, it should be rewritten as:

[0074]

[0075] The system of equations can theoretically converge as the number of iterations increases; however, due to the high noise level in the measurements, the MART algorithm may not converge or may result in an unsatisfactory solution.

[0076] Example 2

[0077] The present invention also provides a nonlinear iterative radar image data reconstruction system based on MART, comprising:

[0078] Module M1: Divide the Earth's surface into layers with a resolution of S c ×S a The radar ground measurement footprint is projected onto the linear grid, where the subscript c represents the scanning direction and the subscript a represents the flight direction;

[0079] Module M2: Each grid covered by the footprint σ0 The weighted average of is taken as the radar measurement value;

[0080] Module M3: Select a program containing N c ×N a The area of ​​the grid cells is collected, and all radar measurements z are collected for which the footprint boundary is completely contained in the area k , where k is the number of measurements, and the measured value is defined as 0 The matrix equation is:

[0081] Z=HS

[0082] Where Z is the measurement value z k N-dimensional vector; H is an N×M matrix containing h(c,a,k), M=N c ×N a ; S is a σ 0 (c, a, k) are M-dimensional vectors arranged in sequence;

[0083] Convert the problem into solving the S matrix in the matrix equation;

[0084] Module M4: Select an initial value image S after solving the S matrix 0 , in the kth iteration, for image S k Each pixel to update.

[0085] Radar measurements and individual grid σ 0 The relationship between the values ​​is expressed as:

[0086]

[0087] Among them, L k 、R k 、B k and T k is the footprint boundary of the kth measurement; h(c,a,k) is the weight function of the (c,a)th grid resolution unit, 0≤h(c,a,k)≤1; σ 0 (c,a,k) is the σ of the (c,a)th grid resolution unit 0 value.

[0088] The weight function h(c,a,k) is calculated based on the intersection area between the footprint and the grid cell. For grid cells completely covered by the footprint, the weight function value is 1; for grid cells partially covered, the weight function value is determined according to the ratio of the intersection area.

[0089] The matrix equation is solved by an iterative optimization algorithm. In each iteration, each pixel of the image is updated nonlinearly to gradually approach the measured value.

[0090] For image S k Each pixel The rules for updating are as follows:

[0091]

[0092] in:

[0093]

[0094] in, is the updated pixel, is the forward estimate; p i is the number of measurements covering the pixel i, q j is the number of pixels covered by the jth measurement; l∈M; j∈N; h ji is the weight value of pixel i in the jth measurement; It is the intermediate parameter for iterating the image S; It is an intermediate variable of the iterative strategy, which indicates the degree of deviation between the forward estimate and the measured value after being controlled by the nonlinear weighting factor w; j is the grids σ covered by the footprint obtained by the jth measurement 0 The weighted average of is the image S obtained at the kth iteration k The lth element of h li Indicates h ji The expression for summing the subscript j, the p obtained after summing i represents the number of measurements of the footprint covering the i-th pixel; h jl Indicates h ji The expression for summing the subscript i, and the q obtained after summing j represents the number of pixels covered by the jth measurement footprint; w is a nonlinear weighting factor that limits the update step size when the deviation between the forward estimate and the measured value exceeds a preset range, thereby improving noise tolerance.

[0095] It also includes post-processing of the reconstructed image, including filtering and smoothing operations, to further improve the image quality.

[0096] Those skilled in the art will appreciate that, in addition to implementing the system, device, and various modules provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like by logically programming the method steps. Therefore, the system, device, and various modules provided by the present invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; the modules for implementing various functions can also be considered both software programs for implementing the method and structures within the hardware component.

[0097] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A nonlinear iterative radar image data reconstruction method based on MART, characterized in that: include: Step S1: Divide the earth's surface into layers with a resolution of S c ×S a The radar ground measurement footprint is projected onto the linear grid, where the subscript c represents the scanning direction and the subscript a represents the flight direction; Step S2: The grids σ covered by the footprint 0 The weighted average of is taken as the radar measurement value; Step S3: Select a c ×N a The area of ​​the grid cells is collected, and all radar measurements z are collected for which the footprint boundary is completely contained in the area k , where k is the number of measurements, and the measured value is defined as 0 The matrix equation is: Z=HS Where Z is the measurement value z k N-dimensional vector; H is an N×M matrix containing h(c,a,k), M=N c ×N a ; S is a σ 0 (c, a, k) are M-dimensional vectors arranged in order; Convert the problem into solving the S matrix in the matrix equation; Step S4: Select an initial value image S after solving the S matrix 0 , in the kth iteration, for image S k Each pixel to update.

2. The MART-based nonlinear iterative radar image data reconstruction method according to claim 1, characterized in that: Radar measurements and individual grid σ 0 The relationship between the values ​​is expressed as: Among them, L k 、R k 、B k and T k is the footprint boundary of the kth measurement; h(c,a,k) is the weight function of the (c,a)th grid resolution unit, 0≤h(c,a,k)≤1; σ 0 (c,a,k) is the σ of the (c,a)th grid resolution unit 0 value.

3. The MART-based nonlinear iterative radar image data reconstruction method according to claim 2, characterized in that: The weight function h(c,a,k) is calculated based on the intersection area between the footprint and the grid cell. For grid cells completely covered by the footprint, the weight function value is 1; for grid cells partially covered, the weight function value is determined according to the ratio of the intersection area.

4. The MART-based nonlinear iterative radar image data reconstruction method according to claim 3, characterized in that: The matrix equation is solved by an iterative optimization algorithm. In each iteration, each pixel of the image is updated nonlinearly to gradually approach the measured value. For image S k Each pixel The rules for updating are as follows: in: in, is the updated pixel, is the forward estimate; p i is the number of measurements covering the pixel i, q j is the number of pixels covered by the jth measurement; l∈M; j∈N; h ji is the weight value of pixel i in the jth measurement; It is the intermediate parameter for iterating the image S; It is an intermediate variable of the iterative strategy, which indicates the degree of deviation between the forward estimate and the measured value after being controlled by the nonlinear weighting factor w; j is the grids σ covered by the footprint obtained by the jth measurement 0 The weighted average of is the image S obtained at the kth iteration k The lth element of h li Indicates h ji The expression for summing the subscript j, the p obtained after summing i represents the number of measurements of the footprint covering the i-th pixel; h jl Indicates h ji The expression for summing the subscript i, and the q obtained after summing j represents the number of pixels covered by the jth measurement footprint; w is a nonlinear weighting factor that limits the update step size when the deviation between the forward estimate and the measured value exceeds a preset range, thereby improving noise tolerance.

5. The MART-based nonlinear iterative radar image data reconstruction method according to claim 1, characterized in that: It also includes post-processing of the reconstructed image, including filtering and smoothing operations, to further improve the image quality.

6. A nonlinear iterative radar image data reconstruction system based on MART, characterized in that: include: Module M1: Divide the Earth's surface into layers with a resolution of S c ×S a The radar ground measurement footprint is projected onto the linear grid, where the subscript c represents the scanning direction and the subscript a represents the flight direction; Module M2: Each grid covered by the footprint σ 0 The weighted average of is taken as the radar measurement value; Module M3: Select a program containing N c ×N a The area of ​​the grid cells is collected, and all radar measurements z are collected for which the footprint boundary is completely contained in the area k , where k is the number of measurements, and the measured value is defined as 0 The matrix equation is: Z=HS Where Z is the measurement value z k N-dimensional vector; H is an N×M matrix containing h(c,a,k), M=N c ×N a ; S is a σ 0 (c, a, k) are M-dimensional vectors arranged in sequence; Convert the problem into solving the S matrix in the matrix equation; Module M4: Select an initial value image S after solving the S matrix 0 , in the kth iteration, for image S k Each pixel to update.

7. The MART-based nonlinear iterative radar image data reconstruction system according to claim 6, characterized in that: Radar measurements and individual grid σ 0 The relationship between the values ​​is expressed as: Among them, L k 、R k 、B k and T k is the footprint boundary of the kth measurement; h(c,a,k) is the weight function of the (c,a)th grid resolution unit, 0≤h(c,a,k)≤1; σ 0 (c,a,k) is the σ of the (c,a)th grid resolution unit 0 value.

8. The MART-based nonlinear iterative radar image data reconstruction system according to claim 7, characterized in that: The weight function h(c,a,k) is calculated based on the intersection area between the footprint and the grid cell. For grid cells completely covered by the footprint, the weight function value is 1; for grid cells partially covered, the weight function value is determined according to the ratio of the intersection area.

9. The MART-based nonlinear iterative radar image data reconstruction system according to claim 8, characterized in that: The matrix equation is solved by an iterative optimization algorithm. In each iteration, each pixel of the image is updated nonlinearly to gradually approach the measured value. For image S k Each pixel The rules for updating are as follows: in: in, is the updated pixel, is the forward estimate; p i is the number of measurements covering the pixel i, q j is the number of pixels covered by the jth measurement; l∈M; j∈N; h ji is the weight value of pixel i in the jth measurement; It is the intermediate parameter for iterating the image S; It is an intermediate variable of the iterative strategy, which indicates the degree of deviation between the forward estimate and the measured value after being controlled by the nonlinear weighting factor w; j is the grids σ covered by the footprint obtained by the jth measurement 0 The weighted average of is the image S obtained at the kth iteration k The lth element of h li Indicates h ji The expression for summing the subscript j, the p obtained after summing i represents the number of measurements of the footprint covering the i-th pixel; h jl Indicates h ji The expression for summing the subscript i, and the q obtained after summing j represents the number of pixels covered by the jth measurement footprint; w is a nonlinear weighting factor that limits the update step size when the deviation between the forward estimate and the measured value exceeds a preset range, thereby improving noise tolerance.

10. The MART-based nonlinear iterative radar image data reconstruction system according to claim 6, characterized in that: It also includes post-processing of the reconstructed image, including filtering and smoothing operations, to further improve the image quality.

Images