ADMM-based SAR imaging low-cost optimization method

Abstract

The invention discloses an SAR imaging low-cost optimization method based on ADMM, and the method comprises the steps: considering two radar motion dimensions and local linear features at the same time, building a radar imaging defocusing fractional optimization model under the inhibition of non-uniform sampling, and enabling the constraint conditions to comprise an array element constant energy constraint and an array element peak value weight constraint; separating the non-convex constraint set by using an ADMM algorithm, and solving a radar imaging defocusing fraction optimization model under the suppression of non-uniform sampling by means of unitary transformation and auxiliary variables to obtain an optimized radar sampling position and a complex weight; the dependence of a model effect on parameter adjustment is reduced by establishing a fractional optimization model; by means of local linear feature modeling and non-convex problem processing, a heuristic algorithm is prevented from being used, and the convergence performance of the algorithm is ensured; the non-convex constraint set is separated to solve the complex non-convex objective function under the non-convex constraint, the model variable value is iteratively updated by using the matrix unitary transformation and the characteristics of the matrix, the defocusing problem in the non-uniform sampling imaging process is solved, and the number of sampling positions is reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a low-cost optimization method for SAR imaging based on ADMM. Background Art

[0002] The Range Migration Algorithm (RMA) is a classic SAR imaging algorithm, especially suitable for systems in planar scanning mode. It achieves target imaging by performing a two-dimensional Fourier transform on the target's echo signal and mapping the time domain data to the range-azimuth plane. The biggest advantage of the RMA algorithm is that it efficiently handles the range migration problem and can quickly restore the target image. A key assumption of this algorithm is that the spatial sampling during the platform movement must reach the Nyquist sampling rate to avoid the aliasing effect. In practical applications, the radar platform needs to perform multiple spatial sampling of the target area during the scanning process, and the reduction of the sampling interval usually means an improvement in imaging quality. However, a higher sampling frequency will significantly increase the system's hardware cost, data storage and processing burden, especially for large-area three-dimensional imaging tasks, the burden of algorithm implementation is relatively heavy.

[0003] In recent years, in order to deal with the resource consumption problem caused by the high sampling frequency in traditional near-field RMA imaging, the commonly used method is undersampling, that is, deliberately reducing the sampling rate during the sampling process so that the sampling point is lower than the Nyquist sampling rate. Although undersampling technology can effectively reduce the collected data, it needs to utilize the prior information or sparsity of the target area and compensate for the distortion caused by insufficient sampling rate by designing a more complex and accurate reconstruction algorithm. In order to solve the distortion problem of the undersampling scheme, a non-uniform sampling scheme was proposed, which captures the main information of the target area through irregular sampling positions. Since it helps to destroy the periodic structure in the signal, it avoids the aliasing problem. Compared with uniform undersampling technology, non-uniform sampling technology may cause a decrease in resolution in some areas while reducing the amount of data of the same scale, but it can still maintain a high imaging quality in global imaging.

[0004] Current designs for spatial sampling of RMA imaging include: (1) Through the analysis of the wavenumber domain and the spatial domain, the distortion of undersampling is concentrated outside the imaging area, while the signal in the effective imaging area is guaranteed not to be distorted. This method can greatly avoid the degradation of imaging quality caused by undersampling, but its undersampling effect is limited by the signal characteristics of the wavenumber domain. If the imaging area is large, the sampling rate after undersampling is even close to the Nyquist sampling rate, which cannot effectively reduce the scale of the sampling data.

[0005] (2) By suppressing the peak sidelobe ratio of the RMA algorithm, spatial non-uniform sampling is achieved during the imaging process, effectively reducing the aliasing problem between under-sampling imaging units. However, in the solution process, this method needs to fully consider the entire process of the RMA algorithm, and the optimization complexity is extremely high. For scenarios such as large-area imaging or high-frequency and high-precision imaging, this method cannot complete the solution of the model, so it can be considered that it has great limitations in actual engineering. Summary of the invention

[0006] The purpose of the present invention is to overcome the problem of high complexity of spatial sampling optimization in RMA imaging, and proposes a low-cost optimization method for SAR imaging based on ADMM. The method makes full use of the local linear characteristics in the imaging algorithm, separates the non-convex constraint set, and provides an efficient solution method for specific fractional features, thereby avoiding the use of heuristic algorithms and ensuring convergence.

[0007] In order to achieve the above object, the present invention adopts the following technical scheme: The low-cost optimization method for SAR imaging based on ADMM includes the following steps: Considering two radar motion dimensions and local linear characteristics of the imaging algorithm at the same time, a radar imaging defocus fractional optimization model under non-uniform sampling suppression is established, wherein the constraint conditions of the radar imaging defocus fractional optimization model under non-uniform sampling suppression include array element constant energy constraint and array element peak weight constraint; The ADMM algorithm is used to separate the non-convex constraint set, and the radar imaging defocus fractional optimization model under non-uniform sampling is solved with the help of unitary transformation and auxiliary variables to obtain the optimized radar sampling position and complex weight.

[0008] Furthermore, the array element constant energy constraint is as follows:

[0009] in, The complex weight of each physically reachable array element position is the total energy of all array elements. This term prevents the model from converging to all zeros in the end; The array element peak weight constraint is as follows:

[0010] in, is the weight matrix after aperture optimization; is the maximum weight for each aperture.

[0011] Furthermore, the radar imaging defocus fractional optimization model for suppressing non-uniform sampling by simultaneously considering two radar motion dimensions and the local linear characteristics of the imaging algorithm is established as follows:

[0012] in, Represents a function Smallest ; For the original data Modeling of defocus after axis linearity changes, For the original data Modeling of defocusing after axis linearity changes; For the original data Modeling of the focusing situation after the axis linear change, For the original data Modeling of focusing after linear changes in the axis; is the weight matrix after aperture optimization, for The l1 norm of , indicating that the number of sampling positions required is minimal; is the lower limit of focus, is the maximum weight for each aperture.

[0013] Furthermore, the ADMM algorithm is used to separate the non-convex constraint set, and the radar imaging defocus fractional optimization model under non-uniform sampling is solved by means of unitary transformation and auxiliary variables, and the optimized radar sampling position and complex weight are obtained as follows: The Lagrangian objective function of the ADMM algorithm is constructed by auxiliary variables and Lagrangian multipliers, and the constraint conditions of the radar imaging defocus fractional optimization under non-uniform sampling are written into the Lagrangian objective function of the ADMM algorithm to construct the radar imaging defocus fractional optimization problem model under non-uniform sampling. After initializing the variables of the radar imaging defocus fractional optimization problem model under non-uniform sampling, the ADMM algorithm is used to carry out alternating optimization until all variables reach the optimal solution, and the optimized radar sampling position and complex weight are output; The alternate optimization is carried out by the ADMM algorithm until all variables reach the optimal solution, including: The variable values ​​of the fractional optimization model for radar imaging defocus suppression under non-uniform sampling are iteratively updated until the ADMM algorithm converges or the maximum number of iterations is reached.

[0014] Furthermore, the Lagrangian objective function is as follows:

[0015] The model of the radar imaging defocus fractional optimization problem under non-uniform sampling suppression is as follows:

[0016] The unitary transformation is as follows:

[0017]

[0018] The introduction of auxiliary variables is as follows:

[0019] Among them, the auxiliary variable Equivalent Representation , auxiliary variables Equivalent Representation , represents the trace of the matrix in brackets, represents the diagonal matrix after the unitary transformation of the molecular intermediate matrix, represents the diagonal matrix after the unitary transformation of the denominator intermediate matrix, and is the Lagrange multiplier, and is the step size factor.

[0020] Furthermore, one iteration update of the alternating optimization includes the following steps: Fix the values ​​of the auxiliary variables and Lagrange multipliers of the ADMM algorithm, and solve the optimal solution of the Lagrange objective function of the ADMM algorithm with respect to the remaining unfixed variables; Fix the value of the solved variable and find the optimal solution of the auxiliary variable; Fix the values ​​of all solved variables again and update the values ​​of the Lagrange multipliers; Completes variable updates in one iteration.

[0021] Furthermore, one iteration update of the alternating optimization is specifically as follows: fixed , remove the Lagrangian function with Unrelated items are updated gradually Each column of fixed , remove the Lagrangian function with The irrelevant terms are solved using BFGS to obtain ; fixed , remove the Lagrangian function with The solution for the irrelevant terms is solved in two steps using CVX and the combination of numbers and shapes. ; Update Lagrange multipliers and , and Update via:

[0022]

[0023] Completes variable updates in one iteration.

[0024] ADMM-based SAR imaging low-cost optimization system, including: A radar imaging defocus fractional optimization modeling module is used to simultaneously consider two radar motion dimensions and local linear characteristics of the imaging algorithm to establish a radar imaging defocus fractional optimization model under non-uniform sampling suppression, wherein the constraints of the radar imaging defocus fractional optimization model under non-uniform sampling suppression include array element constant energy constraints and array element peak weight constraints; The radar sampling position and complex weight solution module is used to separate the non-convex constraint set using the ADMM algorithm and solve the radar imaging defocus fractional optimization model under the suppression of non-uniform sampling. When solving the radar imaging defocus fractional optimization model under the suppression of non-uniform sampling, unitary transformation and auxiliary variables are introduced to obtain the optimized radar sampling position and complex weight.

[0025] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the ADMM-based low-cost optimization method for SAR imaging when executing the computer program.

[0026] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the low-cost optimization method for SAR imaging based on ADMM is implemented.

[0027] Compared with the prior art, the present invention has the following beneficial technical effects: The invention proposes a low-cost optimization method for SAR imaging based on ADMM, an array configuration based on ADMM (Alternating Direction Method of Multipliers) and its weight design, which are applied to the low-cost SAR (Synthetic Aperture Radar) three-dimensional near-field imaging. The ADMM algorithm itself involves the alternating solution of multiple sub-optimization problems. The mathematical model variable values ​​solved by the iterative update of the ADMM algorithm fully utilize the properties of the unitary transformation of the matrix to optimize the sampling position of the radar and its complex weight, so that the defocusing problem in the non-uniform sampling imaging process is effectively solved, the imaging accuracy is improved, and the SAR image is clearer and more accurate. Starting from the selection of the radar imaging sampling position, the focusing and defocusing conditions of the imaging are modeled in a two-dimensional plane, so as to realize high-quality and low-cost three-dimensional SAR imaging. By establishing a fractional optimization model, the dependence of the model effect on the parameter adjustment is reduced, and the non-convex constraint set is separated by means of the Lagrangian function and the ADMM algorithm, so as to realize the solution of the complex non-convex objective function under the non-convex constraint.

[0028] Furthermore, the fractionally optimized non-uniform spatial sampling design of the present invention can achieve low data cost optimization under high-quality imaging conditions without relying on parameter adjustment, and implement alternating optimization for different types of problems in the optimization stage to obtain the optimal solution of the spatial sampling position and the complex weight of each position.

[0029] Furthermore, the present invention simplifies the model by using constraint set separation, which can realize the transformation of the model from a non-convex problem under non-convex constraints to a non-convex problem under convex constraints, greatly simplifying the solution process and effect.

[0030] Furthermore, through the iterative update strategy, the computational complexity can be reduced and the imaging efficiency can be improved while ensuring the imaging quality. The ADMM algorithm has the ability of multi-task learning, which ensures that the present invention can efficiently and robustly process multiple imaging tasks, enhance the application flexibility of the SAR imaging system, and meet more diverse needs.

[0031] Furthermore, in the iterative process, the properties of the matrix are fully utilized to solve each sub-step of the ADMM algorithm, so that the model can still be efficiently solved in large-scale imaging scenarios and obtain excellent iterative effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings described herein are for explanation purposes only and are not intended to limit the scope of the present invention in any way. In addition, the shapes and proportional dimensions of the components in the drawings are only for illustration purposes to help understand the present invention, and are not intended to specifically limit the shapes and proportional dimensions of the components of the present invention. In the drawings: Figure 1 The figure is a flow chart of the low-cost optimization method for SAR imaging based on ADMM of the present invention.

[0033] Figure 2 It is a structural diagram of the low-cost optimization system for SAR imaging based on ADMM of the present invention.

[0034] Figure 3 This is a diagram of an electronic device for the low-cost optimization method for SAR imaging based on ADMM of the present invention.

[0035] Figure 4 Schematic diagram of the radar development board in Embodiment 5 of the present invention Figure 5 Schematic diagram of the imaging target in Embodiment 5 of the present invention.

[0036] Figure 6 This is a diagram of the RMA non-uniform sampling imaging effect in Example 5 of the present invention.

[0037] Figure 7 This is a diagram of the RMA uniform sampling imaging effect in Example 5 of the present invention.

[0038] Figure 8 It is the optimized sampling position weighting coefficient in the fifth embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only 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 creative work should fall within the scope of protection of the present invention.

[0040] Embodiment 1 See also Figure 1 , a low-cost optimization method for SAR imaging based on ADMM, including the following steps: Considering two radar motion dimensions and local linear characteristics of the imaging algorithm at the same time, a radar imaging defocus fractional optimization model under non-uniform sampling suppression is established, wherein the constraint conditions of the radar imaging defocus fractional optimization model under non-uniform sampling suppression include array element constant energy constraint and array element peak weight constraint; The ADMM algorithm is used to separate the non-convex constraint set, and the radar imaging defocus fractional optimization model under non-uniform sampling is solved with the help of unitary transformation and auxiliary variables to obtain the optimized radar sampling position and complex weight.

[0041] In view of the shortcomings of RMA-based imaging, this embodiment proposes a non-uniform spatial sampling design based on the ADMM method, which can achieve low-cost optimization under high-quality imaging conditions. The ADMM algorithm is applied to SAR imaging optimization, which provides new ideas for algorithm innovation and promotes the continuous progress and development of SAR imaging technology. With the continuous development of SAR imaging technology, its application fields are also expanding. By improving imaging efficiency, reducing costs and enhancing application flexibility, it is helpful to expand the application field of SAR imaging technology and provide high-quality imaging services for more industries.

[0042] The constant energy constraint of the array element is as follows:

[0043] in, The complex weight of each physically reachable array element position is the total energy of all array elements. This term prevents the model from converging to all zeros in the end; The element peak weight constraints are as follows:

[0044] in, is the weight matrix after aperture optimization; is the maximum weight for each aperture.

[0045] Considering the two radar motion dimensions and the local linear characteristics of the imaging algorithm, the radar imaging defocus fractional optimization model under non-uniform sampling is established as follows:

[0046] in, Represents a function Smallest ; For the original data Modeling of defocus after axis linearity changes, For the original data Modeling of defocusing after axis linearity changes; For the original data Modeling of the focusing situation after the axis linear change, For the original data Modeling of focusing after linear changes in the axis; is the weight matrix after aperture optimization, for The l1 norm of , indicating that the number of sampling positions required is minimal; is the lower limit of focus, is the maximum weight for each aperture.

[0047] The ADMM algorithm is used to separate the non-convex constraint set, and the radar imaging defocus fractional optimization model under non-uniform sampling is solved with the help of unitary transformation and auxiliary variables. The optimized radar sampling position and complex weight are obtained as follows: The Lagrangian objective function of the ADMM algorithm is constructed by auxiliary variables and Lagrangian multipliers, and the constraint conditions of the radar imaging defocus fractional optimization under non-uniform sampling are written into the Lagrangian objective function of the ADMM algorithm to construct the radar imaging defocus fractional optimization problem model under non-uniform sampling. After initializing the variables of the radar imaging defocus fractional optimization problem model under non-uniform sampling, the ADMM algorithm is used to carry out alternating optimization until all variables reach the optimal solution, and the optimized radar sampling position and complex weight are output; The ADMM algorithm is used to perform alternating optimization until all variables reach the optimal solution, including: The variable values ​​of the fractional optimization model for radar imaging defocus suppression under non-uniform sampling are iteratively updated until the ADMM algorithm converges or the maximum number of iterations is reached.

[0048] The Lagrangian objective function is as follows:

[0049] The model of radar imaging defocus fractional optimization problem under non-uniform sampling is as follows:

[0050] The unitary transformation is as follows:

[0051]

[0052] The introduction of auxiliary variables is as follows:

[0053] Among them, the auxiliary variable Equivalent Representation , auxiliary variables Equivalent Representation , represents the trace of the matrix in brackets, represents the diagonal matrix after the unitary transformation of the molecular intermediate matrix, represents the diagonal matrix after the unitary transformation of the denominator intermediate matrix, and is the Lagrange multiplier, and is the step size factor.

[0054] An iterative update of alternating optimization includes the following steps: Fix the values ​​of the auxiliary variables and Lagrange multipliers of the ADMM algorithm, and solve the optimal solution of the Lagrange objective function of the ADMM algorithm with respect to the remaining unfixed variables; Fix the value of the solved variable and find the optimal solution of the auxiliary variable; Fix the values ​​of all solved variables again and update the values ​​of the Lagrange multipliers; Completes variable updates in one iteration.

[0055] An iterative update of alternating optimization is as follows: fixed , remove the Lagrangian function with Unrelated items are updated gradually Each column of fixed , remove the Lagrangian function with The irrelevant terms are solved using BFGS to obtain ; fixed , remove the Lagrangian function with The solution for the irrelevant terms is solved in two steps using CVX and the combination of numbers and shapes. ; Update Lagrange multipliers and , and Update via:

[0056]

[0057] Completes variable updates in one iteration.

[0058] Embodiment 2 See also Figure 2 , a low-cost optimization system for SAR imaging based on ADMM, including: A radar imaging defocus fractional optimization modeling module is used to simultaneously consider two radar motion dimensions and local linear characteristics of the imaging algorithm to establish a radar imaging defocus fractional optimization model under non-uniform sampling suppression, wherein the constraints of the radar imaging defocus fractional optimization model under non-uniform sampling suppression include array element constant energy constraints and array element peak weight constraints; The radar sampling position and complex weight solution module is used to separate the non-convex constraint set using the ADMM algorithm, and solve the radar imaging defocus fractional optimization model under non-uniform sampling with the help of unitary transformation and auxiliary variables to obtain the optimized radar sampling position and complex weight.

[0059] This embodiment sets the constant energy constraint of the array element and the peak weight constraint of the array element, establishes a mathematical model for optimizing the imaging defocus fraction, and then solves it through the ADMM algorithm. Under the premise of ensuring the imaging quality, the radar sampling position is sparsely spaced to the maximum extent to achieve the effect of reducing costs.

[0060] Embodiment 3 An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the low-cost optimization method for SAR imaging based on ADMM described in Embodiment 1 when executing the computer program.

[0061] Embodiment 4 A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the low-cost optimization method for SAR imaging based on ADMM described in Embodiment 1 is implemented.

[0062] Embodiment 5 This embodiment provides a low-cost optimization method for SAR imaging based on ADMM. By designing Lagrange multiplier terms, complex constraints are transferred to the objective function for optimization. Alternative optimization is performed for different types of problems in the optimization stage to obtain the optimal solution for the spatial sampling position. The specific mathematical model and implementation process are described as follows: The 3D-SAR imaging implemented by the existing RMA algorithm can be simplified into three steps in mathematical expression: two-dimensional linear transformation - nonlinear interpolation operation - two-dimensional linear transformation. Due to the existence of nonlinear interpolation, the process is difficult to express through simple matrix operations without making other improvements to the entire process, which is also the difficulty in aperture optimization for this algorithm.

[0063] However, if we only ensure that the signal is not distorted in the signal processing before the nonlinear interpolation operation, then the two subsequent steps will not have a significant impact. With this idea, the aperture optimization based on the entire imaging process can be transformed into the aperture optimization only for the first linear transformation, that is, to ensure that the data before and after the aperture optimization have the same properties after the first linear change. And considering that the measured data itself is affected by the vibration of the radar platform, imprecise motion, noise, clutter, etc., the weight of the effective aperture is Need to have a larger mold.

[0064] Since the two-dimensional linear transformation in the RMA algorithm can be split into one-dimensional linear transformations in two radar motion dimensions, the two motion axes can be modeled and optimized separately. For a single axis, it can be modeled as: (1) in, That is, the defocusing condition after the linear change of the original data, That is, the focusing condition after the linear change of the original data. is the weight after aperture optimization, The desired pore size sparsity is ensured. Symbol stands for conjugate transpose, is the 2-norm of the vector, is the 1-norm of the vector.

[0065] Similarly, if two dimensions are considered at the same time, the model can be: (2) in, Represents a function Smallest ; For the original data Modeling of defocus after axis linearity changes, For the original data Modeling of defocusing after axis linearity changes; For the original data Modeling of the focusing situation after the axis linear change, For the original data Modeling of focusing after linear changes in the axis; is the weight matrix after aperture optimization, for The l1 norm of , indicating that the required sampling positions are small enough; is the total energy of all array elements, is the maximum weight for each aperture.

[0066] The optimization steps for the above problem (2) are as follows: Step 1: Perform matrix decomposition on the numerator and denominator of the fractional model and introduce auxiliary variables To express equivalently , auxiliary variables Equivalent Representation , to separate the objective function from the constraint set, by introducing the Lagrange multiplier and Constructing Lagrangian functions , transferring complex constraints into the objective function; Step 2: Initialize the initial values ​​of each variable in the Lagrangian function and carry out alternating optimization; Step 3: Fix , solve ;fixed , using BFGS to solve ;fixed , solve ; Update the Lagrange multiplier to obtain ; Step 4: Repeat step 3 until the algorithm convergence condition is met or the maximum number of iterations is reached, and the optimization of the radar sampling position and its weight is completed.

[0067] The following is further explained in combination with the ADMM algorithm framework: Step 1: Perform matrix decomposition on the numerator and denominator of the fractional model and introduce auxiliary variables To express equivalently , auxiliary variables Equivalent Representation , to achieve the separation of objective function and constraint set, the constructed Lagrangian function is .

[0068] Step 2: Initialize the values ​​of all variables .

[0069] Step 3: (1) Fixed , solve

[0070] Remove the Lagrangian function irrelevant items, and Split into column vectors ,about The Lagrangian function is: (3) make , the above formula can be simplified as:

[0071] when fixed, The phase of is 0, then minimum, so formula (3) is about complex numbers The optimization function can be transformed into real numbers Function: (4) According to the properties of unitary transformation, we know is a diagonal matrix, so is a diagonal matrix, and the vector elements can be separated by equation (4): (5) The solution to this problem is: (6) In summary, The solution is: (7) (2) Fixed , solve

[0072] Remove the Lagrangian function Irrelevant items, about The Lagrangian function is: (8) in, ,make ,but: (9) when fixed, The phase of is 0, then minimum, so formula (9) is about complex numbers The optimization function can be transformed into real numbers Function: (10) This problem is an unconstrained optimization problem and can be solved directly by BFGS. Its derivative is: (11) (3) Fixed , solve

[0073] Remove the Lagrangian function Irrelevant items, about The Lagrangian function is: (12) And there are constraints: (13) This problem is due to the non-convex constraints The existence of makes the whole problem non-convex and cannot be solved directly. It can be solved by sub-ADMM, introducing an auxiliary variable The constraint set of the original problem is separated, and its Lagrangian function is: (14) The constraints at this time are: (15) At this time, the steps of sub-ADMM are as follows: Step 1: Fix , solve .

[0074] Remove (14) The irrelevant terms are transformed into: (16) At this time, the objective function is a convex problem, about The constraint (16) is also a convex problem, which can be solved directly by CVX.

[0075] Step 2: Fix , solve .

[0076] Remove the formula (4.116) The irrelevant terms are transformed into: (17) in, , this equation is introduced for the convenience of writing and does not directly affect the calculation. Removing the constant term in equation (17) yields: (18) The problem now turns into: (19) Due to the existence of trace operation in the objective function, there is no need to consider For elements other than the diagonal, the elements on the diagonal are: (20) but: (twenty one) At this time, if we want to ensure formula (21), we get: (twenty two) Formula (21) can be transformed into the model problem (twenty three) If it is expanded into a vector, it can be regarded as finding a situation on a high-dimensional sphere where the linear transformation value is the largest. Obviously, the maximum value is located at the point where the radius is perpendicular to the straight line. Therefore, the point where the equation (23) is the smallest satisfies (twenty four) in, Is a fixed value.

[0077] At this point, the problem turns into (25) This problem can be solved directly.

[0078] Finally, Iterate (26) (4) Update and , can be obtained (27) (28) Step 4: Repeat step 3 until the algorithm convergence condition is met or the maximum number of iterations is reached, and the optimization of the radar sampling position and its weight is completed.

[0079] The mathematical model and optimization process of this embodiment are realized through the above process. Next, the sampling position is optimized by computer simulation, and the imaging effect is verified by using TI's AWR 1443 radar development board. The radar development board and the imaging target are as follows: Figure 4 and Figure 5 shown.

[0080] Experiment 1: The transmission signal of the AWR 1443 radar development board is a frequency modulated continuous wave, with a starting frequency of , the total bandwidth is , the sampling frequency is The imaging area is In this experiment, the center of the imaging area is at a distance of 1.5 meters from the center of the radar motion. Before optimization, the radar sampling position is a quarter wavelength interval as the side length of the spatial sampling interval. The comparison of the slicing effect of non-uniform sampling after optimization and before optimization is shown in Figure 6 and Figure 7 shown.

[0081] pass Figure 6 and Figure 7 It can be seen from the comparison effect that after the sampling position is sparse, the imaging quality does not decrease significantly; Figure 8 It can be seen that the data collected by the sampling position closer to the diagonal of the motion area is more important in imaging, and the effective aperture involved in imaging is reduced to 76833, while the effective aperture of uniform sampling before optimization is 170862, and the amount of sampling data is reduced to 45% of the original. Therefore, it can be considered that the weighted sampling position designed by this method can achieve sparse sampling positions while ensuring imaging quality, so as to achieve the purpose of reducing imaging costs.

[0082] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0083] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0084] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0085] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention is described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation of the present invention can still be modified or replaced by equivalents, and any modification or equivalent replacement that does not deviate from the spirit and scope of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A low-cost optimization method for SAR imaging based on ADMM, characterized in that: The following steps are involved: Considering two radar motion dimensions and local linear characteristics of the imaging algorithm at the same time, a radar imaging defocus fractional optimization model under non-uniform sampling suppression is established, wherein the constraint conditions of the radar imaging defocus fractional optimization model under non-uniform sampling suppression include array element constant energy constraint and array element peak weight constraint; The ADMM algorithm is used to separate the non-convex constraint set, and the radar imaging defocus fractional optimization model under non-uniform sampling is solved with the help of unitary transformation and auxiliary variables to obtain the optimized radar sampling position and complex weight.

2. The low-cost optimization method for SAR imaging based on ADMM according to claim 1, characterized in that: The array element constant energy constraint is as follows: in, The complex weight of each physically reachable array element position is the total energy of all array elements. This term prevents the model from converging to all zeros in the end; The array element peak weight constraint is as follows: in, is the weight matrix after aperture optimization; is the maximum weight for each aperture.

3. The low-cost optimization method for SAR imaging based on ADMM according to claim 2, characterized in that: The radar imaging defocus fractional optimization model that simultaneously considers two radar motion dimensions and the local linear characteristics of the imaging algorithm to suppress non-uniform sampling is as follows: in, Represents a function Smallest ; For the original data Modeling of defocus after axis linearity changes, For the original data Modeling of defocusing after axis linearity changes; For the original data Modeling of the focusing situation after the axis linear changes, For the original data Modeling of focusing after axis linearity changes; is the weight matrix after aperture optimization, for The l1 norm of , indicating that the number of sampling positions required is minimal; is the lower limit of focus, is the maximum weight for each aperture.

4. The low-cost optimization method for SAR imaging based on ADMM according to claim 3, characterized in that: The ADMM algorithm is used to separate the non-convex constraint set, and the radar imaging defocus fractional optimization model under non-uniform sampling is solved by unitary transformation and auxiliary variables to obtain the optimized radar sampling position and complex weight: The Lagrangian objective function of the ADMM algorithm is constructed by auxiliary variables and Lagrangian multipliers, and the constraint conditions of the radar imaging defocus fractional optimization under non-uniform sampling are written into the Lagrangian objective function of the ADMM algorithm to construct the radar imaging defocus fractional optimization problem model under non-uniform sampling. After initializing the variables of the radar imaging defocus fractional optimization problem model under non-uniform sampling, the ADMM algorithm is used to carry out alternating optimization until all variables reach the optimal solution, and the optimized radar sampling position and complex weight are output; The alternate optimization is carried out by the ADMM algorithm until all variables reach the optimal solution, including: The variable values ​​of the fractional optimization model for radar imaging defocus suppression under non-uniform sampling are iteratively updated until the ADMM algorithm converges or the maximum number of iterations is reached.

5. The low-cost optimization method for SAR imaging based on ADMM according to claim 4, characterized in that: The Lagrangian objective function is as follows: The model of the radar imaging defocus fractional optimization problem under non-uniform sampling suppression is as follows: The unitary transformation is as follows: The introduction of auxiliary variables is as follows: Among them, the auxiliary variable Equivalent Representation , auxiliary variables Equivalent Representation , represents the trace of the matrix in brackets, represents the diagonal matrix after the unitary transformation of the molecular intermediate matrix, represents the diagonal matrix after the unitary transformation of the denominator intermediate matrix, and is the Lagrange multiplier, and is the step size factor.

6. The low-cost optimization method for SAR imaging based on ADMM according to claim 5, characterized in that: One iteration update of the alternating optimization comprises the following steps: Fix the values ​​of the auxiliary variables and Lagrange multipliers of the ADMM algorithm, and solve the optimal solution of the Lagrange objective function of the ADMM algorithm with respect to the remaining unfixed variables; Fix the value of the solved variable and find the optimal solution of the auxiliary variable; Fix the values ​​of all solved variables again and update the values ​​of the Lagrange multipliers; Completes variable updates in one iteration.

7. The low-cost optimization method for SAR imaging based on ADMM according to claim 6, characterized in that: The specific iterative update of the alternating optimization is: fixed , remove the Lagrangian function with Unrelated items are updated gradually Each column of fixed , remove the Lagrangian function with The irrelevant terms are solved using BFGS to obtain ; fixed , remove the Lagrangian function with The solution for the irrelevant terms is solved in two steps using CVX and the combination of numbers and shapes. ; Update Lagrange multipliers and , and Update via: Completes variable updates in one iteration.

8. A low-cost optimization system for SAR imaging based on ADMM, characterized in that: include: A radar imaging defocus fractional optimization modeling module is used to simultaneously consider two radar motion dimensions and local linear characteristics of the imaging algorithm to establish a radar imaging defocus fractional optimization model under non-uniform sampling suppression, wherein the constraints of the radar imaging defocus fractional optimization model under non-uniform sampling suppression include array element constant energy constraints and array element peak weight constraints; The radar sampling position and complex weight solution module is used to separate the non-convex constraint set using the ADMM algorithm, and solve the radar imaging defocus fractional optimization model under non-uniform sampling with the help of unitary transformation and auxiliary variables to obtain the optimized radar sampling position and complex weight.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the ADMM-based low-cost optimization method for SAR imaging as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the low-cost optimization method for SAR imaging based on ADMM as described in any one of claims 1 to 7.

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