Digital coding metamaterial forward-looking video imaging method and system based on sparse low-rank decomposition

Abstract

The invention discloses a digital coding metamaterial forward-looking video imaging method and system based on sparse low-rank decomposition, and mainly solves the problems of motion blur and poor imaging stability in a non-sparse observation scene of a moving target in the prior art. According to the implementation scheme, echo data of N frames of observation scenes are collected; decomposing a scattering coefficient vector of an observation scene corresponding to each frame of echo into a low-rank vector of a background area corresponding to the observation scene and a sparse vector of a dynamic change area, and expressing a separation problem of the two change areas as a joint low-rank and sparse optimization problem; performing convex relaxation processing on the optimization problem, and converting the optimization problem subjected to the convex relaxation processing into an optimization problem in an unconstrained form to obtain a sparse low-rank decomposition-based metamaterial forward-looking video imaging model; and solving the constructed imaging model, and realizing multi-frame image reconstruction and video synthesis based on a solving result. According to the method, the imaging resolution and reconstruction stability of the non-sparse scene containing the moving target are improved, and the method can be used for intelligent security check and medical detection.

Description

Technical Field

[0001] The present invention belongs to the field of microwave forward-looking imaging technology, and in particular relates to a digitally coded metamaterial forward-looking video imaging method and system, which can be used for intelligent security inspection and medical detection. Background Art

[0002] Unlike optical imaging systems, microwave sensors can not only penetrate non-conductive obstructing media such as clouds, fog, and walls, but also achieve reliable detection while protecting individual privacy. This makes them have important engineering application value in areas such as autonomous driving environment perception, intelligent security inspection, and medical testing.

[0003] Digitally coded metamaterials are a new type of microwave sensor that has emerged in recent years, providing a low-cost solution for microwave forward-looking imaging. Forward-looking imaging technology based on digitally coded metamaterials uses a field-programmable gate array to control the phase encoding of metamaterial units in real time, thereby efficiently constructing a two-dimensional random radiation field in space and time, enabling multiple rapid observations of the target scene, thus enabling all-day, high-frame-rate forward-looking imaging. Compared to traditional microwave sensors that rely on mechanical scanning or phase shifters for imaging, digitally coded metamaterial sensors significantly reduce system complexity and hardware costs, and have greater engineering applicability.

[0004] At present, forward-looking imaging technology based on digitally coded metamaterials can be mainly divided into two types: intelligent imaging and computational imaging.

[0005] In their paper "Machine-learning reprogrammable metasurface imager" (Nature Communications, 2019, 10: 1082), Li et al. proposed an end-to-end deep learning imaging method. This method directly maps metamaterial radiation patterns to target scenes by training a deep neural network, enabling efficient imaging and target recognition. However, this method requires a massive amount of labeled data to train the network model, which significantly reduces its generalization ability in complex electromagnetic environments, resulting in unstable imaging results.

[0006] In their paper "High-Performance Microwave Computational Imaging System Based on Information Metamaterials," Journal of Radar, 2021, 10(2): 288–295, Han Jiaqi et al. proposed a compressed sensing imaging method based on the aperture of information metamaterials. This method dynamically controls the phase distribution of metamaterial units to generate a spatially random radiation field and uses an iterative shrinkage threshold method to reconstruct sparse target scenes. However, this method strictly relies on the static assumption and sparse prior constraints of the target scene. When there are moving targets or non-sparse distributions in the observation scene, long-term observation will cause motion blur in the reconstructed image. Summary of the Invention

[0007] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a digitally coded metamaterial forward-looking video imaging technology based on sparse low-rank decomposition to improve the resolution and stability of imaging of moving targets in non-sparse scenarios.

[0008] The technical idea of the present invention is to perform imaging analysis on non-sparse observation scenes containing moving targets, construct a digitally coded metamaterial forward-looking video imaging model based on sparse low-rank decomposition, and use the alternating direction multiplier method to efficiently solve the model to achieve high-resolution and stable target imaging.

[0009] According to the above ideas, the implementation scheme of the present invention includes the following:

[0010] 1. A digitally coded metamaterial forward-looking video imaging method based on sparse low-rank decomposition, characterized by comprising:

[0011] (1) Collection Frame observation scene echo data ;

[0012] (2) Constructing a digitally coded metamaterial forward-looking video imaging model based on sparse low-rank decomposition:

[0013] (2a) The scattering coefficient vector of the frame echo corresponding to the observation scene Decomposed into The low-rank vector of the frame echo corresponding to the background area of the observed scene and represents the The sparse vector of the frame echo corresponding to the dynamically changing area of the observation scene ;

[0014] (2b) The problem of separating the background region from the dynamically changing region in the observation scene is formulated as a joint low-rank and sparse optimization problem;

[0015] (2c) Perform convex relaxation on the optimization problem and convert The norm minimization problem and the rank minimization problem are transformed into norm minimization problem and nuclear norm minimization problem;

[0016] (2d) The optimization problem after convex relaxation is further transformed into an unconstrained optimization problem, thus obtaining the digitally coded metamaterial forward-looking video imaging model:

[0017] ;

[0018] in, for The measurement matrix corresponding to the frame echo, express The frame echo corresponds to the low-rank matrix of the background area of the observation scene, express The frame echo corresponds to the sparse matrix of the dynamically changing area of the observation scene, Indicates converting a vector into a matrix form. and Represent the weights of low-rank components and sparse components respectively, 、 、 Respectively The square of the norm, the nuclear norm, norm.

[0019] (3) The constructed imaging model is solved using the alternating direction multiplier method to obtain The frame represents the low-rank matrix of the background area of the observation scene corresponding to the echo and dynamically changing regional sparse matrices ;

[0020] (4) Using the low-rank matrix of the background area and the sparse matrix of the dynamically changing region Complete multi-frame image reconstruction and video synthesis.

[0021] 2. A digitally coded metamaterial forward-looking video imaging system based on sparse low-rank decomposition, comprising:

[0022] Data acquisition module, used to collect Frame observation scene echo data ;

[0023] Imaging model construction module, used to build a digital coding metamaterial forward-looking video imaging model based on sparse low-rank decomposition;

[0024] Imaging model solving module is used to solve the constructed imaging model and obtain The frame represents the low-rank matrix of the background area of the observation scene corresponding to the echo and dynamically changing regional sparse matrices ;

[0025] Imaging and video synthesis module for utilizing low-rank matrices of background regions and dynamically changing regional sparse matrices Finish The frame echo corresponds to the imaging and video synthesis of the observed scene.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] 1. The present invention adopts the sparse low-rank decomposition method to construct a digitally coded metamaterial forward-looking video imaging model based on sparse low-rank decomposition, which overcomes the defects of traditional computational imaging such as dependence on sparse prior constraints and blurring of moving targets, and improves the imaging resolution of dynamic targets in non-sparse environments.

[0028] 2. The present invention adopts a convex relaxation optimization model and an alternating direction multiplier method to solve the digitally encoded metamaterial forward-looking video imaging model, without relying on the large amount of labeled data required for deep learning. This simplifies the solution process and the interdependence between parameters, improves the stability of imaging, and makes it more generalizable in complex electromagnetic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a flow chart for implementing the digitally encoded metamaterial forward-looking video imaging method provided in the first embodiment of the present invention;

[0030] Figure 2 This is a block diagram of a digitally encoded metamaterial forward-looking video imaging system provided by Example 2 of the present invention. DETAILED DESCRIPTION

[0031] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0032] Embodiment 1: A digitally coded metamaterial forward-looking video imaging method based on sparse low-rank decomposition.

[0033] Reference Figure 1 The implementation steps of this example include the following:

[0034] Step 1, Collection Frame observation scene echo data.

[0035] The observation scene is a non-sparsely distributed scene containing moving targets. The implementation of this step includes:

[0036] 1.1) By rapidly switching the digital code of the digitally coded metamaterial, a two-dimensional random radiation field in space and time is efficiently constructed to analyze the observed scene. observations and The observation data are divided into the following Frame echo data:

[0037] ;

[0038] in, It is Frame echo vector, It is The measurement matrix corresponding to the frame echo, It is The frame echo corresponds to the scattering coefficient vector of the observed scene, For the The noise vector of the frame echo, , is the total number of imaging grids of the imaging scene, is the number of grid rows of the imaging scene, is the number of grid columns of the imaging scene, for The total number of observations of the frame echo, The number of observation data included in each frame of echo data;

[0039] 1.2) Arrange the above formulas into the following matrix form:

[0040] ,

[0041] ,

[0042] ,

[0043] ,

[0044] in, Represents the transpose of a matrix;

[0045] 1.3) Using the above matrix form, Echo data matrix of the frame observation scene Expressed as:

[0046] .

[0047] Step 2: Construct a digitally coded metamaterial forward-looking video imaging model based on sparse low-rank decomposition.

[0048] 2.1) The scattering coefficient vector of the frame echo corresponding to the observation scene Decomposed into The low-rank vector of the frame echo corresponding to the background area of the observed scene and sparse vectors in dynamically changing regions , which is expressed as:

[0049] ;

[0050] 2.2) According to the low-rank vector of the background area of the observation scene corresponding to each frame echo and sparse vectors in dynamically changing regions ,get The low-rank matrix of the frame echo corresponding to the background area of the observation scene and the sparse matrix of the dynamically changing region , which is expressed as:

[0051] , ;

[0052] 2.3) According to The low-rank matrix of the frame echo corresponding to the background area of the observation scene and the sparse matrix of the dynamically changing region After obtaining sparse low-rank decomposition Echo data matrix of the frame observation scene The following representation:

[0053] ;

[0054] 2.4) The problem of separating the background region from the dynamically changing region in the observation scene is formulated as a joint low-rank and sparse optimization problem, which is formulated as follows:

[0055] ,

[0056] in, represents the rank of the matrix, for norm, It is a tuning parameter used to adjust the weights of low-rank components and sparse components;

[0057] 2.5) Perform convex relaxation on the optimization problem in step 2.4) and convert The norm minimization problem and the rank minimization problem are transformed into Norm minimization problem and nuclear norm minimization problem, which can be expressed as:

[0058] ,

[0059] in, Indicates converting a vector into a matrix form. is the nuclear norm, for norm;

[0060] 2.6) The optimization problem after convex relaxation in step 2.5) is further transformed into an unconstrained optimization problem, which is expressed as:

[0061] ,

[0062] in, express The square of the norm, and represent the weights of low-rank components and sparse components respectively.

[0063] Step 3: Use the alternating direction multiplier method to solve the constructed imaging model and obtain The frame represents the low-rank matrix of the background area of the observation scene corresponding to the echo and dynamically changing regional sparse matrices .

[0064] The alternating direction multiplier method is a decomposition and coordination optimization algorithm, which is particularly suitable for solving large-scale optimization problems. It solves the original problem by decomposing a complex optimization problem into multiple smaller sub-problems and then solving these sub-problems alternately.

[0065] 3.1) Introducing auxiliary variables , build an optimization model for variable separation, which is expressed as:

[0066] ;

[0067] 3.2) Convert the optimization model into an unconstrained optimization problem, that is, add the Lagrange multiplier term Used to enforce constraints and add augmentation terms Used to force near , and the following optimization formula is obtained:

[0068] ,

[0069] in, represents the inner product of two matrices, represents the Lagrange multiplier, represents the augmentation coefficient;

[0070] 3.3) Solve the optimization formula in step 3.2) and get The low-rank matrix representing the background area of the frame echo corresponding to the observation scene and a sparse matrix representing the dynamically changing region :

[0071] (3.3.1) Initialize the parameters of the alternating direction multiplier method: low-rank component weights , the weight of the sparse component , augmentation coefficient , auxiliary variables , the low-rank matrix of the background region of the observation scene , the sparse matrix of the dynamic change area of the observation scene , Lagrange multiplier ; Set the iterative convergence threshold ;

[0072] (3.3.2) Using the low-rank matrix of the background area of the observation scene , dynamically changing regional sparse matrix , Lagrange multipliers , for auxiliary variables Update and get the currently updated auxiliary variables :

[0073] ;

[0074] in, represents the identity matrix;

[0075] (3.3.3) Using the dynamic change area sparse matrix of the observation scene , Lagrange multipliers and the currently updated auxiliary variables , update the low-rank matrix of the background area of the observation scene , get the currently updated low-rank matrix of the background area :

[0076] ;

[0077] in, represents the singular value soft threshold operation, which aims to retain matrices larger than The singular values of , and set the rest of the singular values to zero;

[0078] (3.3.4) Using Lagrange multipliers and the currently updated auxiliary variables , low-rank matrix , update the sparse matrix of the dynamically changing area of the observation scene , get the sparse matrix of the dynamic change area after the current update :

[0079] ;

[0080] in, Represents a soft threshold operation, the purpose of which is to retain the absolute value greater than , and set the remaining elements to zero;

[0081] (3.3.5) Using the currently updated auxiliary variables , low-rank matrix , sparse matrix , update the Lagrange multiplier , get the current updated Lagrange multiplier :

[0082] ;

[0083] (3.3.6) Determine auxiliary variables The relative change of Is it established?

[0084] If so, then And return to step (3.3.2),

[0085] Otherwise, stop the iteration and get The low-rank matrix representing the background area of the frame echo corresponding to the observation scene and the sparse matrix of the dynamically changing region :

[0086] , .

[0087] Step 4: Using the low-rank matrix of the background area and the sparse matrix of the dynamically changing region Complete multi-frame image reconstruction and video synthesis.

[0088] (4.1) According to the low-rank matrix of the background area and the sparse matrix of the dynamically changing region , the scattering coefficient vector of the observation scene corresponding to each frame echo can be recovered by the following relationship:

[0089] ;

[0090] (4.2) The scattering coefficient vector of the observation scene corresponding to each frame echo is Matrixization is performed to obtain the scattering coefficient matrix of the observation scene corresponding to each frame echo :

[0091] ;

[0092] (4.3) The scattering coefficient matrix The numerical values of each element are converted into the grayscale value of the pixel points of the imaging scene to obtain each frame of the reconstructed image, and then multiple reconstructed image sequences are synthesized to obtain the forward imaging video of the observation scene.

[0093] It should be noted that the flowchart representations or method representations of the above embodiments can be understood as representing a module, segment, or portion of code comprising one or a group of executable instructions configured to implement a specific logical function or process step. The present invention is not limited to the disclosed preferred embodiments, and its implementation may not follow the order presented or discussed, including performing functions substantially simultaneously depending on the functions involved. That is, the step numbers in the flow chart are only for the purpose of clarifying the embodiment of the present invention and facilitating understanding, and the order of the steps is not limiting.

[0094] Example 2: A digitally coded metamaterial forward-looking video imaging system based on sparse low-rank decomposition.

[0095] Reference Figure 2 This example includes: a data acquisition module 1, an imaging model construction module 2, an imaging model solution module 3, and an imaging and video synthesis module 4, wherein the imaging model construction module 2 includes a scattering coefficient decomposition submodule 21, a joint low-rank-sparse optimization modeling submodule 22, a convex relaxation optimization conversion submodule 23, and an unconstrained optimization problem conversion submodule 24; the imaging model solution module 3 includes a variable separation optimization model construction submodule 31, a model unconstrained form conversion submodule 32, a parameter initialization submodule 33, an auxiliary variable update submodule 34, a background area low-rank matrix update submodule 35, a dynamically changing area sparse matrix update submodule 36, a Lagrange multiplier update submodule 37, and an iterative convergence judgment submodule 38; the imaging and video synthesis module 4 includes a scattering coefficient vector recovery submodule 41, a scattering coefficient vector matrixization submodule 42, and an image reconstruction and video synthesis submodule 43. The working principle of the entire system is as follows:

[0096] The data acquisition module 1 is used to collect Echo data of the frame observation scene , and the echo data Transmit to imaging model building module 2;

[0097] The imaging model building module 2 is used to generate the echo data of the data acquisition module 1 according to the Construct a digital coding metamaterial forward-looking video imaging model based on sparse low-rank decomposition, in which the scattering coefficient decomposition submodule 21 converts the first The scattering coefficient vector of the frame echo corresponding to the observation scene Decomposed into The low-rank vector of the frame echo corresponding to the background area of the observed scene and represents the The sparse vector of the frame echo corresponding to the dynamically changing area of the observation scene ; The joint low-rank-sparse optimization modeling submodule 22 expresses the separation problem of the observation scene background area and the dynamic change area in the scattering coefficient decomposition submodule 21 as a joint low-rank and sparse optimization problem; the convex relaxation optimization conversion submodule 23 performs convex relaxation on the optimization problem constructed by the joint low-rank-sparse optimization modeling submodule 22, that is, The norm minimization problem and the rank minimization problem are transformed into norm minimization problem and nuclear norm minimization problem; unconstrained optimization problem conversion submodule 24, converts the constrained optimization problem after convex relaxation processing of convex relaxation optimization conversion submodule 23 into an unconstrained optimization problem; finally, the imaging model is transmitted to the imaging model solution module 3.

[0098] The imaging model solving module 3 is used to calculate the echo data of the data acquisition module 1 Solve the imaging model constructed by imaging model building module 2 and obtain The low-rank matrix of the background area of the observation scene corresponding to the frame echo and dynamically changing regional sparse matrices , wherein, the variable separation optimization model construction submodule 31 introduces auxiliary variables into the imaging model constructed by the imaging model construction module 2 to construct a variable separation optimization model; the model unconstrained form conversion submodule 32 converts the variable separation optimization model constructed by the variable separation optimization model construction submodule 31 into an unconstrained form, that is, adds Lagrange multiplier terms and augmentation terms; the parameter initialization submodule 33 initializes the parameters of the alternating direction multiplier method according to the unconstrained form optimization model converted by the model unconstrained form conversion submodule 32, and transmits them to the auxiliary variable update submodule 34, the background area low rank matrix update submodule 35, the dynamic change area sparse matrix update submodule 36 and the Lagrange multiplier update submodule 37, and each variable update submodule performs iterative updates in turn; the auxiliary variable update submodule 34 uses the background area low rank matrix of the observation scene , dynamically changing regional sparse matrix , Lagrange multipliers , for auxiliary variables Update and get the currently updated auxiliary variables ; Background area low rank matrix update submodule 35, using the dynamic change area sparse matrix of the observation scene , Lagrange multipliers and the auxiliary variables updated by the current auxiliary variable updating submodule 34 , update the low-rank matrix of the background area of the observation scene , get the currently updated low-rank matrix of the background area Dynamically changing regional sparse matrix update submodule 36, using Lagrange multipliers and the auxiliary variables updated by the current auxiliary variable updating submodule 34 , low rank matrix after background region low rank matrix update submodule 35 update , update the sparse matrix of the dynamically changing area of the observation scene , get the sparse matrix of the dynamic change area after the current update ; Lagrange multiplier update submodule 37, using the auxiliary variable updated by the current auxiliary variable update submodule 34 , low rank matrix after background region low rank matrix update submodule 35 update , the sparse matrix after the dynamic change area sparse matrix update submodule 36 is updated , update the Lagrange multiplier , get the current updated Lagrange multiplier Iteration convergence judgment submodule 38, for judging the auxiliary variable updated by the current auxiliary variable update submodule 34 The relative change of Whether the convergence condition is met, if it does not meet the convergence condition, let And return to the auxiliary variable update submodule 34 to continue iterating. If the convergence condition is met, the iteration is stopped and the result is The low-rank matrix representing the background area of the frame echo corresponding to the observation scene and the sparse matrix of the dynamically changing region , and the resulting low-rank matrix and sparse matrices Transmitted to the imaging and video synthesis module 4.

[0099] The imaging and video synthesis module 4 is used to obtain the image model solution module 3 The low-rank matrix of the background area of the observation scene corresponding to the frame echo and dynamically changing regional sparse matrices Complete the imaging and video synthesis of the observation scene, wherein the scattering coefficient vector recovery submodule 41 obtains the scattering coefficient vector of the observation scene corresponding to each frame echo according to the low rank matrix L and sparse matrix S obtained by the imaging model solution module 3 ; Scattering coefficient vector matrix submodule 42, the scattering coefficient vector recovery submodule 41 obtained by each frame echo corresponding to the observation scene scattering coefficient vector Matrixization is performed to obtain the scattering coefficient matrix of the observation scene corresponding to each frame echo Image reconstruction and video synthesis submodule 43, the scattering coefficient matrix submodule 42 obtained by the scattering coefficient matrix of each frame echo The numerical values of each element are converted into the grayscale value of the pixel points of the imaging scene to obtain each frame of the reconstructed image, and then multiple reconstructed image sequences are synthesized to obtain the forward imaging video of the observation scene.

[0100] It should be noted that the above-mentioned functional modules can be implemented in whole or in part through software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a program instruction product. The program instruction product includes one or a group of program instructions. When the program instructions are loaded and executed on a computer, the process or function described is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The program instructions can be stored in a computer-readable and writable storage medium, or transferred from a computer-readable and writable storage medium to another computer-readable and writable storage medium.

[0101] The direct coupling or communication connection between the modules shown or discussed in this embodiment can be achieved through indirect coupling or communication connection of some interfaces, devices or modules. The various functional modules and submodules in this embodiment can be dynamically located in a processing component, or each module can exist physically separately, or two or more modules can be dynamically located in a processing component. When the above-mentioned dynamic components are implemented in the form of software functional modules and sold or used as independent products, they can also be stored in a computer-readable and writable storage medium. The storage medium can be a memory, a magnetic disk, an optical disk, etc.

[0102] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. Obviously, for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A digitally coded metamaterial forward-looking video imaging method based on sparse low-rank decomposition, characterized in that: include: (1) Collection Frame observation scene echo data ; (2) Constructing a digitally coded metamaterial forward-looking video imaging model based on sparse low-rank decomposition: ； in, for The measurement matrix corresponding to the frame echo, express The frame echo corresponds to the low-rank matrix of the background area of the observation scene, express The frame echo corresponds to the sparse matrix of the dynamically changing area of the observation scene, Indicates converting a vector into a matrix form. and Represent the weights of low-rank components and sparse components respectively, 、 、 Respectively The square of the norm, the nuclear norm, norm; (3) The constructed imaging model is solved using the alternating direction multiplier method to obtain The frame represents the low-rank matrix of the background area of the observation scene corresponding to the echo and dynamically changing regional sparse matrices ; (4) Using the low-rank matrix of the background area and the sparse matrix of the dynamically changing region Complete multi-frame image reconstruction and video synthesis.

2. The method according to claim 1, characterized in that The collection in (1) Frame observation scene echo data , whose implementation includes: (1a) By rapidly switching the digital coding of digitally coded metamaterials, a two-dimensional random radiation field in space and time is efficiently constructed to image the scene. Observation, will The observation data are divided into Frame, get Frame observation scene echo data: ； in, It is Frame echo vector, It is The measurement matrix corresponding to the frame echo, It is The frame echo corresponds to the scattering coefficient vector of the observed scene, For the The noise vector of the frame echo, , , r is the number of rows of the imaging scene grid, c is the number of columns of the imaging scene grid, is the total number of imaging grids of the imaging scene, for The total number of observations of the frame echo, The number of observation data included in each frame of echo data; Arrange the above formulas into: , , , , we get the following The echo data matrix form of the frame observation scene is: 。 3. The method according to claim 1, characterized in that The digital coding metamaterial forward-looking video imaging model based on sparse low-rank decomposition is constructed in (2), and its implementation includes: (2a) The scattering coefficient vector of the frame echo corresponding to the observation scene Decomposed into The low-rank vector of the frame echo corresponding to the background area of the observed scene and represents the The sparse vector of the frame echo corresponding to the dynamically changing area of the observation scene , which is expressed as: ； (2b) The problem of separating the background region from the dynamically changing region in the observation scene is formulated as a joint low-rank and sparse optimization problem, which is formulated as: ； Where, for The frame echo corresponds to the low-rank matrix of the background area of the observation scene, for The frame echo corresponds to the sparse matrix of the dynamically changing area of the observation scene, represents the rank of the matrix, for norm, It is a tuning parameter used to adjust the weights of low-rank components and sparse components; (2c) Perform convex relaxation on the optimization problem in step 2b) and convert The norm minimization problem and the rank minimization problem are transformed into Norm minimization problem and nuclear norm minimization problem, which can be expressed as: ； Where, Indicates that the vector Converted to matrix form, is the nuclear norm, for norm; (2d) The optimization problem after convex relaxation in step 2c) is further transformed into an unconstrained optimization problem, which is expressed as: 。 4. The method according to claim 1, wherein In (3), the imaging model is solved by using the alternating direction multiplier method, which includes: (3a) Introducing auxiliary variables , build an optimization model for variable separation, which is expressed as: ； (3b) Convert the optimization model into an unconstrained optimization problem, that is, add the Lagrange multiplier term Used to enforce constraints and add augmentation terms Used to force near , and the following optimization formula is obtained: ； in, represents the inner product of two matrices, represents the Lagrange multiplier, represents the augmentation coefficient; (3c) Solve the optimization formula in (3b) and get The low-rank matrix representing the background area of the frame echo corresponding to the observation scene and a sparse matrix representing the dynamically changing region .

5. The method according to claim 4, characterized in that The optimization formula in (3c) Solve, its implementation includes: (3c1) Initialize the parameters of the alternating direction multiplier method: low-rank component weights , the weight of the sparse component , augmentation coefficient , auxiliary variables , the low-rank matrix of the background region of the observation scene , the sparse matrix of the dynamic change area of the observation scene , Lagrange multiplier ; Set the iterative convergence threshold ; (3c2) Using the low-rank matrix of the background area of the observation scene , dynamically changing regional sparse matrix , Lagrange multipliers , for auxiliary variables Update and get the currently updated auxiliary variables : ； in, represents the identity matrix; (3c3) Using the dynamic change area sparse matrix of the observation scene , Lagrange multipliers and the currently updated auxiliary variables , update the low-rank matrix of the background area of the observation scene , get the currently updated low-rank matrix of the background area : ； in, represents the singular value soft threshold operation, which aims to retain matrices larger than The singular values of , and set the rest of the singular values to zero; (3c4) Using Lagrange multipliers and the currently updated auxiliary variables , low-rank matrix , update the sparse matrix of the dynamically changing area of the observation scene , get the sparse matrix of the dynamic change area after the current update : ； in, Represents a soft threshold operation, the purpose of which is to retain the absolute value greater than , and set the remaining elements to zero; (3c5) Using the currently updated auxiliary variables , low-rank matrix , sparse matrix , update the Lagrange multiplier , get the current updated Lagrange multiplier : ； (3c6) Determine auxiliary variables The relative change of Is it established? If so, then and returns (3c2), Otherwise, stop the iteration and get The low-rank matrix representing the background area of the frame echo corresponding to the observation scene and the sparse matrix of the dynamically changing region : ， 。 6. The method according to claim 1, characterized in that Said (4) utilizes the low rank matrix of the background region and the sparse matrix of the dynamically changing region Complete multi-frame image reconstruction and video synthesis, which includes: (4a) According to the low-rank matrix of the background area and the sparse matrix of the dynamically changing region , the scattering coefficient vector of the observation scene corresponding to each frame echo can be restored by the following relationship : ； (4b) The scattering coefficient vector of the observation scene corresponding to each frame echo is Matrixization is performed to obtain the scattering coefficient matrix of the observation scene corresponding to each frame echo : ； (4c) The scattering coefficient matrix The numerical values of each element are converted into the grayscale value of the pixel points of the imaging scene to obtain each frame of the reconstructed image, and then multiple reconstructed image sequences are synthesized to obtain the forward imaging video of the observation scene.

7. A digitally coded metamaterial forward-looking video imaging system based on sparse low-rank decomposition, characterized in that: include: Data acquisition module, used to collect Frame observation scene echo data ; Imaging model construction module, used to build a digital coding metamaterial forward-looking video imaging model based on sparse low-rank decomposition; Imaging model solving module is used to solve the constructed imaging model and obtain The low-rank matrix of the background area of the observation scene corresponding to the frame echo and dynamically changing regional sparse matrices ; Imaging and video synthesis module for utilizing low-rank matrices of background regions and dynamically changing regional sparse matrices Finish The frame echo corresponds to the imaging and video synthesis of the observed scene.

8. The system according to claim 7, characterized in that The imaging model building module includes: Scattering coefficient decomposition submodule is used to The scattering coefficient vector of the frame echo corresponding to the observation scene Decomposed into The low-rank vector of the frame echo corresponding to the background area of the observed scene and represents the The sparse vector of the frame echo corresponding to the dynamically changing area of the observation scene ; The joint low-rank-sparse optimization modeling submodule is used to formulate the problem of separating the background region from the dynamically changing region in the observation scene as a joint low-rank and sparse optimization problem. Convex relaxation optimization conversion submodule is used to perform convex relaxation on the joint low-rank and sparse optimization problem, that is, The norm minimization problem and the rank minimization problem are transformed into norm minimization problem and nuclear norm minimization problem; The unconstrained optimization problem conversion submodule is used to convert the constrained optimization problem after convex relaxation processing into an unconstrained optimization problem.

9. The system according to claim 7, wherein: The imaging model solving module includes: The variable separation optimization model construction submodule is used to introduce auxiliary variables and build a variable separation optimization model; The model unconstrained form conversion submodule adds Lagrange multiplier terms and augmentation terms to convert the variable separation optimization model into an unconstrained form; Parameter initialization submodule, used to initialize the parameters of the alternating direction multiplication method; Auxiliary variable update submodule, used to utilize the low-rank matrix of the background area of the observation scene , dynamically changing regional sparse matrix , Lagrange multipliers , for auxiliary variables Update and get the currently updated auxiliary variables ; The background region low-rank matrix update submodule uses the sparse matrix of the dynamically changing region of the observation scene , Lagrange multipliers and the currently updated auxiliary variables , update the low-rank matrix of the background area of the observation scene , get the currently updated low-rank matrix of the background area ; Dynamically changing region sparse matrix update submodule for utilizing Lagrange multipliers and the currently updated auxiliary variables , low-rank matrix , update the sparse matrix of the dynamically changing area of the observation scene , get the sparse matrix of the dynamic change area after the current update ; Lagrange multiplier update submodule, used to utilize the currently updated auxiliary variables , low-rank matrix , sparse matrix , update the Lagrange multiplier , get the current updated Lagrange multiplier ; Iterative convergence judgment submodule: used to judge the relative change of auxiliary variables Whether the convergence condition is met, if it is met, the iteration is stopped and the result is The low-rank matrix representing the background area of the frame echo corresponding to the observation scene and the sparse matrix of the dynamically changing region ; For those that do not meet the convergence conditions, let And return the auxiliary variable update submodule.

10. The system according to claim 7, wherein: The imaging and video synthesis module includes: The scattering coefficient vector recovery submodule is used to obtain the scattering coefficient vector of the observation scene corresponding to each frame echo based on the low-rank matrix L of the background area and the sparse matrix S of the dynamically changing area. ; Scattering coefficient vector matrix submodule is used to convert the scattering coefficient vector of the observation scene corresponding to each frame echo into Matrixization is performed to obtain the scattering coefficient matrix of the observation scene corresponding to each frame echo ; Image reconstruction and video synthesis submodule is used to transform the scattering coefficient matrix The numerical values of each element are converted into the grayscale value of the pixel points of the imaging scene to obtain each frame of the reconstructed image, and then multiple reconstructed image sequences are synthesized to obtain the forward imaging video of the observation scene.

Images