MIMO three-dimensional imaging method fusing sparsity and signal support domain prior

Abstract

The invention discloses an MIMO three-dimensional imaging method fusing sparsity and signal support domain prior, and relates to the technical field of MIMO radar three-dimensional imaging, and the method comprises the following steps: S1, constructing an MIMO radar three-dimensional imaging model; s2, converting the MIMO radar three-dimensional imaging model into a multi-dimensional tensor model; s3, based on the multi-dimensional tensor model, MIMO three-dimensional imaging fusing sparsity and signal support domain prior is realized; and solving is carried out through a multi-dimensional sparse recovery solving algorithm for the optimization problem under sparsity and signal support domain prior constraints. According to the MIMO three-dimensional imaging method fusing sparsity and signal support domain priori, after envelope adjustment and phase compensation are carried out on transmitted and received signals, MIMO radar echoes are expressed in a tensor form of a target three-dimensional image, and solution can be completed by using smaller storage space and shorter calculation time.

Description

Technical Field

[0001] The present invention relates to the technical field of MIMO radar three-dimensional imaging, and in particular to a MIMO three-dimensional imaging method integrating sparsity and signal support domain prior. Background Art

[0002] Inverse synthetic aperture radar (ISAR) imaging has been widely studied for extracting image information of air and space targets. ISAR images are only two-dimensional projections of targets on the range-Doppler plane, while interferometric ISAR (InISAR) technology can obtain three-dimensional images of targets. However, InISAR cannot separate scatterers at different altitudes but with the same range-Doppler values. More importantly, it faces complex motion compensation problems, especially for maneuvering targets.

[0003] MIMO radar uses MIMO multiple-input multiple-output (MIMO) technology to obtain multiple virtual array elements, which can obtain the three-dimensional information of the target under a single snapshot. Since the target is assumed to be stationary under a single snapshot, the motion compensation problem is avoided. Therefore, the three-dimensional imaging technology of MIMO radar has attracted much attention in recent years. Sparse recovery (SR) is an effective method to solve the problem of underdetermined equations by using the sparse characteristics of the signal. Due to the inherent sparsity of radar target images, sparse recovery has been widely studied in ISAR imaging in recent years. In MIMO radar imaging, sparse signal recovery is used to reduce the number of antennas and improve resolution. In addition, it can also suppress the coupling noise of non-orthogonal waveforms of broadband MIMO radar. Commonly used sparse recovery algorithms include matched filtering (MF) and fast Fourier transform (FFT) methods.

[0004] There are some problems with existing sparse recovery algorithms, including: information loss due to sparsity, insufficient accuracy, which may affect the quality and details of the image, and may result in poor recovery effects when processing complex images; due to high computational complexity, the calculation time is long, which is a significant disadvantage in application scenarios with high real-time requirements such as radar direction finding and tracking; complex recovery algorithms require larger computing and storage space and have higher requirements for hardware equipment. Summary of the invention

[0005] The purpose of the present invention is to provide a MIMO three-dimensional imaging method that integrates sparsity and signal support domain priors. After envelope adjustment and phase compensation of the transmitted and received signals, the MIMO radar echo is represented in the form of a tensor of a target three-dimensional image, which can be solved using smaller storage space and less computing time, and obtain good three-dimensional imaging effects.

[0006] To achieve the above object, the present invention provides a MIMO three-dimensional imaging method integrating sparsity and signal support domain prior, the steps are as follows:

[0007] S1. Construct MIMO radar three-dimensional imaging model;

[0008] S2, converting the MIMO radar three-dimensional imaging model into a multi-dimensional tensor model;

[0009] S3. Based on the multidimensional tensor model, MIMO three-dimensional imaging that integrates sparsity and signal support domain priors is realized; the optimization problem under the constraints of sparsity and signal support domain priors is solved by a multidimensional sparse recovery solution algorithm.

[0010] Preferably, in S1, the steps of constructing the MIMO radar three-dimensional imaging model are as follows:

[0011] S1.1. Establish the MIMO radar's transceiver array and solve the baseband echo of the scattering point:

[0012] like Figure 1 As shown, establish M 2 Send N 2 The MIMO array includes M 2 transmit array elements and N 2 There are N receiving array elements, 2 The receiving array elements form a square receiving array, the distance between each element is 2d, and the center of the array is located at the origin of the coordinate system;

[0013] Assume that the MIMO radar transmits a set of large time-bandwidth product signals with the same center frequency. is the mth baseband transmission signal, where t is the fast time, and Q is a scattering point in the far-field target, such as Figure 2 As shown, let T m Q, R n Q represents the distance between the scattering point Q and the mth transmitting array element and the nth receiving array element respectively. Then, at the nth receiving array element, the baseband echo signal of the scattering point Q is expressed as:

[0014]

[0015] Where n = 0, 1, ..., N 2 -1, λ, c and σ q are the wavelength, wave speed and scattering coefficient Q respectively;

[0016] S1.2. Adjust the baseband echo based on prior information:

[0017] Let O be the reference point on the target, is the unit vector of the target sight direction, assuming that O and is known. By using the prior information of the reference point and the target sight direction, the transmission signal time of different transmitting array elements and the recording time of different receiving signals are adjusted. At this time, the baseband echo signal of the scattering point Q is expressed as:

[0018]

[0019] S1.3. Realize envelope alignment adjustment for far-field targets:

[0020] Using approximation The baseband echo signal after envelope alignment is expressed as:

[0021]

[0022] in,

[0023] S1.4. Convert the three-dimensional image into a one-dimensional vector to obtain a three-dimensional imaging model:

[0024] definition:

[0025]

[0026] The three-dimensional imaging model is:

[0027]

[0028] It can be expressed as:

[0029] y(t)=σ q ab T Φ(t-τ q ) (8)

[0030] Preferably, the method for implementing three-dimensional imaging based on the three-dimensional imaging model (8) proposed in S1 is as follows:

[0031] Let Y be the matrix form of y(t) after discrete sampling in the time domain, y=vec(Y) is the vector form of Y, Ψ q =vec[ab T Φ(t-τ q )] is a basis vector that divides the three-dimensional imaging area into grids and then forms the scattering coefficient vector of each grid:

[0032] σ=[σ1,…,σ q , …, σ U ] T (9)

[0033] Basis matrix:

[0034] Ψ=[Ψ1,…,Ψ q ,…,ΨU ] (10)

[0035] Where U is the total number of grids in the imaging area, and the dimension of Ψ is expressed as is the discrete sampling number of the time domain signal;

[0036] The received discrete signal is represented by a vector form y=Ψσ, σ is solved by a one-dimensional sparse recovery algorithm, and then three-dimensional imaging is performed.

[0037] Preferably, in S2, if Figure 5 As shown in FIG. 1 , the steps of converting the MIMO radar three-dimensional imaging model into a multi-dimensional tensor model are as follows:

[0038] S2.1. Envelope pre-adjustment and phase pre-compensation are performed on the transmission signal of the MIMO radar, and envelope adjustment and phase compensation are performed on the target echo of the MIMO radar:

[0039] definition:

[0040]

[0041] Taking a0 and b0 as reference vectors and using a0 for phase compensation, the received signal is expressed as:

[0042]

[0043] Where ⊙ represents the Hadamard product, The phase of the (m, n)th element of is 2π(T m O+R n OT m QR n Q) / λ,T m O+R n OT m QR n Q is further expressed as:

[0044]

[0045] Where r = T0O, according to Figure 2 The configuration shown, T m and R n The positions are expressed as (2m1Nd, 2m2Nd, 0)+P T and (2n1d, 2n2d, 0)+P R , where P T and P R are the positions of T0 and R0, m1 = 0, 1, ..., M-1; m2 = 0, 1, ..., M-1; n1 = 0, 1, ..., N-1; n2 = 0, 1, ..., N-1;

[0046] So we have:

[0047]

[0048] definition:

[0049]

[0050] Then formula (14) can be further expressed as:

[0051]

[0052] Before transmitting, phase compensation is performed on the transmitting signal, and the transmitting signal is Then the received signal of the receiving antenna in the n1th row and n2th column is expressed as:

[0053]

[0054] in,

[0055] S2.2. Divide the imaging area into several unambiguous sub-areas:

[0056] and The unambiguous distances are W x =λr / 2d and W y =λr / 2d, so:

[0057]

[0058] Formula (18) is and The periodic functions of x / N,W y / N;

[0059] definition:

[0060]

[0061] Formula (19) is also a and The periodic functions of x / N,W y / N;

[0062] Then the unblurred imaging area Divided into N×N parts, each part is further divided into Sub-parts, total sub-regions, The value of is determined by the two-dimensional lateral resolution of the image. like Figure 3 As shown, N = 2, Example:

[0063] Define and for and The distance between grids in the direction The sub-regions are reorganized into A set, defined as:

[0064]

[0065] Indicates A set of sub-regions, where p1 = 0, 1, ..., N-1; p2 = 0, 1, ..., N-1, for The coordinates of any scattering point in the X and Y axes are

[0066] Will and W y Substituting into formula (18), we get:

[0067]

[0068] Then Corresponding for:

[0069]

[0070] S2.2. Components of building a multidimensional tensor model

[0071] Consider a The echo of the scattering point at the (n1, n2)th receiving array element is re-expressed as:

[0072]

[0073] Therefore, the scattering point echoes at all receiving array elements can be written in matrix form:

[0074]

[0075] in, The n1th element of is The n2th element of is

[0076] Assuming that the area And the delay is τ qThe scattering matrix of the scattering points is is located in the area The time delay is τ q The echo of the scattering point is expressed as:

[0077]

[0078] in:

[0079]

[0080] S2.3. Components of constructing a multidimensional tensor model

[0081] Taking O as the reference point, the imaging area is divided along the distance in the range [0, (T-1)cΔτ / 2], where cΔτ / 2 is the distance between the distance units and T is the number of distance units. In order to express the reflection coefficient of the three-dimensional space Using a third-order tensor Will Seen as The two-dimensional cross section of The echo from the scattering point is:

[0082]

[0083] in, × k represents the modulo-k tensor matrix product;

[0084] make for The discrete sampling form of for The discrete sampling form of formula (25) is:

[0085]

[0086] S2.4, construct component A1 of the multidimensional tensor model, A2, C, get the multidimensional tensor model:

[0087] The signal received in the entire imaging area is expressed as:

[0088]

[0089] Transform formula (27) into a tensor equation, let express An element in for A slice matrix in defines a tensor in

[0090] but can be re-expressed as:

[0091]

[0092] in:

[0093]

[0094] Further, define:

[0095]

[0096] in

[0097] Then the target echo is finally expressed by the tensor equation:

[0098]

[0099] Preferably, in S3, the steps of realizing MIMO three-dimensional imaging integrating sparsity and signal support domain prior based on a multidimensional tensor model are as follows:

[0100] S3.1. Based on sparse constraints, a solution is proposed The minimization problem is:

[0101]

[0102] in, When considering noise, the equality constraints are relaxed to inequality constraints:

[0103]

[0104] in, ε is the noise level;

[0105] S3.2. Add support domain constraints and form a solution together with sparse constraints The objective function is:

[0106] like Figure 4 As shown, The area containing the target image is called the signal support domain, which is known prior information;

[0107] Define a signal support tensor The elements in the signal support domain are 0, and the others are 1. The minimization problem is:

[0108]

[0109] in, ξ∈[0,1] is the trade-off factor;

[0110] S3.3, reconstruct the three-dimensional image and solve the real coordinates of the scattering point Q through coordinate transformation:

[0111] recover Finally, the three-dimensional image of the real target is reconstructed using the elements in the signal support domain, and the coordinates of the target are obtained. represents the projection of the scattering point Q on a set of non-orthogonal bases,

[0112] according to have:

[0113] in,

[0114] make Find the real coordinates of Q in

[0115] Preferably, in S3.3, the tensor in formula (37) is recovered by a multidimensional sparse recovery solution algorithm The steps are as follows:

[0116] S3.3.1. Definitions:

[0117]

[0118] When β→0, make Then the solution method is determined according to the value of β:

[0119] For a decreasing β, by minimizing Solve formula (37);

[0120] For β with a fixed value, the steepest descent gradient projection method is used to solve it. Each iteration consists of two steps: steepest descent and feasible domain projection. The steepest descent direction is along the negative gradient direction:

[0121]

[0122] The steepest descent result is expressed as:

[0123]

[0124] Among them, μ is the descending step size;

[0125] Will The step size is set to μβ 2 ,Will The step size is a constant μ, and the steepest descent result is expressed as:

[0126]

[0127] S3.3.2. Projection to the feasible set On, when When it falls outside the feasible set, the projection process is approximated so that Projected onto get:

[0128]

[0129] Based on the above steps, the final multi-dimensional sparse recovery (MD-SR) algorithm is as follows:

[0130] ● Initialization

[0131] 1. Order

[0132] 2. Choose a suitable descending sequence β, [β1, β2, …, β z ] and ξ, [ξ1, ξ2,…,ξ z ].

[0133] ●For ξ=1,2,…,Z:

[0134] 1. Let β = β ξ , ξ=ξ ξ

[0135] 2. In the feasible domain On the other hand, we use the L-times steepest ascent algorithm (including projection to the feasible region) to (approximately) maximize

[0136] ■ Initialization:

[0137] ■For l = 1, 2, ..., L (L is the number of iterations):

[0138] 1) Order where μ is a small positive constant;

[0139] 2) If Will Projection to the feasible domain:

[0140]

[0141] 3. Settings

[0142] The final result is

[0143] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0144] The present invention provides a MIMO three-dimensional imaging method integrating sparsity and signal support domain prior, including two paths of reshaping three-dimensional target images: a one-dimensional vector model and a multi-dimensional tensor model.

[0145] (1) The existing sparse recovery algorithm is used to directly solve the target three-dimensional image from the one-dimensional vector model, and the image quality is better than that of conventional imaging methods.

[0146] (2) By establishing a multidimensional tensor model, the target three-dimensional image is reshaped into a three-dimensional tensor. The sparsity of the signal of the strong scattering points in the imaging area is used to form a sparse constraint on the tensor model. The limited area corresponding to the target image is made into the signal support domain. The signal support domain is used as prior information to form a support domain constraint on the tensor model. Under the dual constraints of the sparse constraint and the support domain constraint, the three-dimensional image of the real target is reconstructed using the elements in the signal support domain, which can make the final image clearer and the calculation speed faster.

[0147] (3) The multidimensional sparse recovery (MD-SR) algorithm proposed in the present invention is adopted, a balancing factor ξ is added to the prior of the signal support domain, which improves the effect of sparse recovery, considers the noise level ε in the projection process, and increases the robustness of the algorithm.

[0148] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0149] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0150] Figure 1 It is a MIMI array configuration diagram of an embodiment of a MIMO three-dimensional imaging method integrating sparsity and signal support domain prior of the present invention;

[0151] Figure 2 A schematic diagram of a three-dimensional imaging geometry according to an embodiment of the present invention;

[0152] Figure 3 An imaging area division diagram according to an embodiment of the present invention;

[0153] Figure 4 For the embodiment of the present invention Schematic diagram of the signal support domain in the middle;

[0154] Figure 5 A processing flow chart of a three-dimensional imaging method according to an embodiment of the present invention;

[0155] Figure 6 is the target model of embodiment 1 of the present invention;

[0156] Figure 7 This is a schematic diagram of imaging results of a conventional method according to Example 1 of the present invention;

[0157] Figure 8 This is a schematic diagram of imaging results using the SLO method according to Example 1 of the present invention;

[0158] Fig. 9 It is a schematic diagram of signal support in the tensor model of Example 1 of the present invention;

[0159] Fig.10 Schematic diagram of imaging results using the MD-SR method in Example 1 of the present invention, (a) represents the sparse signal restored when ξ=0, (b) represents the sparse signal restored when ξ≠0; (c) is the target image reconstructed using the elements in (a); (d) is the target image reconstructed using the elements in (b);

[0160] Fig.11 The target model of Example 2 of the present invention, (a) represents a three-dimensional target geometric image; (b) represents a front view of the target model; (c) represents a top view of the target model; (d) represents a left view of the target model;

[0161] Fig.12 Schematic diagram of a three-dimensional imaging result using a conventional method according to Example 2 of the present invention, (a) represents a front view of the imaging result; (b) represents a top view of the imaging result; (c) represents a left view of the imaging result;

[0162] Fig.13 Schematic diagram of a three-dimensional imaging result using the MD-SR method according to Example 2 of the present invention, (a) represents a front view of the imaging result; (b) represents a top view of the imaging result; (c) represents a left view of the imaging result;

[0163] Fig.14 Schematic diagram of reconstructing a three-dimensional target using a conventional method according to Embodiment 2 of the present invention; (a) represents a three-dimensional geometric image; (b) represents a front view of the target model; (c) represents a top view of the target model; (d) represents a left view of the target model;

[0164] Fig.15This is a schematic diagram of reconstructing a three-dimensional target using the MD-SR (ξ≠0) method in Example 2 of the present invention; (a) represents a three-dimensional geometric image; (b) represents a front view of the target model; (c) represents a top view of the target model; and (d) represents a left view of the target model. DETAILED DESCRIPTION

[0165] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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 are within the scope of protection of the present invention.

[0166] The purpose of the present invention is to formulate technical solutions for calculating the overpressure peak value and positive pressure action time of the shock wave under the conditions of single-point explosion, multiple-point simultaneous explosion and multiple-point delayed explosion, respectively, to accurately predict the two key parameters of the overpressure peak value and positive pressure action time of the shock wave, thereby effectively shortening the test cycle, saving test costs, and improving the use efficiency of the explosion wave simulation device.

[0167] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0168] Example 1

[0169] Conduct simulation experiments on MIMO radar two-dimensional imaging.

[0170] Use a linear MIMO array and consider two-dimensional imaging. This embodiment 1 uses 4 transmitting elements and 10 receiving elements. The transmitting elements and receiving elements are evenly distributed on the Y axis, and the distances between the elements are 100m and 10m respectively. Four multi-phase coded signals with 100 code elements are transmitted. The bandwidth is 100MHz and the center frequency is 10Ghz. The target is located in the direction of [0,0,1], and the distance between the target and the radar is 15 kilometers. The target model is as follows Figure 6 As shown, the size of the dots in the figure is proportional to the RCS of the scatterer. According to the MIMO radar parameters, the range resolution of the conventional method is 1.5m and the lateral range resolution is 1.125m. The range in the re-range and lateral imaging range directions are 40m and 45m respectively.

[0171] Figure 7It represents the imaging results using the matched filter (MF) and fast Fourier transform (FFT) methods. It can be seen that there are a large number of high side lobes in the image, and the target is almost submerged in the coupled noise. When using the sparse recovery method, the preset azimuth range resolution is 0.5625m, that is, sampling 2 times super resolution. The range resolution of the sparse recovery method is not determined by the signal bandwidth, but by the size of the divided range unit. In this experiment, the range resolution is set to 0.375m. Therefore, the size of the basis matrix Ψ of the one-dimensional vector model is 5060×8480, while the size of the basis matrix C, A of the tensor model is only 506×848 and 10×80.

[0172] The SL0 algorithm is used to solve the one-dimensional vector model, and the MD-SR algorithm is used to solve the multi-dimensional tensor model. In both SL0 and MD-SR, the decreasing sequence is selected as β ζ =0.5β ζ-1 The initial value is set to four times the maximum absolute value of the initial solution, and the final value of the termination iteration is 0.01. The other parameters in the algorithm are set to L = 3, μ = 2, ε = 0. Figure 8 The following is the imaging result using SL0. It can be seen that the image obtained by SL0 is significantly improved compared with the traditional method. The CPU time of SL0 method is 496.2082s.

[0173] Fig. 9 is the signal support under the tensor model. When using MD-SR to recover sparse signals, two cases are considered: ξ≠0 and ξ=0, that is, whether the prior information of signal support is used. Using the signal support, the initial value of the trade-off factor ξ is set to 0.99, and ξ ζ =0.5ξ ζ-1 Determine the iteration value. The recovered sparse signals when ξ=0 and ξ≠0 are respectively as follows: Fig.10 As shown in (a) and (b) in Figure 1, it can be seen that when ξ≠0, the recovered signal is well confined to the signal support area, but when ξ=0, a large amount of the signal outside the support is also recovered, and the signal in the support area is weakened to a certain extent. Fig.10 (c) and (d) in the figure are respectively Fig.10 The target image reconstructed by the elements in (a) and (b). It can be seen that the reconstructed target image contains a large number of false points when ξ=0, but not when ξ≠0. This shows that the image quality can be improved by using signal support. In addition, the CPU calculation time of MD-SR (ξ=0) and MD-SR (ξ≠0) is 0.5781s and 0.5874s, respectively, which are much smaller than SL0.

[0174] Example 2

[0175] Conduct simulation experiments on MIMO radar three-dimensional imaging.

[0176] This experiment used 2 2 20 2 The distance between the transmitting and receiving elements is 100 meters and 10 meters respectively. In the experiment, 4 multi-phase coded signals of 100 code elements are transmitted, and the sub-pulse width is 100μs. The carrier frequency is 10GHz. The target is 15 kilometers away from the radar and is located in the direction of [0.2491, 0.4983, 0.8305]. The three-dimensional model of the target is as follows: Fig.11 As shown, the size of the point is proportional to the amplitude of the scatterer. Adding the standard deviation σ to the radar echo n The output signal-to-noise ratio (SNR) is defined as Where α is the scatterer amplitude, M 2 ,N 2 is the number of transmitting array elements and receiving array elements, K' is the code length. The output signal-to-noise ratio of the minimum scattering point is 31.2495dB (σ n =10.9653). The imaging ranges in the range and lateral range directions are 25m and 45×45m respectively, and the preset range and lateral range resolutions are 0.375m and 0.5625m respectively.

[0177] In the tensor model, the matrices of A1, A2, and C are 20×80, 20×80, and 466×1056, respectively. However, in the one-dimensional vector model, the dimension of the basis matrix Ψ is 186400×422400. Since the one-dimensional vector model requires a huge storage space, it cannot be calculated under general computing conditions. The MD-SR algorithm is used to solve the tensor model. Some parameters are set to β Z =1×10 -4 ,ξ1=0.99,ξ ζ =0.1ξ ζ-1 , ε=2.85×10 4 , other parameters are the same as those in Example 1. Fig.12 and Fig.13 These are three views of the imaging results of the conventional method and the MD-SR method. It can be seen that the results of the MD-SR method have lower edge values ​​and higher resolution. 300 strong scatterers are extracted from the 3D imaging results, and the coordinates are transformed according to the method in Section 3 to reconstruct the 3D target. The results are shown in Fig.14 and Fig.15 As shown in the figure. By comparing the reconstructed target with the target model, it can be seen that the traditional method has a large number of false points. The reconstructed target using MD-SR contains fewer false points and can accurately reproduce the true shape and size of the target model. The calculation time of the conventional method and the MD-SR method is 0.1795s and 50.0102s respectively.

[0178] According to the above test results, it can be seen that the imaging effect obtained by using the SL0 algorithm to solve the one-dimensional vector model is better than the conventional matched filter (MF) and fast Fourier transform (FFT) methods. In this process, the three-dimensional image is first converted into a one-dimensional vector through the three-dimensional imaging model, and then the one-dimensional vector is reconstructed through the one-dimensional sparse recovery algorithm. However, this method takes a long time because the dimension of the basis matrix Ψ in the solution process is too high. For general three-dimensional imaging situations, the matrix dimension is an extremely large value. Assuming that the number of receiving array elements is 10 2 , the number of signal samples is 400, and the number of grids in the 3D imaging area is 100 3 , then the number of elements of Ψ is 4×10 10 , which will take up a lot of memory space and computing time.

[0179] The imaging effect obtained by using the MD-SR algorithm to solve the multidimensional tensor model is optimal, with lower edge values ​​and higher resolution. It can accurately reproduce the true shape and size of the target model, and its CPU calculation time is much shorter than the calculation time required by the SL0 algorithm to solve the one-dimensional vector model.

[0180] The remaining technical features in the above embodiments can be flexibly selected by those skilled in the art according to actual conditions to meet different specific practical needs. However, it is obvious to those skilled in the art that it is not necessary to adopt these specific details to implement the present invention. In other examples, in order to avoid confusing the present invention, the well-known components, structures or parts are not specifically described, which are all within the technical protection scope defined by the technical solution claimed for protection in the claims of the present invention.

[0181] Modifications and changes made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the scope of protection of the claims attached to the present invention. In the above description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details are not necessary to practice the present invention. In other examples, in order to avoid confusing the present invention, well-known technologies, such as specific construction details, operating conditions and other technical conditions, are not specifically described.

[0182] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A MIMO three-dimensional imaging method integrating sparsity and signal support domain prior, characterized in that: Here are the steps: S1. Construct MIMO radar three-dimensional imaging model; S2, converting the MIMO radar three-dimensional imaging model into a multi-dimensional tensor model; S3. Based on the multidimensional tensor model, MIMO three-dimensional imaging that integrates sparsity and signal support domain priors is realized; the optimization problem under the constraints of sparsity and signal support domain priors is solved by a multidimensional sparse recovery solution algorithm.

2. The MIMO 3D imaging method integrating sparsity and signal support domain prior according to claim 1, characterized in that: In S1, the steps to construct the MIMO radar 3D imaging model are as follows: S1.

1. Establish the MIMO radar's transceiver array and solve the baseband echo of the scattering point: Build M 2 Send N 2 The MIMO array includes M 2 transmit array elements and N 2 There are N receiving array elements, 2 The receiving array elements form a square receiving array, the distance between each element is 2d, and the center of the array is located at the origin of the coordinate system; Assume that the MIMO radar transmits a set of large time-bandwidth product signals with the same center frequency. is the mth baseband transmission signal, where t is the fast time, Q is a scattering point in the far-field target, and T m Q, R n Q represents the distance between the scattering point Q and the mth transmitting array element and the nth receiving array element respectively. Then, at the nth receiving array element, the baseband echo signal of the scattering point Q is expressed as: Where n = 0, 1, ..., N 2 -1, λ, c and σ q are the wavelength, wave speed and scattering coefficient Q respectively; S1.

2. Adjust the baseband echo based on prior information: Let O be the reference point on the target, is the unit vector of the target sight direction, assuming that O and is known. By using the prior information of the reference point and the target sight direction, the transmission signal time of different transmitting array elements and the recording time of different receiving signals are adjusted. At this time, the baseband echo signal of the scattering point Q is expressed as: S1.

3. Realize envelope alignment adjustment for far-field targets: Using approximation The baseband echo signal after envelope alignment is expressed as: in, S1.

4. Convert the three-dimensional image into a one-dimensional vector to obtain a three-dimensional imaging model: definition: The three-dimensional imaging model is: It can be expressed as: y(t)=σ q ab T Φ(t-τ q ) (8).

3. The MIMO 3D imaging method integrating sparsity and signal support domain prior according to claim 2, characterized in that: In S2, the steps of converting the MIMO radar three-dimensional imaging model into a multi-dimensional tensor model are as follows: S2.

1. Envelope pre-adjustment and phase pre-compensation are performed on the transmission signal of the MIMO radar, and envelope adjustment and phase compensation are performed on the target echo of the MIMO radar: definition: Taking a0 and b0 as reference vectors and using a0 for phase compensation, the received signal is expressed as: Where ⊙ represents the Hadamard product, The phase of the (m,n)th element of is 2π(T m O+R n OT m QR n Q) / λ,T m O+R n OT m QR n Q is further expressed as: Where r = T0O, T m and R n The positions are expressed as (2m1Nd, 2m2Nd, 0) + P T and (2n1d, 2n2d, 0) + P R , where P T and P R are the positions of T0 and R0, m1=0,1,…,M-1; m2=0,1,…,M-1; n1=0,1,…,N-1; n2=0,1,…,N-1; So we have: definition: Then formula (14) can be further expressed as: Before transmitting, phase compensation is performed on the transmitting signal, and the transmitting signal is Then the received signal of the receiving antenna in the n1th row and n2th column is expressed as: in, S2.

2. Divide the imaging area into several unambiguous sub-areas: and The unambiguous distances are W x =λr / 2d and W y =λr / 2d, so: Formula (18) is and The periodic functions of x / N,W y / N; definition: Formula (19) is also a and The periodic functions of x / N,W y / N; Then the unblurred imaging area Divided into N×N parts, each part is further divided into Sub-parts, total sub-regions, The value of is determined by the two-dimensional lateral resolution of the image. Define and for and The distance between grids in the direction The sub-regions are reorganized into A set, defined as: Indicates A set of sub-regions, where p1 = 0, 1, ..., N-1; p2 = 0, 1, ..., N-1, for The coordinates of any scattering point in the X and Y axes are Will W x and W y Substituting into formula (18), we get: Then Corresponding for: S2.

2. Components of building a multidimensional tensor model Consider a The echo of the scattering point at the n1, n2)th receiving array element is re-expressed as: Therefore, the scattering point echoes at all receiving array elements can be written in matrix form: in, The n1th element of is The n2th element of is Assuming that the area And the delay is τ q The scattering matrix of the scattering points is In the area The time delay is τ q The echo of the scattering point is expressed as: in: S2.

3. Components of building a multidimensional tensor model Taking O as the reference point, the imaging area is divided along the distance in the range [0, (T-1) cΔτ / 2], where cΔτ / 2 is the distance between the distance units and T is the number of distance units. In order to express the reflection coefficient of the three-dimensional space Using a third-order tensor Will Seen as The two-dimensional cross section of The echo from the scattering point is: in, ×k represents the modulo-k tensor matrix product; make for The discrete sampling form of for The discrete sampling form of formula (25) is: S2.4, building components of the multidimensional tensor model A1, A2,C, get the multidimensional tensor model: The signal received in the entire imaging area is expressed as: Transform formula (27) into a tensor equation, let express An element in for A slice matrix in defines a tensor in but can be re-expressed as: in: Further, define: in Then the target echo is finally expressed by the tensor equation:

4. The MIMO 3D imaging method integrating sparsity and signal support domain prior according to claim 3, characterized in that: In S3, based on the multidimensional tensor model, the steps to achieve MIMO 3D imaging that integrates sparsity and signal support domain priors are as follows: S3.

1. Based on sparse constraints, a solution is proposed The minimization problem is: in, When considering noise, the equality constraints are relaxed to inequality constraints: in, ε is the noise level; S3.

2. Add support domain constraints and form a solution together with sparse constraints The objective function is: The region of g containing the target image is called the signal support domain, which is known prior information; Define a signal support tensor The elements in the signal support domain are 0, and the others are 1. The minimization problem is: in, ξ∈[0,1] is the trade-off factor; S3.3, reconstruct the three-dimensional image and solve the real coordinates of the scattering point Q through coordinate transformation: recover Finally, the three-dimensional image of the real target is reconstructed using the elements in the signal support domain, and the coordinates of the target are obtained. represents the projection of the scattering point Q on a set of non-orthogonal bases, according to have: in, make Find the real coordinates of Q in 5. The MIMO 3D imaging method integrating sparsity and signal support domain prior according to claim 4, characterized in that: In S3.3, the tensor in formula (37) is recovered by the multidimensional sparse recovery algorithm The steps are as follows: S3.3.

1. Definitions: When β→0, make Then the solution method is determined according to the value of β: For a decreasing β, by minimizing Solve formula (37); For β with a fixed value, the steepest descent gradient projection method is used to solve it. Each iteration consists of two steps: steepest descent and feasible domain projection. The steepest descent direction is along the negative gradient direction: The steepest descent result is expressed as: Among them, μ is the descending step size; Will The step size is set to μβ 2 ,Will The step size is a constant μ, and the steepest descent result is expressed as: S3.3.

2. Projection to the feasible set On, when When it falls outside the feasible set, the projection process is approximated so that Projected onto get:

6. The MIMO three-dimensional imaging method integrating sparsity and signal support domain prior according to claim 2, characterized in that: The method for implementing three-dimensional imaging based on the three-dimensional imaging model (8) proposed by S1 is as follows: Let Y be the matrix form of y(t) after discrete sampling in the time domain, y=vec(Y) is the vector form of Y, Ψ q =vec[ab T Φ(t-τ q )] is a basis vector that divides the three-dimensional imaging area into grids and then forms the scattering coefficient vector of each grid: σ=[σ1,…,σ q ,…,s U ] T (9) Basis matrix: Ψ=[Ψ1,…,Ψ q ,…,Ψ U ] (10) Where U is the total number of grids in the imaging area, and the dimension of Ψ is expressed as is the discrete sampling number of the time domain signal; The received discrete signal is represented by a vector form y=Ψσ, σ is solved by a one-dimensional sparse recovery algorithm, and then three-dimensional imaging is performed.

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