Matrix completion sparse meshless chromatography SAR (Synthetic Aperture Radar) super-resolution three-dimensional imaging method

Abstract

The invention discloses a matrix completion sparse meshless chromatography SAR (Synthetic Aperture Radar) super-resolution three-dimensional imaging method, which comprises the following steps of: constructing a multi-channel observation vector in a data field, and then further constraining an observation signal in an MMV (Modulation Modulation Virtualization) into a Hankel Lift matrix with a joint low-rank structure characteristic by utilizing an elevation consistency hypothesis between neighborhood pixels. And constructing a corresponding low-rank matrix completion model in combination with the tomographic SAR signal model. And modeling is carried out on the joint matrix completion problem. The model is solved based on a symmetric projection gradient descent algorithm, Root-Music solution is utilized to obtain elevation normalization frequency, the normalization frequency is inverted to obtain elevation information, and a scene three-dimensional imaging result is obtained by combining distance-orientation two-dimensional information of a target scene. According to the method, the elevation information of the tomographic SAR model is solved through a joint matrix completion method, tomographic SAR three-dimensional point cloud imaging is realized, a clear and complete imaging result is obtained, and a good miscellaneous point suppression effect is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of radar signal processing, and in particular to a matrix completion sparse gridless tomography SAR super-resolution three-dimensional imaging method. Background Art

[0002] As an all-day, all-weather active microwave remote sensing detection system, Synthetic Aperture Radar (SAR) has been widely used in many fields such as terrain mapping, environmental monitoring and reconnaissance. SAR uses the relative motion between the radar platform and the target to form a virtual aperture, thereby achieving high-resolution imaging. The 2D complex image obtained by traditional SAR imaging is essentially the projection of the 3D spatial scene on a 2D plane, which inevitably brings problems such as overlap and geometric distortion. For the same scene, Tomographic SAR (Tomographic SAR) can reconstruct the 3D structure of the scene target based on acquiring multiple 2D SAR images at different incident angles.

[0003] For tomographic SAR, due to the limitation of the elevation aperture, the resolution of its elevation dimension is usually much lower than the resolution of the distance and azimuth dimensions. For example, the distance and azimuth resolution of airborne SAR can reach the centimeter and decimeter level, but the elevation resolution is only about tens of meters. Therefore, how to effectively improve the elevation resolution is a key issue in promoting the application of tomographic SAR imaging. Generally speaking, the observation scene has a sparse distribution characteristic in the elevation dimension, so super-resolution imaging methods such as compressed sensing (CS) are feasible. However, the classic grid CS algorithm generally represents the sparsity of the signal through a pre-set over-complete discrete sparse dictionary, that is, it assumes that all scatterers are located on a pre-designed grid, which inevitably leads to discrete errors and sparse orthogonal basis mismatch problems, and the super-resolution imaging performance is limited.

[0004] In order to further improve the super-resolution performance, the sparsity of the signal can be exploited by gridless constraints, thereby avoiding problems such as discrete errors. Currently, the commonly used gridless constraints include atomic norm minimization (ANM) and matrix completion (MC). At present, ANM has been widely used in gridless tomographic SAR super-resolution imaging tasks, but it usually faces the challenges of high computational complexity and data homogenization. In contrast, MC methods have not yet been applied to tomographic SAR imaging tasks. According to MC theory, the low rank of the observation data in the data domain is actually equivalent to the sparsity of the sparse domain in the CS method. Therefore, through this binary equivalence, the target observation signal can be constrained to a low rank in the data domain, thereby avoiding the limitation of discrete sparse basis. At the same time, compared with the common practice of using convex optimization algorithms to solve ANM models, several efficient non-convex optimization algorithms have been proposed for MC problems. These non-convex algorithms usually have higher solution efficiency than convex optimization algorithms such as the alternating direction multiplier method. Summary of the invention

[0005] Technical problem: In order to further improve the three-dimensional reconstruction performance of tomographic SAR, the present invention provides a matrix completion sparse gridless tomographic SAR super-resolution three-dimensional imaging method, which can improve the reconstruction performance of three-dimensional point cloud of tomographic SAR.

[0006] Technical solution: In order to achieve the above-mentioned invention object, the present invention provides a matrix completion sparse gridless tomographic SAR super-resolution three-dimensional imaging method, comprising the following steps:

[0007] Step 1, construct a multi-channel observation vector MMV in the data domain;

[0008] Step 2, using the elevation consistency assumption between neighboring pixels, the observation signal in the multi-channel observation vector MMV is further constrained to a Hankel Lift matrix with joint low-rank structural characteristics;

[0009] Step 3, based on the constructed Hankel Lift matrix, a low-rank matrix completion model corresponding to tomographic SAR is proposed to describe the three-dimensional reconstruction process of SAR images;

[0010] Step 4, transform the low-rank matrix completion model into a joint matrix completion problem, and systematically express its optimization objectives and constraints;

[0011] Step 5: Solve the joint matrix completion problem model based on the symmetric projection gradient descent algorithm to obtain the SAR image three-dimensional reconstruction super-resolution result.

[0012] In step 1, constructing a multi-channel observation vector MMV in the data domain includes:

[0013] Since the discrete model of traditional tomographic SAR elevation inversion is expressed as

[0014] g=Aγ+n

[0015] Where g=[g1,g2,…,g M ] T is the observation vector, A is the neighborhood-shared steering matrix γ = [γ1,…,γ L ]] T is the backscattering coefficient vector, n is the additive Gaussian white noise, and the observation vector is constructed into a multi-channel observation signal matrix according to the neighborhood.

[0016] G=[g1,g2,...,g K ].

[0017] g1,g2,...,g K are K adjacent observation vectors.

[0018] In step 2, the multi-pixel joint solution signal model introduced by using the elevation consistency assumption between neighboring pixels is expressed as:

[0019] G=AΓ+N

[0020] Among them, A is the neighborhood-shared steering matrix, G is the multi-channel observation signal matrix constructed according to the neighborhood, Γ=[1,γ2,...,γ K ] is the backscattering matrix; where the assumed height distribution γ is approximately the same K There are K pixel units. N is the assumed additive Gaussian white noise.

[0021] In step 2, the multi-channel observation vector is further constrained to be a joint low-rank expression:

[0022]

[0023] in, Represents the square of the matrix 2-norm. To solve the result, Γ is the backscattering matrix; ζ is the penalty coefficient, A is the neighborhood-shared steering matrix, and G is the multi-channel observation signal matrix constructed according to the neighborhood.

[0024] In step 2, the process of constraining the Hankel Lift matrix with the joint low-rank structural characteristics also includes:

[0025] Assume that g corresponding to the non-uniform baseline is a complete observed uniform data Partial sampling of , introducing the linear mapping operator It can be gc Mapped to a Hankel matrix

[0026]

[0027] Wherein, n1 and n2 satisfy n1+n2-1=M, and M represents the number of partial sampling channels.

[0028] In step 3, the low-rank matrix completion model expression corresponding to tomographic SAR is constructed as follows:

[0029]

[0030] Among them, g mmv The multi-channel observation signal matrix G constructed for MMV is converted into a vector form and then passed through the Hankel operator Mapped into the enhanced low-rank structure matrix as the object of matrix completion, the subscripts k1 and k2 satisfy k1+k2-1=KN. K is the number of neighborhoods of the assumed approximate elevation, and N is the number of complete observation data channels.

[0031] In step 4, the expression obtained by modeling the joint matrix completion problem is:

[0032]

[0033] in, * represents the adjoint matrix, the operator can be regarded as a linear weighted operator. is a linear mapping operator, is the identity matrix; g mmv The multi-channel observation signal matrix G constructed for MMV is converted into a vector form; Z U , Yes The Burer-Monteiro decomposition is performed, and the subscripts U and V represent the left and right matrices respectively; p is the sampling projection operator The corresponding sampling rate.

[0034] In step 5, solving the joint matrix completion problem model based on the symmetric projected gradient descent algorithm includes:

[0035] right and Perform Takagi decomposition and get the optimization target:

[0036]

[0037] in, * represents the adjoint matrix, ZZ T yes The result of Takagi decomposition, p is the sampling projection operator The corresponding sampling rate, is the identity matrix. g mmv The multi-channel observation signal matrix G constructed for MMV is converted into a vector form; operator can be regarded as a linear weighted operator. is a linear mapping operator;

[0038] After the symmetric projected gradient descent initialization operation: Project the original factors onto a convex set The objective function gradient is:

[0039]

[0040] in, is a hard threshold operation, y is a signal, Ω is a sampling sequence set, and p is a sampling projection operator The corresponding sampling rate, operator can be regarded as a linear weighted operator. is a linear mapping operator;

[0041] Iteratively update Z:

[0042]

[0043] is the gradient result of the tth iteration of the above formula, is the projection operator, η is the iteration step; after solving the target variable Z, g can be restored by the inverse operation O .

[0044] Obtaining the SAR image three-dimensional reconstruction super-resolution result in step 5 includes:

[0045] The matrix completion result is solved by Root-Music to obtain the normalized frequency of elevation. The normalized frequency is inverted to obtain the elevation information, and the three-dimensional imaging result of the scene is obtained by combining the two-dimensional distance-azimuth information of the target scene.

[0046] Beneficial effects: Compared with the prior art, the present invention remodels the tomographic SAR super-resolution problem into a low-rank Hankel lift matrix completion model based on a gridless joint low-rank constraint, and uses a non-convex symmetric projection gradient descent algorithm to efficiently solve the model under incoherent conditions to achieve three-dimensional reconstruction. The present invention proposes an effective matrix completion method model for the tomographic SAR super-resolution problem and solves it. Compared with the traditional grid super-resolution method, the present invention can effectively avoid the discrete error and sparse orthogonal basis mismatch problems, and uses a non-convex optimization algorithm to improve the solution efficiency, thereby improving the super-resolution performance and solution efficiency of three-dimensional reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic diagram of the overall process of the matrix completion sparse gridless tomographic SAR super-resolution three-dimensional imaging method proposed in the present invention.

[0048] Figure 2 The figure is a comparison diagram of the processing results of the method of the present invention and the L1NM and ANM algorithms for Z-shaped building simulation, wherein (a) is a schematic diagram of the true value of the simulated building, (b) is the processing result of the L1NM algorithm, (c) is the processing result of the ANM algorithm, and (d) is the processing result of the present invention.

[0049] Figure 3 The figures are a comparison of the processing results of the method of the present invention and the L1NM and ANM algorithms for measured building data, where (a) is the reference result in the data set, (b) is the processing result of the L1NM algorithm, (c) is the processing result of the ANM algorithm, and (d) is the processing result of the present invention.

[0050] Figure 4 1 is a comparison chart of the processing results of satellite data by the method of the present invention and the L1NM and ANM algorithms, wherein (a) is the processing result of the L1NM algorithm, (b) is its plane section result, (c) is the processing result of the ANM algorithm, (d) is its plane section result, (e) is the processing result of the present invention, and (f) is its plane section result. DETAILED DESCRIPTION

[0051] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0052] The present invention may be implemented in many different forms and should not be considered limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0053] like Figure 1 As shown, Figure 1 The overall process diagram of a matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method proposed by the present invention is as follows:

[0054] Step 1, construct a multi-channel observation vector in the data domain;

[0055] Specifically, constructing a multi-channel observation vector in the data domain includes the following steps:

[0056] The discrete model of traditional tomographic SAR elevation inversion can be expressed as:

[0057] g=Aγ+n

[0058] in, is the observation vector, is the orientation matrix, where

[0059] As a guide

[0060] quantity, is the backscattering coefficient vector, is additive Gaussian white noise, and the observation vector is constructed into a multi-channel observation signal matrix G = [g1, g2, ..., g K ].

[0061] Step 2: Using the elevation consistency assumption between neighboring pixels, the observation signal in the MMV is further constrained to a Hankel Lift matrix with joint low-rank structural characteristics;

[0062] Specifically, using the elevation consistency assumption between neighboring pixels, the introduced multi-pixel joint solution signal model can be expressed as:

[0063] G=AP+N

[0064] Among them, A is the neighborhood shared steering matrix, G is the observation matrix, Γ=[γ1,γ2,...,γ K ] is the backscattering matrix. In the formula, it is assumed that the distribution of γ k There are K pixel units. The joint low-rank model expression constraining the observation signal is:

[0065]

[0066] in is the penalty coefficient.

[0067] Assume that g corresponding to the non-uniform baseline is a complete observed uniform data Partial sampling of , introducing the linear mapping operator It can be g c Mapped to a Hankel matrix

[0068]

[0069] Wherein, n1 and n2 satisfy n1+n2-1=M, and M represents the number of partial sampling channels.

[0070] Step 3, construct a low-rank matrix completion model corresponding to tomographic SAR;

[0071] Specifically, the constructed tomographic SAR matrix completion model expression is:

[0072]

[0073] Among them, g mmv The multi-pixel signal G constructed for MMV is converted into a vector form, and then mapped to the enhanced low-rank structure matrix as the object of matrix completion through the Hankel operator. The subscripts k1 and k2 satisfy k1+k2-1=KN, where K is the number of neighborhoods of the assumed approximate elevation. N is the number of complete observation data channels.

[0074] Step 4, modeling the joint matrix completion problem;

[0075] Specifically, the following steps are included:

[0076] The expression obtained by modeling the joint matrix completion problem is:

[0077]

[0078] Among them, the operator In the formula is the identity matrix. Z U , Yes The Burer-Monteiro decomposition is performed. p is the sampling projection operator The corresponding sampling rate.

[0079] Step 5, solving the model based on the symmetric projection gradient descent algorithm to obtain the SAR image three-dimensional reconstruction super-resolution result.

[0080] Specifically, yes and Do Takagi decomposition and record the results as:

[0081]

[0082] get

[0083]

[0084] After symmetric projection gradient descent, the initialization operation is:

[0085]

[0086] in, is a hard threshold operation, is the T that divides the column set Ω into N +1 sets with the same number of elements and no two of them intersect, where T N is the number of iterations. Project the original factors onto a convex set On the top, find the objective function gradient:

[0087]

[0088] Iteratively update Z:

[0089]

[0090] After solving the target variable Z, g can be restored by the inverse operation. O The matrix completion result is solved by Root-Music to obtain the normalized frequency of the elevation. The normalized frequency is inverted to obtain the elevation information, and the three-dimensional imaging result of the scene is obtained by combining the two-dimensional distance-azimuth information of the target scene.

[0091] In order to verify the beneficial effects of the present invention, the following experiment was carried out:

[0092] 1. Construct the simulation experimental data of L-band single-building SAR tomography, and use different algorithms to process the data set for tomographic SAR 3D imaging under the same data conditions. 2. Use different algorithms to process the SARMV3D-1.0 Yuncheng airborne data set, a public data set of the Institute of Space Information Innovation of the Chinese Academy of Sciences, for 3D imaging. 3. Use different algorithms to process the 3D imaging of the space-borne Lutan-1 data. After obtaining the 3D reconstruction results, compare the image quality reconstructed by different algorithms through structure, clarity and stray points.

[0093] The experimental results are as follows: Figure 2 , Figure 2 The simulation experiment results of SAR tomography of a single building are compared with those of L1NM, ANM and the algorithm of the present invention. It can be seen from the simulation experiment results that the present invention restores the building structure of the building most clearly and completely, with a compact structure, relatively few stray points, and the highest imaging quality. Figure 3 , Figure 3 This is a comparison chart of the imaging results of the Yuncheng dataset L1NM, ANM and the algorithm of the present invention. The present invention can clearly reconstruct the staircase structure, the positions of the rooftop and windows are clearer, and the noise is significantly reduced. Figure 4 , Figure 4 The three-dimensional imaging and slice comparison results of the Lutan-1 data set show that the building structure is clear and complete, and the noise is significantly reduced.

[0094] It should be noted that the above-described embodiments only express some implementation methods of the present invention, and the description thereof cannot be understood as limiting the scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the concept of the present invention, and these should all fall within the scope of protection of the present invention.

Claims

1. A matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method, characterized by: The following steps are included: Step 1, construct a multi-channel observation vector MMV in the data domain; Step 2, using the elevation consistency assumption between neighboring pixels, the observation signal in the multi-channel observation vector MMV is further constrained to a Hankel Lift matrix with joint low-rank structural characteristics; Step 3, based on the constructed HankelLift matrix, a low-rank matrix completion model corresponding to tomographic SAR is proposed to describe the three-dimensional reconstruction process of SAR images; Step 4, transform the low-rank matrix completion model into a joint matrix completion problem, and systematically express its optimization objectives and constraints; Step 5, solving the joint matrix completion problem model based on the symmetric projection gradient descent algorithm to obtain the SAR image three-dimensional reconstruction super-resolution result.

2. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 1, characterized in that: In step 1, constructing a multi-channel observation vector MMV in the data domain includes: Since the discrete model of traditional tomographic SAR elevation inversion is expressed as g = Aγ + n Where g = [g1, g2, ..., g M ] T is the observation vector, A is the neighborhood-shared steering matrix γ = [γ1, ..., γ L ] T is the backscattering coefficient vector, n is the additive Gaussian white noise, and the observation vector is constructed into a multi-channel observation signal matrix according to the neighborhood. G=[g1,g2,...,g K ]。 g1, g2, ..., g K are K adjacent observation vectors.

3. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 1, characterized in that: In step 2, the multi-pixel joint solution signal model introduced by using the elevation consistency assumption between neighboring pixels is expressed as: G=AΓ+N Among them, A is the neighborhood-shared steering matrix, G is the multi-channel observation signal matrix constructed according to the neighborhood, Γ = [γ1, γ2, ..., γ K ] is the backscattering matrix; where the assumed height distribution γ is approximately the same K There are K pixel units. N is the assumed additive Gaussian white noise.

4. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 3, characterized in that: In step 2, the multi-channel observation vector is further constrained to be a joint low-rank expression: in, Represents the square of the matrix 2-norm. To solve the result, Γ is the backscattering matrix; ζ is the penalty coefficient, A is the neighborhood-shared steering matrix, and G is the multi-channel observation signal matrix constructed according to the neighborhood.

5. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 4, characterized in that: In step 2, the process of constraining the Hankel Lift matrix with the joint low-rank structural characteristics also includes: Assume that g corresponding to the non-uniform baseline is a complete observed uniform data Partial sampling of , introducing the linear mapping operator It can be g c Mapped to a Hankel matrix Wherein, n1 and n2 satisfy n1+n2-1=M, and M represents the number of partial sampling channels.

6. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 5, characterized in that: In step 3, the low-rank matrix completion model expression corresponding to tomographic SAR is constructed as follows: Among them, g mmv The multi-channel observation signal matrix G constructed for MMV is converted into a vector form and then passed through the Hankel operator Mapped into the enhanced low-rank structure matrix as the object of matrix completion, the subscripts k1 and k2 satisfy k1+k2-1=KN, K is the number of neighbors of the assumed approximate elevation, and N is the number of complete observation data channels.

7. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 6, characterized in that: In step 4, the expression obtained by modeling the joint matrix completion problem is: Among them, * represents the adjoint matrix, the operator can be regarded as a linear weighted operator. is a linear mapping operator, is the identity matrix; g mmv The multi-channel observation signal matrix G constructed for MMV is converted into a vector form; Z U , Yes The Burer-Monteiro decomposition is performed, and the subscripts U and V represent the left and right matrices respectively; p is the sampling projection operator The corresponding sampling rate.

8. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 7, characterized in that: In step 5, solving the joint matrix completion problem model based on the symmetric projected gradient descent algorithm includes: right and Perform Takagi decomposition and get the optimization target: in, * represents the adjoint matrix, ZZ T yes The result of Takagi decomposition, p is the sampling projection operator The corresponding sampling rate, is the identity matrix. g mmv The multi-channel observation signal matrix G constructed for MMV is converted into a vector form; operator can be regarded as a linear weighted operator. is a linear mapping operator; After the symmetric projected gradient descent initialization operation: Project the original factors onto a convex set The objective function gradient is: in, is a hard threshold operation, y is a signal, Ω is a sampling sequence set, and p is a sampling projection operator The corresponding sampling rate, operator can be regarded as a linear weighted operator. is a linear mapping operator; Iteratively update Z: is the gradient result of the tth iteration of the above formula, is the projection operator, η is the iteration step; after solving the target variable Z, g can be restored by the inverse operation O .

9. The matrix completion sparse gridless tomographic SAR super-resolution 3D imaging method according to claim 8, characterized in that: Obtaining the SAR image three-dimensional reconstruction super-resolution result in step 5 includes: The matrix completion result is solved by Root-Music to obtain the normalized frequency of elevation. The normalized frequency is inverted to obtain the elevation information, and the three-dimensional imaging result of the scene is obtained by combining the two-dimensional distance-azimuth information of the target scene.

Images