A matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method

Abstract

The application discloses a kind of matrix completion sparse meshless tomography SAR super-resolution three-dimensional imaging methods, including the following steps, in data domain, construct multi-channel observation vector, then utilize the elevation consistency assumption between neighborhood pixels, the observation signal in MMV is further constrained to have the Hankel Lift matrix with joint low-rank structure characteristics.Combining tomography SAR signal model, construct corresponding low-rank matrix completion model.This joint matrix completion problem is modeled.Further based on symmetric projection gradient descent algorithm, the model is solved, and the elevation normalized frequency is obtained by using Root-Music solution, and the elevation information is obtained by inversion of normalized frequency, combined with the range-azimuth two-dimensional information of target scene, the scene three-dimensional imaging result is obtained.The elevation information of the tomography SAR model is solved by the method of joint matrix completion, the tomography SAR three-dimensional point cloud imaging is realized, the clear and complete imaging result is obtained, and good spur suppression effect is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, and particularly relates to a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method. BACKGROUND

[0002] As an all-weather and all-day active microwave remote sensing system, synthetic aperture radar (SAR) has been widely used in topographic mapping, environmental monitoring and reconnaissance and many other fields. SAR uses the relative motion between the radar platform and the target to form a virtual aperture, and then realizes high-resolution imaging. The 2D complex image obtained by traditional SAR imaging is essentially the projection of a 3D 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 multiple 2D SAR images obtained at different incident angles.

[0003] For tomographic SAR, due to the limitation of the aperture in the height direction, the resolution in the height direction is usually much lower than that in the range and azimuth directions. For example, the range and azimuth resolution of airborne SAR can reach centimeter and decimeter level, but the height resolution is only tens of meters. Therefore, how to effectively improve the height resolution is a key problem for the application of tomographic SAR imaging. Generally speaking, the observed scene has a sparse distribution in the height direction, so the compressed sensing (CS) and other super-resolution imaging methods are feasible. However, the classical grid CS algorithm generally represents the sparsity of the signal by using a pre-designed overcomplete discrete sparse dictionary, that is, it assumes that all scatterers are located on a pre-designed grid, which inevitably brings the problems of discrete error and mismatch of sparse orthogonal basis, 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 utilized by using the meshless constraint method, so as to avoid the discrete error and the like. The commonly used meshless constraint methods currently include atomic norm minimization (ANM) and matrix completion (MC). At present, the ANM has been widely applied to the meshless tomographic SAR super-resolution imaging task, but usually faces the challenges of high computational complexity and data uniformization. In comparison, the MC method has not yet been applied to the tomographic SAR imaging task. According to the MC theory, the low rank of the observation data in the data domain is actually equivalent to the sparsity in the sparse domain in the CS method. Therefore, by virtue of the binary equivalence, the low rank constraint can be imposed on the target observation signal in the data domain, so as to avoid the restriction of the discrete sparse basis. Meanwhile, in comparison with the common practice of solving the ANM model by using the convex optimization algorithm, several efficient non-convex optimization algorithms have been proposed for the MC problem. These non-convex algorithms usually have higher solving efficiency than the convex optimization algorithms based on the alternating direction multiplier method and the like. SUMMARY

[0005] TECHNICAL PROBLEM: In order to further improve the three-dimensional reconstruction performance of the tomographic SAR, the application provides a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method, which can improve the reconstruction performance of the three-dimensional point cloud of the tomographic SAR.

[0006] TECHNICAL SCHEME: In order to achieve the above application purposes, the application provides a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method, which comprises the following steps,

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

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

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

[0010] Step 4, converting the low rank matrix completion model into a joint matrix completion problem, and systematically describing the optimization objective and the constraint condition thereof;

[0011] Step 5, solving the joint matrix completion problem model based on the symmetric projection gradient descent algorithm, and obtaining the super-resolution result of the three-dimensional reconstruction of the SAR image.

[0012] The step 1 of constructing the multi-channel observation vector MMV in the data field comprises:

[0013] Since the discrete model of the traditional tomographic SAR height inversion is represented as

[0014] g=Aγ+n

[0015] Wherein, g=[g1, g2, …, g M ] T is an observation vector, A is a neighborhood-shared steering matrix γ=[γ1, …, γ L ]] T is a backscattering coefficient vector, and n is an additive Gaussian white noise.

[0016] The observation vector is constructed into a multi-channel observation signal matrix G=[g1, g2, …, g K ] according to the neighborhood.

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

[0018] In the step 2, a multi-pixel joint solution signal model is introduced according to the height consistency assumption between the neighborhood pixels, and the expression is:

[0019] G=AΓ+N

[0020] Wherein, A is a neighborhood-shared steering matrix, G is a multi-channel observation signal matrix constructed according to the neighborhood, Γ=[1, γ2, …, γ K ] is a backscattering matrix; and the assumed pixel units with approximately same height distribution γ K have K. N is an assumed additive Gaussian white noise.

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

[0022]

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

[0024] In the step 2, the Hankel Lift matrix process with the joint low-rank structure characteristics obtained by the constraint further comprises:

[0025] It is assumed that g corresponding to the non-uniform baseline is a partial sampling of a complete observation uniform data A linear mapping operator It can map gc Mapping to a Hankel matrix

[0026]

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

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

[0029]

[0030] where g mmv is the vector form of the multi-channel observation signal matrix G constructed by MMV, and is mapped to the enhanced low-rank structure matrix as a matrix completion object through a Hankel operator where the subscripts k1 and k2 satisfy k1+k2-1=KN. K is the number of the assumed approximate height neighborhood, and N is the number of complete observation data channels.

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

[0032]

[0033] where, * represents the adjoint matrix, and the operator can be regarded as a linear weighted operator, is a linear mapping operator, is a unit matrix; g mmv is the vector form of the multi-channel observation signal matrix G constructed by MMV; Z U , is obtained by Burer-Monteiro decomposition on , and the subscripts of U and V respectively represent the left and right matrices obtained; p is a sampling projection operator corresponding to the sampling rate.

[0034] The step 5 of solving the joint matrix completion problem model based on the symmetric projection gradient descent algorithm includes:

[0035] Takagi decomposition is performed on and to obtain the optimization objective:

[0036]

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

[0038] After the symmetric projection gradient descent initialization operation: project the original factor to the convex set , the gradient of the objective function is:

[0039]

[0040] where, is a hard threshold operation, y is a signal, Ω is a set of sampling sequences. p is the sampling projection operator corresponding sampling rate, operator can be regarded as a linear weighted operator, is a linear mapping operator;

[0041] Iterative 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 size; complete the solution of the target variable Z, can be restored by inverse operation g O .

[0044] The step 5 obtains the SAR image three-dimensional reconstruction super-resolution result, which includes:

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

[0046] Beneficial effects: compared with the prior art, the present application re-models the tomographic SAR super-resolution problem as a low-rank Hankel lift matrix completion model based on a meshless joint low-rank constraint, and efficiently solves the model under incoherent conditions by using a non-convex symmetric projection gradient descent algorithm to realize three-dimensional reconstruction. The present application proposes an effective matrix completion method model for the tomographic SAR super-resolution problem and solves it, which can effectively avoid the problems of discrete error and sparse orthogonal basis mismatch compared with the traditional mesh super-resolution method, and improves the solving efficiency by using a non-convex optimization algorithm, and improves the super-resolution performance and solving efficiency of three-dimensional reconstruction. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The present application proposes a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method.

[0048] Figure 2 The present application proposes a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method.

[0049] Figure 3 The present application proposes a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method.

[0050] Figure 4 The present application proposes a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method. DETAILED DESCRIPTION

[0051] The technical solutions of the present application will be further described in detail below in combination with the drawings:

[0052] The present application can be implemented in many different forms, and should not be considered limited to the embodiments described herein. On the contrary, these embodiments are provided to make the present disclosure thorough and complete, and to fully convey the scope of the present application to those skilled in the art.

[0053] As Figure 1 shown, Figure 1 The present application proposes a matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method, which includes the following steps:

[0054] Step 1: A multi-channel observation vector was constructed in the data domain;

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

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

[0057] g=Aγ+n

[0058] in, For the observation vector, For the guiding matrix, in which

[0059] For guide vector

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

[0061] Step 2: Using the elevation consistency assumption among neighboring pixels, the observed signal within the MMV is further constrained into a Hankel Lift matrix with joint low-rank structure characteristics.

[0062] Specifically, based on the assumption of consistent elevation among neighboring pixels, the multi-pixel joint signal solution model can be expressed as:

[0063] G = AP + N

[0064] Where A is the neighborhood-shared steering matrix, G is the observation matrix, and Γ=[γ1,γ2,...,γ K [ ] is the backscattering matrix. The equation assumes that γ has approximately the same elevation distribution. k There are K pixel units. The joint low-rank model expression constrained by the observed signals is:

[0065]

[0066] in This is the penalty coefficient.

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

[0068]

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

[0070] Step 3: Construct the low-rank matrix completion model corresponding to tomographic SAR;

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

[0072]

[0073] Among them, g mmv The multi-pixel signal G constructed for MMV is converted into vector form and then mapped to the enhanced low-rank structure matrix as the object of matrix completion using 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, and N is the number of complete observation data channels.

[0074] Step 4: Model the joint matrix completion problem;

[0075] Specifically, it includes the following steps:

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

[0077]

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

[0079] Step 5: Solve the model based on the symmetric projection gradient descent algorithm to obtain the super-resolution results of SAR image 3D reconstruction.

[0080] Specifically, for and Perform Takagi decomposition, and record the results as follows:

[0081]

[0082] get

[0083]

[0084] The initialization operation is performed using symmetric projection gradient descent.

[0085]

[0086] wherein, is a hard thresholding operation, is the T N +1 sets of the same number of elements and pairwise disjoint, wherein T N is the iteration number. Project the original factor onto the convex set , and solve the gradient of the objective function:

[0087]

[0088] Iteratively update Z:

[0089]

[0090] After the solution of the target variable Z is completed, the g O can be restored by the inverse operation. The matrix completion result is used to solve the elevation normalized frequency by Root-Music, the elevation information is obtained by inverting the normalized frequency, and the three-dimensional imaging result of the scene is obtained by combining the range-azimuth two-dimensional information of the target scene.

[0091] In order to verify the beneficial effects of the present application, the following experiments are carried out:

[0092] 1. Construct a simulation experiment data of L-band single building SAR tomography imaging, and use different algorithms to respectively perform tomographic SAR three-dimensional imaging processing on the data set under the same data condition. 2. Use different algorithms to respectively perform three-dimensional imaging processing on the public data set of China Academy of Space Technology Information: SARMV3D-1.0 Yuncheng airborne data set. 3. Use different algorithms to respectively perform three-dimensional imaging processing on the land exploration-1 data of satellite. After obtaining the three-dimensional reconstruction results, compare the image quality of the reconstruction images of different algorithms by structure, definition and clutter points.

[0093] The experimental results are as follows: Figure 2 , Figure 2 is a comparison chart of simulation experiment results of single building SAR tomography imaging of L1NM, ANM and the algorithm of the present application. It can be seen from the simulation experiment results that the building structure recovery of the present application is the most clear and complete, the structure is compact, the clutter points are relatively the least, and the imaging quality is the highest. Referring to Figure 3 , Figure 3 is a comparison chart of imaging results of Yuncheng data set L1NM, ANM and the algorithm of the present application, the stair structure can be clearly reconstructed by the present application, the roof and window positions are more clear, and the clutter points are significantly reduced. Referring to Figure 4 , Figure 4 is a comparison result of three-dimensional imaging and slicing of the land exploration-1 data set, the building structure of the result obtained by the present application is clear and complete, and the clutter points are significantly reduced.

[0094] It should be noted that the above-described embodiments merely express some of the embodiments of the present application, and the description cannot be understood as limiting the patent scope of the present application. It should be noted that for those skilled in the art, several improvements can be made without departing from the concept of the present application, and these should all fall within the protection scope of the present application.

Claims

1. A matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method, characterized in that: Includes the following steps, Step 1: Construct the multi-channel observation vector MMV in the data domain; Step 2: Using the elevation consistency assumption among neighboring pixels, the observation signal in the multi-channel observation vector MMV is further constrained into a Hankel Lift matrix with joint low-rank structure characteristics. 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. Step 4: Transform the low-rank matrix completion model into a joint matrix completion problem, and systematically state its optimization objective and constraints. Step 5: Solve the joint matrix completion problem model based on the symmetric projection gradient descent algorithm to obtain the super-resolution results of SAR image 3D reconstruction.

2. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 1, characterized in that: Step 1, which involves constructing the multi-channel observation vector (MMV) in the data domain, includes: Because the discrete model of traditional tomographic SAR elevation inversion is expressed as g=Aγ+n Where g = [g1, g2, ..., g M ] T Let M be the observation vector, M represent the number of partial sampling channels, and A be the neighborhood-shared steering matrix γ = [γ1, ..., γ]. L ] T Let n be the backscattering coefficient vector, and n be additive white Gaussian noise. The observation vectors are constructed into a multi-channel observation signal matrix according to their neighborhoods. G=[g1,g2,...,g K ] g1,g2,...,g K There are K neighboring observation vectors.

3. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 1, characterized in that: In step 2, the multi-pixel joint solution signal model introduced by utilizing the elevation consistency assumption among neighboring pixels is expressed as follows: G=AΓ+N Where A is the neighborhood-shared steering matrix, G is the multi-channel observation signal matrix constructed according to the neighborhood, and Γ=[γ1,γ2,…,γ K [ ] is the backscattering matrix; in the formula, it is assumed that γ has approximately the same elevation distribution. K There are K pixel units, and N is assumed additive white Gaussian noise.

4. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 3, characterized in that: In step 2, the multi-channel observation vector is further constrained into a joint low-rank expression as follows: in, This represents the square of the 2-norm of a matrix; In the formula, For the solution, 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 meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 4, characterized in that: Step 2, the process of obtaining the Hankel Lift matrix with joint low-rank structure characteristics by constraint, further includes: Assume that g corresponding to the non-uniform baseline is a complete set of uniformly observed data. Partial sampling, introducing a linear mapping operator It can g c Mapped to a Hankel matrix Where n1 and n2 satisfy n1+n2-1=M, M represents the number of partial sampling channels.

6. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 5, characterized in that: In step 3, the expression for the low-rank matrix completion model 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 vector form and then processed by 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, where K is the number of neighborhoods of the assumed approximate elevation and N is the number of complete observation data channels.

7. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 6, characterized in that: In step 4, the expression obtained by modeling the joint matrix completion problem is: Where * denotes the adjoint matrix. It is the identity matrix; g mmv The multi-channel observation signal matrix G constructed for MMV is converted into vector form; Z U , Yes The result is obtained by performing Burer-Monteiro decomposition, where U and V subscripts denote the left and right matrices, respectively; p is the sampling projection operator. The corresponding sampling rate.

8. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 7, characterized in that: Step 5, which involves solving the joint matrix completion problem model based on the symmetric projection gradient descent algorithm, includes: right and Perform Takagi decomposition to obtain the optimization objective: Where * denotes the adjoint matrix, ZZ T yes The result of the Takagi decomposition, where p is the sampling projection operator. The corresponding sampling rate, It is the identity matrix; g mmv The multi-channel observation signal matrix G constructed for MMV is converted into vector form; operators It can be viewed as a linear weighted operator. It is a linear mapping operator; Initialization operation after symmetric projection gradient descent: Project the original factor onto the convex set Above, the gradient of the objective function is: in, This is a hard thresholding operation, where y is the signal, Ω is the sampled sequence set, and p is the sampling projection operator. Corresponding sampling rate, operator It can be viewed as a linear weighted operator. It is a linear mapping operator; Iterative update Z: Let be the gradient result of the t-th iteration of the above equation. The projection operator is η, where η is the iteration step size; this completes the solution for the objective variable Z, and g can be restored through the inverse operation. O .

9. The matrix completion sparse meshless tomographic SAR super-resolution three-dimensional imaging method as described in claim 8, characterized in that: The SAR image 3D reconstruction super-resolution results obtained in step 5 include: The matrix completion result is used to solve for the elevation normalized frequency using Root-Music. The normalized frequency is then used to invert the elevation information. Combined with the distance-azimuth two-dimensional information of the target scene, the three-dimensional imaging result of the scene is obtained.

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