CN115508835A - Tomography SAR three-dimensional imaging method based on blind compressed sensing - Google Patents
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Abstract
The invention discloses a tomography SAR three-dimensional imaging method based on blind compressed sensing, which relates to the technical field of tomography SAR imaging and comprises the following steps: s1: preprocessing an SAR sequence dataset acquired from an observation object region, and sequentially constructing high-latitude signals by pixels in each image and arranging the high-latitude signals into a matrix form; s2: reconstructing image information by using a blind compressed sensing frame by using the correlation of the elevation directions of adjacent azimuth-distance units, and modeling an image signal into a product of a sparse matrix and a dictionary matrix; establishing a tomography SAR imaging model based on blind compressed sensing; s3: continuously transforming and solving the imaging model; and solving the target optimization problem by using an alternative multiplier method, solving the target optimization problem through variable alternative circulation, and solving the sub-problem in a circulation mode to obtain a high-resolution tomography SAR imaging result. Aiming at the sparse target point scene, the invention can still ensure the imaging quality and reduce the complexity of the flow when the navigation number is less.
Description
Technical Field
The invention relates to the technical field of tomography SAR imaging, in particular to a tomography SAR three-dimensional imaging method based on blind compressed sensing.
Background
In tomosynthesis aperture radar (TomoSAR), a synthetic aperture principle is applied to the elevation direction, and a plurality of two-dimensional SAR images of the same scene are utilized to perform aperture synthesis from different incidence angles in the elevation direction to obtain the elevation resolution. The method can reconstruct the three-dimensional information of scatterers and invert the elevation profile, and can effectively solve the overlapping and masking effect existing when the target scattering point in the same scattering unit in two-dimensional SAR imaging is equal to the slant distance between radars, thereby realizing three-dimensional imaging. Compared with Interferometric synthetic aperture radar (InSAR), the tomography SAR imaging technology can obtain not only the elevation information of the target scatterer, but also the distribution of the scatterer in the elevation direction, and can completely recover the real three-dimensional scene.
Blind Compressed Sensing (BCS) is a sparse linear combination of high-level basis functions that models a signal as a large-scale dictionary, and the theory incorporates a dictionary construction theory, where dictionary construction refers to constructing an optimal sparse basis under sparse representation, which needs to satisfy the condition of coefficient uniqueness, and performs solution optimization to obtain a more accurate result. The traditional compressed sensing technology utilizes fixed analytic sparse transform to reconstruct an image, signals are often unknown and complex, a potential sparse model in blind compressed sensing is unknown a priori, the theory of the traditional compressed sensing technology does not assume a fixed dictionary, dictionary learning is not carried out according to prior information, but an adaptive compressed sensing model is built on the basis of dictionary replacement learning, the fact that dictionaries are needed in the sampling and recovery processes is avoided, and a sparse basis in the dictionaries corresponds to a specific scene target, so that the sparse basis in the dictionaries is not constrained by orthogonality. Therefore, the blind compressed sensing algorithm can enable the sparse model to be adaptive to the considered fixed data, and the final dictionary of the model can be suitable for all sparse images no matter how sparse basis of the images is.
The prior art discloses a full-polarization SAR super-resolution imaging method based on distributed compressed sensing, which comprises the following steps: s1: establishing a fully-polarized synthetic aperture radar signal model according to a fully-polarized channel arranged in a synthetic aperture radar; the fully polarized channels include an HH polarized channel, an HV polarized channel, and a VV polarized channel; s2: receiving corresponding backscatter echo data using each of the synthetic aperture radar fully-polarized channels; obtaining a synthetic aperture radar backscattering coefficient matrix according to backscattering echo data received by each polarization channel; s3: aiming at the problem of the super-resolution imaging of the fully-polarized synthetic aperture radar, an optimization problem model of a synthetic aperture radar backscattering coefficient matrix is established by adopting a distributed compressed sensing algorithm; s4: solving the optimization problem of the synthetic aperture radar backscattering coefficient matrix to obtain a synthetic aperture radar backscattering coefficient matrix; s5: performing super-resolution imaging processing on each polarization channel according to the synthetic aperture radar backscattering coefficient matrix to obtain a corresponding pseudo-color image; s6: and aiming at the pseudo-color images corresponding to each polarization channel, performing pseudo-color fusion by adopting a pseudo-color image fusion algorithm based on an RGB space to obtain a pseudo-color fusion image. However, the targeted target scene is a distributed target scene, a sparse point target scene cannot be processed, the imaging effect of the SAR cannot be ensured when the number of the voyages is small, and the complexity of the process is high.
Disclosure of Invention
The invention provides a tomography SAR three-dimensional imaging method based on blind compressed sensing, aiming at solving the problems that the existing target scene is a distributed target scene, a sparse point target scene cannot be processed, the imaging effect of an SAR cannot be ensured when the number of navigates is small, and the complexity of the process is high.
In order to solve the technical problems, the invention adopts the technical scheme that:
a tomography SAR three-dimensional imaging method based on blind compressed sensing comprises the following steps:
s1: : preprocessing a plurality of navigation SAR sequence data sets in the same imaging area in the obtained observation object, and constructing high-altitude signals one by pixels in each SAR image according to the sequence and arranging the high-altitude signals into a matrix form; the navigation means that the airborne SAR repeatedly flies at different height positions, the flight tracks are all straight lines, and the same scene is repeatedly observed for many times;
s2: reconstructing image information by using a blind compressed sensing frame by utilizing the correlation of the adjacent azimuth-distance unit elevation directions of an observed object, and modeling an image signal into a product of a sparse matrix and a dictionary matrix; establishing a tomography SAR imaging model based on blind compressed sensing; the image signal is an image signal in a data set after preprocessing;
s3: continuously transforming and solving the tomography SAR imaging model based on the blind compressed sensing; and solving the target optimization problem by using an alternative multiplier method, solving the target optimization problem through variable alternative circulation, and solving the sub-problem in a circulating manner to obtain a high-resolution tomography SAR imaging result.
The working principle of the invention is as follows:
the method comprises the steps of establishing a tomography SAR imaging model combined with blind compressive sensing by combining a blind compressive sensing algorithm, introducing the blind compressive sensing algorithm to process the elevation direction of an azimuth-distance unit of a target by utilizing the structural characteristic of target sparsity, combining the sparse characteristic of the target with the structural characteristic of the target, modeling an image into a product of a sparse matrix and a dictionary matrix by using a blind compressive sensing scheme, decomposing a plurality of complex problems into simple subproblems by adopting an alternating multiplier optimization algorithm, solving through variable alternation and circulation, and optimally solving the subproblems in circulation so as to obtain a high-resolution tomography SAR imaging result.
Preferably, the pretreatment comprises: single-vision complex image sequence registration, pathogen elimination, phase compensation and baseline estimation.
Preferably, the expression of the blind compressed sensing-based tomographic SAR imaging model is as follows:
in the formula (1), U is a data fidelity term and a sparse coefficient, V is a dictionary matrix, A represents a chromatographic operator of a chromatographic SAR, y is echo data, lambda is a regularization parameter, and s.t. is a constraint condition; the dictionary matrix V is added with a unit F-norm;
in the formula (1)
For ensuring data consistency;
by using non-convex terms l on U P (p<1) To promote sparsity of spatial coefficients; u and V are decoupled by introducing the constraint S = UV, where S is an auxiliary variable for UV.
Further, the solving step of the tomography SAR imaging model based on blind compressed sensing comprises the following steps:
s301: convergence of the decoupling acceleration equation is performed through variable decomposition, and a constraint Z = S is introduced, wherein Z is an auxiliary variable, and the constraint optimization problem is written as:
approximating the p penalty of U in equation (2) as
Wherein L is an auxiliary variable and β is a regularization parameter;
s302: using the enhanced lagrangian framework to enforce the constraints in S301, the expression of the AL function is:
in which Q is an auxiliary variable of V, Λ S 、Λ V 、Λ Z Is an augmented Lagrangian multiplier, Λ' S 、Λ′ V 、Λ′ Z Is the inverse of the Lagrange multiplier, beta S 、β V 、β U 、β z Is a penalty parameter, and solves variables U, V, Q, L, S and Z by using a strategy of alternately learning minimization;
s303: resolving into six subproblems, resolving all the subproblems through a minimization formula (3), resolving one variable at a time, and keeping other variables fixed; the six sub-problems include: an L sub-problem, a U sub-problem, a Q sub-problem, a V sub-problem, an S sub-problem, and a Z sub-problem.
Further, the method of resolving the L variable is as follows:
problem L: ignoring all terms that are independent of the L variable, equation (3) is written as:
solving using a contraction rule:
wherein "+" is defined as (τ) + Convergence operator of = max {0, τ }.
Further, the method of resolving the U variable is as follows:
problem of the U son: minimizing equation (3) yields a quadratic problem with respect to the U variable:
the quadratic sub-problem analytic solution is as follows:
in the formula, S n 、V n 、V′ n To solve for the process variable of U, I is the identity matrix,
is a penalty parameter.
The method for resolving the Q variable is as follows:
q, the subproblem: obtained by minimizing equation (3) with respect to the Q variable:
equation (8) is solved using the projection method specified in the following equation;
the projection equation is as follows:
if the F-norm of the Q variable is less than 1, Q = V; otherwise, the variable V is a unit F-norm; due to Q n Is through V n Scaled so that the F-norm is uniform.
Further, the method of resolving the V variable is as follows:
problem V: a quadratic question about the V variable is obtained according to equation (3):
minimizing equation (10) with respect to V yields the following closed form solution:
V n+1 ＝(β S U′ n+1 U n+1 +β V I) -1 (β S U′ n+1 S n +U′ n+1 Λ x +β V Q n+1 -Λ V ) (11)
further, the method of resolving the S variable is as follows:
s, a sub-problem: removing terms that are independent of the S variable according to equation (3) yields:
minimizing equation (12) with respect to S yields the following closed form solution:
S n+1 ＝(β S I+β Z ) -1 (β S U n+1 V n+1 -Λ s +β Z Z n +Λ Z ) (13) further, the method for resolving the Z variable is as follows:
problem Z: ignoring constants that are independent of the Z variable according to equation (3) yields:
equation (14) is a fourier domain replacement problem, which is resolved as follows:
in the formula (15), a' is an inverse operation of a, and y is echo data;
the calculation is performed by loop iteration of six subproblems to obtain the solution of formula (1).
Compared with the prior art, the invention has the beneficial effects that:
1. an alternative multiplier method is introduced to decompose the optimization algorithm into simple subproblems for a plurality of complex problems, and the subproblems are circularly optimized and solved, so that a high-resolution chromatographic SAR imaging result is obtained;
2. aiming at the sparse target point scene, when the number of the navigated objects is small, the reconstruction result of the target area can still be ensured, and the ground and canopy area imaging can be more comprehensively realized;
3. the imaging quality is ensured, and the complexity of the process is reduced.
Drawings
Fig. 1 is a flowchart of the tomography SAR three-dimensional imaging method based on blind compressed sensing.
Fig. 2 is a parameter diagram of an L-band radar system in an embodiment.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
Example 1
In this embodiment, as shown in fig. 1, a tomography SAR three-dimensional imaging method based on blind compressed sensing includes the following steps:
s1: : preprocessing a plurality of acquired SAR sequence datasets navigating through the same imaging region in an observed object, and sequentially constructing high-latitude signals one by pixels in each SAR image and arranging the high-latitude signals into a matrix form; the navigation means that the airborne SAR repeatedly flies at different height positions, the flight tracks are all straight lines, and the same scene is repeatedly observed for many times;
s2: reconstructing image information by using a blind compressed sensing frame by utilizing the correlation of the elevation directions of adjacent azimuth-distance units of an observation object, and modeling an image signal into a product of a sparse matrix and a dictionary matrix; establishing a tomography SAR imaging model based on blind compressed sensing; the image signal is an image signal in a data set after preprocessing;
s3: continuously transforming and solving the tomography SAR imaging model based on the blind compressed sensing; and solving the target optimization problem by using an alternative multiplier method, solving the target optimization problem through variable alternative circulation, and solving the sub-problem in a circulation mode to obtain a high-resolution tomography SAR imaging result.
The working principle of the invention is as follows:
in the tomography SAR imaging process, too many voyages increase the calculated amount and complexity, and too few voyages affect the imaging quality;
the method comprises the steps of establishing a tomography SAR imaging model combined with blind compressive sensing by combining a blind compressive sensing algorithm, introducing the blind compressive sensing algorithm to process the elevation direction of an azimuth-distance unit of a target by utilizing the structural characteristic of target sparsity, combining the sparse characteristic of the target with the structural characteristic of the target, modeling an image into a product of a sparse matrix and a dictionary matrix by using a blind compressive sensing scheme, decomposing a plurality of complex problems into simple subproblems by adopting an alternating multiplier optimization algorithm, solving through variable alternation and circulation, and optimally solving the subproblems in circulation so as to obtain a high-resolution tomography SAR imaging result.
In this embodiment, the preprocessing includes: single-vision complex image sequence registration, pathogen elimination, phase compensation and baseline estimation.
Specifically, the expression of the tomography SAR imaging model based on blind compressed sensing is as follows:
in the formula (1), U is a data fidelity term and a sparse coefficient, V is a dictionary matrix, A represents a chromatographic operator of a chromatographic SAR, y is echo data, lambda is a regularization parameter, and s.t. is a constraint condition; the dictionary matrix V is added with a unit F-norm;
in the formula (1)
For ensuring data consistency;
by using non-convex terms l on U P (p<1) To promote sparsity of spatial coefficients; u and V are decoupled by introducing the constraint S = UV, where S is an auxiliary variable for UV.
More specifically, the solving step of the blind compressed sensing-based tomographic SAR imaging model in S3 is as follows:
s301: convergence of the decoupling acceleration equation is performed through variable decomposition, and a constraint Z = S is introduced, wherein Z is an auxiliary variable, and the constraint optimization problem is written as:
approximating the p penalty of U in equation (2) as
Where L is an auxiliary variable and β is a regularization parameter;
s302: using the enhanced lagrangian framework to enforce the constraints in S301, the expression of the AL function is:
in which Q is an auxiliary variable of V, Λ S 、Λ V 、A z Is an augmented Lagrangian multiplier, Λ' S 、Λ′ V 、Λ′ z Is the inverse of the Lagrange multiplier, beta S 、β V 、β U 、β Z Is a punishment parameter, and solves variables U, V, Q, L, S and Z by using a strategy of alternately learning minimization;
s303: resolving into six subproblems, resolving all the subproblems through a minimization formula (3), resolving one variable at a time, and keeping other variables fixed; the six sub-problems include: an L sub-problem, a U sub-problem, a Q sub-problem, a V sub-problem, an S sub-problem, and a Z sub-problem.
Example 2
In the embodiment, based on the tomographic SAR three-dimensional imaging method based on blind compressed sensing in embodiment 1, six sub-problems and the analytic methods thereof are as follows:
the method of resolving the L variable is as follows:
problem L: ignoring all terms that are independent of the L variable, equation (3) is written as:
solving using a contraction rule:
in the formula, "+" is defined as (tau) + Convergence operator of = max {0, τ }.
The method for resolving the U variable is as follows:
problem of the U son: minimizing equation (3) yields a quadratic problem with the U variable:
the quadratic sub-problem analytic solution is as follows:
in the formula, S n 、V n 、V′ n To solve for the process variable of U, I is the identity matrix,
is a penalty parameter.
The method for resolving the Q variable is as follows:
q, problem: obtained by minimizing equation (3) with respect to the Q variable:
equation (8) is solved using the projection method specified in the following equation;
the projection equation is as follows:
if the F-norm of the Q variable is less than 1, Q = V; otherwise, the variable V is a unit F-norm; due to Q n Is through V n Scaled so that the F-norm is uniform.
The method for resolving the V variable is as follows:
problem V: the quadratic problem with the V variable is found from equation (3):
minimizing equation (10) with respect to V yields the following closed form solution:
V n+1 ＝(β S U′ n+1 U n+1 +β V I) -1 (β S U′ n+1 S n +U′ n+1 Λ x +β V Q n+1 -Λ V ) (11)
the method for resolving the S variable is as follows:
s sub-problem: removing terms that are independent of the S variable according to equation (3) yields:
minimizing equation (12) with respect to S yields the following closed form solution:
S n+1 ＝(β S I+β Z ) -1 (β S U n+1 V n+1 -Λ s +β Z Z n +Λ Z ) (13)
the method for resolving the Z variable is as follows:
problem Z: ignoring constants that are independent of the Z variable according to equation (3) yields:
equation (14) is a fourier domain replacement problem, which is resolved as follows:
in the formula (15), a' is an inverse operation of a, and y is echo data;
the calculation is performed by loop iteration of six subproblems to obtain the solution of formula (1). After the blind compressive sensing-based tomography SAR imaging model is solved, a high-resolution tomography SAR imaging result is obtained; the imaging quality is ensured, and meanwhile, the complexity of the flow and the complexity of calculation are reduced.
Example 3
Constructing a relevant experiment based on the blind compressed sensing-based chromatography SAR three-dimensional imaging method described in the embodiment 1 and the embodiment 2;
as shown in fig. 2, the experimental data is L-band data of HV polarization channel provided by an airborne F-SAR system of the germany space agency (Deutsches zentrum fur Luftund Raumfahrt, DLR), and the acquisition region is a partial region of distance bits of the germany trockenborn; the area is mainly composed of forests and flat ground.
In this example, the experiment was carried out using the parameters:
the radar center frequency of the experimental parameters is 1.325GHz, the azimuth resolution is 0.4m, the range resolution is 1.5m, and different types of methods are used for reconstructing data, wherein the methods are a classical spectrum estimation algorithm CAPON compressed sensing method and a chromatography SAR imaging method based on a blind compressed sensing method;
in this embodiment, the effectiveness of the imaging method is described by Mean Squared Error (MSE), when the signal-to-noise ratio is 5dB, the Mean Squared Error value of the imaging method is 0.0610, the Mean Squared Error value of capon is 0.0932, and the Mean Squared Error value of cs is 0.0854; when the signal-to-noise ratio is 25dB, the mean square error value of the imaging method is 0.0132, the mean square error value of CAPON is 0.0297, and the mean square error value of CS is 0.0215; compared with other methods, CAPON has larger error and is not stable enough, CS and the imaging method have the tendency of gradual reduction along with the change of signal to noise ratio, but the imaging method has lower mean square error and more stable imaging result. Therefore, compared with the traditional method, the imaging method can more accurately detect the ground and crown regions in the data, and the reconstruction precision of the target region is higher.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A chromatography SAR three-dimensional imaging method based on blind compressed sensing is characterized by comprising the following steps:
s1: preprocessing a plurality of acquired SAR sequence datasets navigating through the same imaging region in an observed object, and sequentially constructing high-latitude signals one by pixels in each SAR image and arranging the high-latitude signals into a matrix form;
s2: reconstructing image information by using a blind compressed sensing frame by utilizing the correlation of the elevation directions of adjacent azimuth-distance units of an observation object, and modeling an image signal into a product of a sparse matrix and a dictionary matrix; establishing a tomography SAR imaging model based on blind compressed sensing; the image signal is an image signal in a data set after preprocessing;
s3: continuously transforming and solving the tomography SAR imaging model based on blind compressed sensing; and solving the target optimization problem by using an alternative multiplier method, solving the target optimization problem through variable alternative circulation, and solving the sub-problem in a circulating manner to obtain a high-resolution tomography SAR imaging result.
2. The method for tomographic SAR three-dimensional imaging based on blind compressed sensing as claimed in claim 1, wherein the preprocessing comprises: single-vision complex image sequence registration, pathogen elimination, phase compensation and baseline estimation.
3. The method as claimed in claim 1, wherein the expression of the blind compressed sensing-based SAR imaging model is as follows:
in the formula (1), U is a data fidelity term and a sparse coefficient, V is a dictionary matrix, A represents a chromatography operator of a chromatography SAR, y is echo data, lambda is a regularization parameter, and s.t. is a constraint condition; the dictionary matrix V is added with a unit F-norm;
in formula (1)
For ensuring data consistency;
by using non-convex terms l on U P (p<1) To promote sparsity of spatial coefficients; u and V are decoupled by introducing the constraint S = UV, where S is an auxiliary variable of UV.
4. The method according to claim 3, wherein the step of solving the blind compressed sensing-based tomographic SAR imaging model comprises:
s301: convergence of the decoupling acceleration equation is performed through variable decomposition, and a constraint Z = S is introduced, wherein Z is an auxiliary variable, and the constraint optimization problem is written as:
approximating the p penalty of U in equation (2) as
Where L is an auxiliary variable and β is a regularization parameter;
s302: the constraint in S301 is enforced using an enhanced lagrangian framework, the expression of the AL function being:
in which Q is an auxiliary variable of V, Λ S 、Λ V 、Λ Z Is an augmented Lagrangian multiplier, Λ' S 、Λ′ V 、Λ′ Z Is the inverse of the Lagrange multiplier, beta S 、β V 、β U 、β Z Is a penalty parameter, and solves the variables U, V, Q, L by using a strategy of alternately learning minimization,S、Z；
S303: resolving into six subproblems, resolving all the subproblems through a minimization formula (3), resolving one variable at a time, and keeping other variables fixed; the six sub-problems include: an L sub-problem, a U sub-problem, a Q sub-problem, a V sub-problem, an S sub-problem, and a Z sub-problem.
5. The method for tomographic SAR three-dimensional imaging based on blind compressed sensing according to claim 4, wherein the method for analyzing L variable is as follows:
l sub-problem: ignoring all terms that are independent of the L variable, equation (3) is written as:
solving using a contraction rule:
wherein "+" is defined as (τ) + Convergence operator of = max {0, τ }.
6. The method for tomographic SAR three-dimensional imaging based on blind compressed sensing according to claim 5, wherein the method for analyzing the U variable is as follows:
problem of the U son: minimizing equation (3) yields a quadratic problem with the U variable:
the quadratic sub-problem solution is as follows:
in the formula, S n 、V n 、V′ n To solve for the process variable of U, I is the identity matrix,
is a penalty parameter.
7. The method for tomographic SAR three-dimensional imaging based on blind compressed sensing according to claim 6, wherein the method for analyzing Q variable is as follows:
q, problem: obtained by minimizing equation (3) with respect to the Q variable:
equation (8) is solved using the projection method specified in the following equation;
the projection equation is as follows:
if the F-norm of the Q variable is less than 1, Q = V; otherwise, the variable V is a unit F-norm; due to Q n Is through V n Scaled so that the F-norm is uniform.
8. The method for tomographic SAR three-dimensional imaging based on blind compressed sensing of claim 7, wherein the method for analyzing V variables is as follows:
problem V: the quadratic problem with the V variable is found from equation (3):
minimizing equation (10) with respect to V yields the following closed form solution:
V n+1 ＝(β S U′ n+1 U n+1 +β V I) -1 (β S U′ n+1 S n +U′ n+1 Λ x +β V Q n+1 -Λ V ) (11)。
9. the method for tomographic SAR three-dimensional imaging based on blind compressed sensing of claim 8, wherein the method for analyzing S variable is as follows:
s, a sub-problem: removing terms that are independent of the S variable according to equation (3) yields:
minimizing equation (12) with respect to S yields the following closed form solution:
S n+1 ＝(β S I+β Z ) -1 (β S U n+1 V n+1 -Λ s +β Z Z n +Λ Z ) (13)。
10. the method for tomographic SAR three-dimensional imaging based on blind compressed sensing according to claim 9, wherein the method for analyzing Z variable is as follows:
problem Z: ignoring constants that are independent of the Z variable according to equation (3) yields:
equation (14) is a fourier domain replacement problem, which is resolved as follows:
in the formula (15), a' is an inverse operation of a, and y is echo data;
the calculation is performed by loop iteration of six subproblems to obtain the solution of equation (1).
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