CN110244299B - Distributed method for SAR image recovery based on ADMM - Google Patents

Distributed method for SAR image recovery based on ADMM Download PDF

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CN110244299B
CN110244299B CN201910544976.8A CN201910544976A CN110244299B CN 110244299 B CN110244299 B CN 110244299B CN 201910544976 A CN201910544976 A CN 201910544976A CN 110244299 B CN110244299 B CN 110244299B
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CN110244299A (en
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孙丽娜
靖稳峰
朱海振
许鑫
李星
刘欢
岳广德
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Xian Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

Abstract

The invention provides a distributed method for SAR image recovery based on ADMM, which comprises the following steps: step 1, constructing an observation matrix; step 2, constructing an SAR image sparse information recovery model according to the observation matrix obtained in the step 1; step 3, designing a distributed solving algorithm based on an ADMM algorithm for the SAR image sparse information recovery model obtained in the step 2 according to a strategy of variable grouping; step 4, building a distributed solving algorithm based on the ADMM algorithm obtained by the design in the step 3 by using a Spark platform, and finally obtaining a recovered SAR image; the invention utilizes the information theory principle and the machine learning distributed algorithm to establish a compressed sensing model, and solves the sparse reconstruction target through the distributed ADMM algorithm.

Description

Distributed method for SAR image recovery based on ADMM
Technical Field
The invention relates to the technical field of radars in the electronic industry, in particular to an ADMM-based distributed SAR image recovery method.
Background
Synthetic Aperture Radar (SAR) technology has the characteristics of all-weather and all-weather, and is widely applied to the fields of environmental protection, disaster monitoring, ocean observation and the like. At present, the synthetic aperture radar technology is moving towards wider swaths to acquire high resolution images, and thus the requirements for data sampling, transmission, processing, etc. are increasing. Sparse synthetic aperture radar imaging is a new imaging mode combining a sparse information processing method with synthetic aperture radar imaging technology, and the technology accurately reconstructs a target under the sampling number far lower than the Nyquist sampling theorem by compressing and sampling and utilizing the sparsity of ground feature scenes. A Compression Sensing (CS) method is a typical sparse signal processing method developed in recent years, and can implement accurate or approximate reconstruction of a sparse signal from severely under-sampled data. In recent years, a compressed sensing technology for SAR images has great potential in the aspects of reducing radar sampling, making up for the defects of radar data, improving radar imaging quality and the like, and achieves certain results, but the method still cannot reconstruct the SAR images in a large scene. As big data distributed computing platforms are mature day by day, a new way is provided for solving the technical problem. The large-scale SAR image compression sensing problem is a practical problem to be solved urgently, and the reconstruction of the large-scale SAR scene image is realized by utilizing a large-data distributed computing technology, so that the method has very important theoretical and practical significance.
Disclosure of Invention
The invention aims to provide an ADMM-based distributed method for SAR image recovery, which solves the problem that the existing traditional method can not reconstruct a large-scene SAR image.
In order to achieve the purpose, the invention adopts the technical scheme that:
the invention provides a distributed method for SAR image recovery based on ADMM, which comprises the following steps:
step 1, constructing an observation matrix;
step 2, constructing an SAR image sparse information recovery model according to the observation matrix obtained in the step 1;
step 3, designing a distributed solving algorithm based on an ADMM algorithm for the SAR image sparse information recovery model obtained in the step 2 according to a strategy of variable grouping;
and 4, building a distributed solving algorithm based on the ADMM algorithm and designed in the step 3 by using a Spark platform, and finally obtaining the recovered SAR image.
Preferably, in step 1, the method for constructing the observation matrix is as follows: and vectorizing the two-dimensional sampling echo and the two-dimensional image to be reconstructed.
Preferably, in step 2, the mathematical expression of the SAR image sparse information recovery model is as follows:
Figure BDA0002103679160000021
s.t.y＝Ax
wherein x ∈ RnRepresenting the reconstructed signal, A ∈ Rm×nFor the constructed observation matrix y ∈ RmRepresents an observed signal; i | · | purple wind1Representing a 1-norm.
Preferably, in step 3, the distributed solving algorithm based on the ADMM algorithm is designed for the SAR image sparse information recovery model obtained in step 2 according to a strategy of variable grouping, and specifically includes:
s1, constructing a variable grouping SAR image sparse information recovery distributed model according to the SAR image sparse information recovery model obtained in the step 2;
and S2, solving the SAR image sparse information recovery distributed model by using a distributed ADMM algorithm to obtain a distributed solving algorithm based on the ADMM algorithm.
Preferably, in S1, constructing a variable-grouping SAR image sparse information recovery distributed model according to the SAR image sparse information recovery model obtained in step 2 specifically includes:
setting an SAR image sparse information recovery model to contain N independent sub-problems, and performing parallelization solution on each independent sub-problem to obtain a variable grouping SAR image sparse information recovery distributed model; the mathematical expression of the SAR image sparse information recovery distributed model is as follows:
Figure BDA0002103679160000031
Figure BDA0002103679160000032
wherein A ═ A1；A2；…；AN]，
Figure BDA0002103679160000033
λ is the regularization parameter.
Preferably, in S2, the expression of the distributed solution algorithm based on the ADMM algorithm is:
Figure BDA0002103679160000034
wherein S isλ(a) The vector obtained by acting on each component of a as represented by soft threshold operator is shown as follows:
Figure BDA0002103679160000035
githe gradient is represented by the number of lines,
Figure BDA0002103679160000036
tau, beta, gamma are initialization parameters, pnIs an iteration multiplier.
Preferably, in step 4, the distributed solving algorithm based on the ADMM algorithm, which is obtained by the design in step 3, is built by using a Spark platform, and specifically includes:
s1, initializing parameters including regularization parameters lambda, tau, beta, gamma step size stepsize and iteration precision epsilon>0, while giving the initial point x0,p0,res0；
S2, calculating a residual res ═ Ax-b by using a distributed multiplication of the matrix and the vector;
s3, calculating gradient g ═ A by matrix transposition and vector distributed multiplication*(Ax-b-p/β), wherein p is an algorithmic multiplier;
s4, updating x to soft (x-stepsize · g) by using a threshold operator;
s5, if | | xk+1-xkIf | | < epsilon, the iteration is stopped and x is outputkWherein x iskThe recovered SAR image is obtained; otherwise go to S2.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a distributed method for SAR image recovery based on ADMM, which solves the problem that the existing traditional method can not reconstruct a large-scene SAR image, and specifically comprises the following steps:
firstly, as most of sparse synthetic aperture radar imaging is processed in a time domain, the calculation complexity and memory consumption of the existing method are too high, and difficulty is brought to satellite-borne or airborne large scene imaging recovery. The invention realizes the distributed method for SAR image recovery based on ADMM by using a Spark big data platform, and solves the problem that the existing traditional method can not reconstruct the SAR image in a big scene. The method brings great potential for the field of earth remote sensing, on one hand, the method reduces the radar sampling rate and transfers the high radar storage to the hardware storage and processing on the ground, on the other hand, the technology can make up the noise and the defect of radar data, and plays an important role in improving the radar imaging quality;
secondly, the ADMM algorithm is converted into a distributed algorithm according to a variable grouping strategy, has the characteristics of easy distribution and decomposability, and can effectively solve the problems of large data scale such as compressed sensing, signal processing and control, picture storage and reconstruction and the like;
finally, a distributed model of variable grouping and a distributed ADMM solving method are provided for large-scale data, the characteristics of scalability, memory-based and the like of a Spark big data platform are utilized, the iterative operation efficiency is far higher than that of other big data platforms such as MapReduce and the like, an ADMM algorithm iterative framework is efficiently fit, and the operability and the efficiency of Spark platform calculation are fully utilized.
In conclusion, the compressed sensing model is established by utilizing the information theory principle and the machine learning distributed algorithm, and the sparse reconstruction target is solved through the distributed ADMM algorithm. The compressed sensing problem of the SAR image is a hotspot problem in the field of big data, and the compressed sensing problem is combined with a machine learning distributed algorithm, so that the problems of airborne SAR images in any motion state and reconstruction of large-scale scenes can be solved, and the method has very important theoretical and practical significance and has very good popularization and application scenes.
Drawings
FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic flow chart of the present invention framework for solving sparse models using ADMM algorithm;
FIG. 3 is a schematic diagram of MapReduce of the ADMM distributed algorithm of the present invention;
fig. 4 is a diagram of the real data effect of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides an effective distributed method for restoring an SAR image based on ADMM, which establishes a radar model based on compressive sensing imaging by using a variable grouping strategy, and solves a correct reconstruction target of a sparse model by using a Spark big data platform through a distributed ADMM method, and specifically includes the following steps:
step 1, constructing an observation matrix: vectorizing the two-dimensional sampling echo and the two-dimensional image to be reconstructed;
step 2, constructing an SAR image sparse information recovery model according to the observation matrix obtained in the step 1, wherein the mathematical expression of the SAR image sparse information recovery model is as follows:
Figure BDA0002103679160000051
s.t.y＝Ax
wherein x ∈ RnRepresenting the reconstructed signal, A ∈ Rm×nFor the constructed observation matrix y ∈ RmRepresenting the observed signal. I | · | purple wind1Representing a 1-norm.
Step 3, designing a distributed solving algorithm based on an ADMM algorithm for the SAR image sparse information recovery model obtained in the step 2 according to a strategy of variable grouping;
as shown in fig. 2, specifically:
in S1, constructing a variable-grouping SAR image sparse information recovery distributed model according to the SAR image sparse information recovery model obtained in step 2, specifically including:
and setting that the SAR image sparse information recovery model comprises N independent sub-problems, and performing parallelization solution on each independent sub-problem to obtain a variable-grouping SAR image sparse information recovery distributed model. The mathematical expression of the SAR image sparse information recovery distributed model is as follows:
Figure BDA0002103679160000061
Figure BDA0002103679160000062
wherein A ═ A1；A2；…；AN]，
Figure BDA0002103679160000063
λ is the regularization parameter.
S2, solving the SAR image sparse information recovery distributed model by using a distributed ADMM algorithm, wherein the solving expression is as follows:
Figure BDA0002103679160000064
wherein soft is a soft threshold algorithm, Sλ(a) The vector obtained by acting on each component of a as represented by soft threshold operator is shown as follows:
Figure BDA0002103679160000065
githe gradient is represented by the number of lines,
Figure BDA0002103679160000066
tau, beta, gamma are initialization parameters, pnIs an iteration multiplier.
And 4, building a distributed solving algorithm based on the ADMM algorithm, which is obtained by the design in the step 3, by using the Spark platform, correcting a punishment parameter lambda of the iterative algorithm according to convergence and convergence speed, optimizing data cache, check point setting and parameter configuration in the Spark platform, and finally obtaining the recovered SAR image.
As shown in fig. 3, the distributed solving algorithm based on the ADMM algorithm, which is obtained by using the design in the Spark platform building step 3, specifically includes:
s1, initializing parameters including regularization parameters lambda, tau, beta, gamma, step size stepsize and iteration precision epsilon>0, while giving the initial point x0,p0,res0；
S2, calculating a residual res ═ Ax-b by using a distributed multiplication of the matrix and the vector;
s3, calculating gradient g ═ A by matrix transposition and vector distributed multiplication*(Ax-b-p/β), wherein p is an algorithmic multiplier;
s4, updating x to soft (x-stepsize · g) by using a threshold operator;
s5, if | | xk+1-xkIf | | < epsilon, the iteration is stopped and x is outputk，xkThe recovered SAR image is obtained; otherwise go to S2.
According to the technical scheme, the embodiment of the invention discloses an ADMM-based distributed method for SAR image recovery, which is characterized in that a compressed sensing model is established by utilizing an information theory principle and a machine learning distributed algorithm, and a sparse reconstruction target is solved through the distributed ADMM algorithm. The compressed sensing problem of the SAR image is a hotspot problem in the field of big data, and the compressed sensing problem is combined with a machine learning distributed algorithm, so that the problems of airborne SAR images in any motion state and reconstruction of large-scale scenes can be solved, and the method has very important theoretical and practical significance and has very good popularization and application scenes.
The principle of the invention is as follows:
in the prior art, an image sparse information recovery model is constructed according to the observation matrix obtained in the step 1, and an expression of the image sparse information recovery model is as follows:
Figure BDA0002103679160000071
wherein x ∈ RnRepresenting the reconstructed signal, A ∈ Rm×nFor the constructed observation matrix y ∈ RmRepresenting the observed signal.
Due to L0The problem is NP-difficult, which is usually converted to Lq(q is more than 0 and less than or equal to 1) solving the problem:
Figure BDA0002103679160000072
theoretical research of compressed sensing shows that when an observation matrix meets the properties of RIP, incoherent and the like, L can be solvedqProblem equivalence solution L0Problem and the smaller q, LpThe closer to L the solution of0But the greater the corresponding solution difficulty. With the requirement of acquiring high-resolution images, the increase of the mapping bandwidth directly causes the measurement matrix to become large, so that the measurement matrix cannot be solved under a single-machine condition, and therefore a real or approximate solution is obtained by combining a large data platform with a distributed algorithm.
When q is 0,1/2,2/3,1, the above problem has an analytic solution, and in consideration of the sparsity and solving speed of the solution, we choose a soft threshold operator (q is 1), and the above derivation is also applicable to complex space, so that it can be directly applied to synthetic aperture radar imaging.
For a large-scale problem, the convergence rate of the traditional threshold iteration method is too low, the ADMM algorithm is adopted to solve the problem, and the specific steps are as follows:
adding a regularization parameter λ, the model becomes the following form:
Figure BDA0002103679160000084
the regularization parameter λ is used to balance approximation capability with sparsity of the solution.
Introducing a multiplier p, and solving the model by using an ADMM algorithm to obtain the following calculation model:
Figure BDA0002103679160000081
wherein soft is a soft threshold operator in a specific form
softλ(a)＝sign(a)·max{0,|a|-λ}
Because the data volume is very large, the solution is carried out by using a big data distributed algorithm, because the observation matrix A is generated by columns,
considering grouping variables, the model is as follows:
minimize f1(x1)+…+fN(xN)
subject to A1x1+…+ANxN＝c,
x1∈χ1,…,xN∈χN.
suppose fi(xi) For a convex function, the augmented Lagrangian function of the above problem is
Figure BDA0002103679160000082
Wherein
Figure BDA0002103679160000083
Is a Lagrange multiplier, and rho is a penalty parameter;
thereby obtaining parallelized updates
Figure BDA0002103679160000091
The invention groups variables, considers a compressed sensing model:
Figure BDA0002103679160000092
Figure BDA0002103679160000093
solving the distributed model yields the following framework:
Figure BDA0002103679160000094
wherein, giIn order to be a gradient of the magnetic field,
Figure BDA0002103679160000095
the Spark big data platform is used for carrying out experiments, is a novel big data engine, and is mainly characterized in that distributed memory abstraction of a data set is provided, memory calculation is based on, and better support is provided for iterative data processing.
The echo information of the synthetic aperture radar image recording wave band is recorded in a binary complex form, and the corresponding amplitude and phase information can be extracted through conversion based on the complex data of each pixel. The real part and the imaginary part of the observation matrix are respectively stored in columns, and the complex number packet carried by the Spark platform occupies a memory far larger than a double-precision type, so that the memory has a great requirement.
Examples
Specific numerical operation examples and real SAR image examples are given below to illustrate the effectiveness of the algorithm, all experiments are realized on a Spark platform by using a Scala language, the cluster environment has 28 nodes, namely iNode1-iNode28, the available memory of each node is 256G, 12 cores, the available total memory is 4.6T, the number of cores is 324 cores, the Driver available memory is 300G, and the external available memory is 256G.
Table one: numerical calculation result
Data dimension Data size Number of iteration steps Accuracy of measurement Time of use
(500000*1500000) 55.9G 100 1.24e-4 138s
(512*256)*(512*512) 234.0G 100 9.00e-5 234s
(512*512)*(1024*512) 937.5G 100 8.42e-5 1309s
(3000000*6000000) 1341.1G 100 8.30e-5 1674s
Experiments prove that the algorithm is feasible and the operation speed is high under a big data Spark platform.
An example of a real SAR image is given below to verify the validity of the algorithm, the following figure is a synthetic aperture radar image of RADARSAT-1, the image is acquired at a george time of 16-th-day-2002 of 03:50 to 02:04:05, the number of the ascending track is #34522, the size of the fine mode beam 2 is 1024 × 512, a sensing matrix is obtained by using a sampling rate of 30% and is 571392 × (1024 × 512) and is complex data, and the data is stored by adopting a double-precision type to be nearly 3.6T, wherein parameters are set to be tau 10/| | y |, eta 10/| y |, lambda 0.2, and gamma is 1; FIG. 4 shows the results obtained by running 180 steps, at this point
rNorm＝0.003371 (rNorm＝||x-xold)/||x||)
In the above embodiments, the purpose, technical solutions and advantages of the present invention have been described in further detail, it should be understood that the above embodiments are merely illustrative of the present invention and are not intended to limit the present invention, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. An efficient distributed method of ADMM-based SAR image recovery, comprising the steps of:
step 1, constructing an observation matrix;
step 2, constructing an SAR image sparse information recovery model according to the observation matrix obtained in the step 1;
step 3, designing a distributed solving algorithm based on an ADMM algorithm for the SAR image sparse information recovery model obtained in the step 2 according to a strategy of variable grouping;
step 4, building a distributed solving algorithm based on the ADMM algorithm obtained by the design in the step 3 by using a Spark platform, and finally obtaining an SAR image to be recovered;
in step 3, designing a distributed solving algorithm based on an ADMM algorithm for the SAR image sparse information recovery model obtained in step 2 according to a strategy of variable grouping, specifically comprising:
s1, constructing a variable grouping SAR image sparse information recovery distributed model according to the SAR image sparse information recovery model obtained in the step 2;
s2, solving the SAR image sparse information recovery distributed model by using a distributed ADMM algorithm to obtain a distributed solving algorithm based on the ADMM algorithm;
in S1, constructing a variable-grouping SAR image sparse information recovery distributed model according to the SAR image sparse information recovery model obtained in step 2, specifically including:
setting an SAR image sparse information recovery model to contain N independent sub-problems, and performing parallelization solution on each independent sub-problem to obtain a variable grouping SAR image sparse information recovery distributed model; the mathematical expression of the SAR image sparse information recovery distributed model is as follows:
Figure FDA0003314995830000011
Figure FDA0003314995830000012
wherein A ═ A1；A2；…；AN]，
Figure FDA0003314995830000013
λ is a regularization parameter; x is formed by RnRepresenting the reconstructed signal, A ∈ Rm×nFor the constructed observation matrix y ∈ RmRepresents an observed signal; i | · | purple wind1A 1 norm representing a matrix; x is the number ofiThe ith SAR image to be restored.
2. The distributed method for effective ADMM-based SAR image recovery as claimed in claim 1, wherein in step 1, the observation matrix is constructed by: and vectorizing the two-dimensional sampling echo and the two-dimensional image to be reconstructed.
3. The distributed method for efficient ADMM-based SAR image recovery as claimed in claim 1, wherein in step 2, the mathematical expression of the SAR image sparse information recovery model is:
Figure FDA0003314995830000021
s.t.y＝Ax
wherein x ∈ RnRepresenting the reconstructed signal, A ∈ Rm×nFor the constructed observation matrix y ∈ RmRepresents an observed signal; i | · | purple wind1Representing the 1 norm of the matrix.
4. The distributed method for efficient ADMM-based SAR image recovery as claimed in claim 1, wherein in S2, the expression of the distributed solving algorithm based on the ADMM algorithm is:
Figure FDA0003314995830000022
wherein S isλ(a) The vector obtained by acting on each component of a as represented by soft threshold operator is shown as follows:
Figure FDA0003314995830000023
githe gradient is represented by the number of lines,
Figure FDA0003314995830000024
tau, beta, gamma are initialization parameters, pnIs an iteration multiplier.
5. The effective distributed method for SAR image recovery based on ADMM according to claim 1, wherein in step 4, the distributed solving algorithm based on the ADMM algorithm designed in step 3 is constructed by using a Spark platform, and specifically comprises:
s401, initializing parameters including regularization parameters lambda, tau, beta, gamma, step size stepsize and iteration precision epsilon > 0, and simultaneously giving an initial point x0,p0,res0；
S402, calculating a residual res-Ax-b by utilizing distributed multiplication of a matrix and a vector;
s403, calculating gradient g ═ A by using matrix transposition and vector distributed multiplication*(Ax-b-p/β), wherein p is an algorithmic multiplier;
s404, updating x to soft (x-stepsize · g) by using a threshold operator;
s405, if | | xk+1-xkIf | | < epsilon, the iteration is stopped and x is outputkWherein x iskThe recovered SAR image is obtained; otherwise go to S402.
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