CN104459695B - Sparsity microwave imaging method based on compression phase restoring - Google Patents

Abstract

The invention provides a sparsity microwave imaging method based on compression phase restoring. The sparsity microwave imaging method comprises the steps that A, a radar return intensity signal generating model is constructed according to original radar return data of an observing target scene; B, the radar return intensity signal generating model is utilized for determining the optimizing goal of a reconstructing target scene backscattering coefficient; C, a compression phase restoring algorithm is utilized for solving the optical goal of the reconstructing target scene backscattering coefficient to estimate the backscattering coefficient of the target scene. According to the method, radar return intensity signals are utilized for reconstructing the backscattering coefficient of the target scene to achieve microwave imaging, and the negative influence on an imaging result due to the fact that radar return data phase errors can not be compensated accurately can be avoided.

Description

Based on the sparse microwave imaging method that compression phase recovers

Technical field

The present invention relates to microwave Imaging Technique field, more particularly to a kind of sparse microwave imaging recovered based on compression phase Method.

Background technology

Compared with optical image technology, with synthetic aperture radar (Synthetic Aperture Radar, SAR) for representative Modern microwave imaging technique, because which has round-the-clock, a round-the-clock observing capacity, and higher imaging resolution etc. is many excellent Point, is widely used in fields such as resource exploration, environmental monitoring, Disaster Assessments.And with to SAR system imaging point Resolution and the continuous improvement of mapping bandwidth requirement, cause the structure complexity of actual radar system and realize that difficulty steeply rises, The limit of existing electronic device performance and industrial technology level is reached, the performance of SAR system is difficult further to be carried Rise.

In order to solve the above problems, the scientific research personnel in microwave remote sensing field proposes sparse microwave imaging theory.It is sparse micro- Ripple imaging is referred to and for sparse signal treatment theory to introduce microwave imaging, and organically combines the microwave imaging new theory of formation, new body System and new method, i.e., by the sparse representation domain of searching object being observed, carried out in space, time, frequency spectrum or polarizing field sparse Sampling, obtains the sparse microwave signal of object being observed, by signal processing and information retrieval, obtains the space of object being observed The geometry such as position, scattering signatures and kinetic characteristic and physical features.Compared with traditional microwave is imaged, sparse microwave imaging not only may be used To reduce the structure complexity of SAR system, moreover it is possible to improve SAR systems at the aspect such as target resolution capability, fuzzy suppression, Sidelobe Suppression The imaging performance of system.

Because the movement locus for carrying the airborne platform of imaging radar system are highly prone to platform property, weather conditions, drive The impact of the factors such as technology is sailed, so causing airborne platform to be difficult the linear motion flight path that strictly remains a constant speed.Phase Than in ideal situation, this can make the radar echo signal that system is an actually-received produce certain deviation, so as in radar return Additive phase error, sampling time error and range delay on signal.Wherein, performance is the most obvious and image quality is affected most Big is exactly phase error.Phase error in radar echo signal would generally cause the decline of radar image image quality, go out Now defocus, the phenomenon such as displacement.As phase error increases, in some instances it may even be possible to cause the failure to observing scene rebuilding.For in solution State problem, it usually needs in microwave imaging before processing, phase error compensation is carried out to radar echo signal.

Existing radar echo signal phase error compensation method be mostly based on traditional microwave imaging system, due to microwave into As the difference in theoretical and method, said method is caused effectively to be applied under sparse microwave imaging system.Institute In the case of needing condition meet and cause radar return data phase error accurately cannot compensate, using based on matched filtering Conventional imaging method and plus improved sparse microwave imaging method, cannot realize the microwave imaging to target scene at all.

The content of the invention

(1) technical problem to be solved

In view of above-mentioned technical problem, the invention provides a kind of sparse microwave imaging method recovered based on compression phase, With avoid because radar return data phase error accurately cannot compensate caused by negative effect to imaging results.

(2) technical scheme

The present invention is included based on the sparse microwave imaging method that compression phase recovers：Step A：According to observed object scene Original radar return data, build radar echo intensity signal generation model；Step B：Using radar echo intensity signal generation Model, it is determined that rebuilding the optimization aim of target scene backscattering coefficient；And step C：It is using compression phase recovery algorithms, right The optimization aim for rebuilding target scene backscattering coefficient is solved, and estimates the backscattering coefficient of target scene.

(3) beneficial effect

From above-mentioned technical proposal as can be seen that the sparse microwave imaging method that recovered based on compression phase of the present invention with Lower beneficial effect：

(1) backscattering coefficient of target scene using radar echo intensity signal, is rebuild, microwave imaging is realized, so as to Avoid because radar return data phase error accurately cannot compensate caused by negative effect to imaging results；

(2) when the strong scattering center distribution in target scene has openness, compare based on general phase recovery Sparse microwave imaging method, in the case of radar echo intensity signal data amount identical to be dealt with, the present invention to mesh The reconstruction precision of mark scene backscattering coefficient is higher.

Description of the drawings

Fig. 1 is a kind of flowchart of the sparse microwave imaging method recovered based on compression phase；

Fig. 2A～Fig. 2 D are to process radar return data of the identical with phase error using different imaging methods, right The result rebuild by reference target scene backscattering coefficient；

When Fig. 3 is 0.16 for target scene degree of rarefication, in the case of the different down-sampled rates of correspondence, based on PhaseLift The sparse microwave imaging method reconstruction precision (curve (a)) of algorithm and the present embodiment methods described reconstruction precision (curve (b)) Comparative result.

Specific embodiment

To make the object, technical solutions and advantages of the present invention become more apparent, below in conjunction with specific embodiment, and reference Accompanying drawing, the present invention is described in more detail.It should be noted that in accompanying drawing or description description, similar or identical portion Divide and all use identical figure number.The implementation for not illustrating in accompanying drawing or describing, is those of ordinary skill in art Known form.In addition, though the demonstration of the parameter comprising particular value can be provided herein, it is to be understood that parameter is without the need for definite etc. In corresponding value, but corresponding value can be similar in acceptable error margin or design constraint.Mention in embodiment Direction term, for example " on ", D score, "front", "rear", "left", "right" etc., be only the direction of refer to the attached drawing.Therefore, the side for using It is for illustrating not for limiting the scope of the invention to term.

During the present invention is applied to microwave imaging compression phase Restoration model, radar return number can need not be being estimated In the case of according to phase error, using radar echo intensity signal, the backscattering coefficient of target scene is rebuild, is realized sparse micro- Ripple is imaged.

In one exemplary embodiment of the present invention, there is provided a kind of sparse microwave imaging recovered based on compression phase Method.It should be noted that due to, during solving to optimization aim, having differences between specific algorithm used, this Embodiment is disturbed with the presence or absence of additive noise according in the radar echo intensity signal returned by target scene, and point situation builds mesh Mark scene radar echo intensity signal generation model.

Fig. 1 is the flowchart of the sparse microwave imaging method recovered based on compression phase according to the embodiment of the present invention. As shown in figure 1, the step that implements of sparse microwave imaging method described in the present embodiment includes：

Step A：According to the original radar return data of observed object scene, radar echo intensity signal generation mould is built Type；

When original radar return data only exist phase error, sparse microwave imaging phase error model can be represented For：

Wherein,It is the radar return data without phase error,To cause radar to return Sparse microwave imaging system observing matrix of the wave number according to phase error,It is and the radar return without phase error The corresponding sparse microwave imaging system observing matrix of data y,For the backscattering coefficient of target scene, θ₁, θ₂..., θ_NFor the error phase being attached in radar return data,Be with For the N rank diagonal matrix of diagonal element.During in formula (1), the meaning of each amount is described, N is radar return number According to the number of sampled point, numbers of the n for target scene backscattering coefficient.

By formula (1), just available radar echo intensity signal generation model now is：

Wherein,For radar echo intensity signal, | | to take the amplitude computing of plural number.Radar echo intensity is believed Number further can be write as：

Wherein, b_iFor i-th element of vectorial b, i.e.,For sparse microwave imaging The vector that i-th row element of systematic observation matrix A is constituted, ＜, ＞ are the computing for solving two inner product of vectors.

When there is phase error in original radar return data and radar echo intensity signal is subject to additive noise to disturb, thunder Can be expressed as up to echo signal intensity generation model：

B=| Ax |²+e (4)

Wherein,For the additive noise being attached on radar echo intensity signal, and the l of vector e₂- norm meets ||e||₂≤ε.The radar echo intensity signal disturbed by additive noise further can be write as：

b_i=|<X, a_i〉|²+ ei, i=1 ..., N (5)

Wherein, e_iFor i-th element of vectorial e, i.e.,

Step B：Using radar echo intensity signal generation model, it is determined that rebuilding the optimization of target scene backscattering coefficient Target；

The situation of phase error is only existed for original radar return data, it is assumed that the strong scattering in target scene to be reconstructed Center distribution can be obtained with openness, the target scene radar echo intensity signal generation model according to formula (3) To the optimization aim for rebuilding target scene backscattering coefficient it is：

Formula is meant that expressed by (6), is meetingConstraints under, solution is obtained Make | | x | |₀Minimum vector x.

Due to | | | |₀The l of expression₀- norm is non-convex function, causes the optimization problem shown in formula (6) to be answered in Practical Project Effectively solution is hardly resulted in in.To solve the above problems, using the l1- norm relaxing techniquess in compressive sensing theory, can Formula (6) is turned to：

Formula is meant that expressed by (7), is meetingConstraints under, solution is obtained Make | | x | |₁Minimum vector x.

Because the equality constraint in formula (7) is a nonlinear equation, the optimization problem shown in formula (7) is one Individual non-convex optimization problem, is generally also highly difficult to the solution of non-convex optimization problem, and phase is wanted in the solution to convex optimization problem To simplicity, therefore for the computation complexity for further reducing solving optimization aim, needing will be the non-convex shown in formula (7) excellent Change problem is converted into convex optimization problem.

Assume according to required vectorial legitimate reading x₀The matrix of structureIt is positive semidefinite that order is 1 Matrix, then can turn to formula (7)：

Formula is meant that expressed by (8), is meetingThe constraint bar of i=1 ..., N, rank (X)=1 Under part, solution is made | | X | |₁Minimum matrix X.

Wherein,It is a positive semidefinite matrix, | | X | |₁The l of representing matrix X₁- norm, Tr () are represented The computing of trace of a matrix, rank () is asked to represent the computing for seeking rank of matrix.

Then, using lift technique, formula (8) can be turned to：

Formula is meant that expressed by (9), is meeting b_i=Tr (Φ_iX), under the constraints of i=1 ..., N, solution is obtained Make Tr (X)+λ | | X | |₁Minimum matrix X.

Wherein,λ ＞ 0 are for the mark Tr (X) and l in matrix X₁- norm | | X | |₁Between adjust The parameter of balance.Optimization problem shown in formula (9) is when radar return data only exist phase error, for rebuilding target field The optimization aim of scape backscattering coefficient.

There is phase error for original radar return data and radar echo intensity signal is subject to additive noise interference Situation, with reference to the derivation for not being subject to optimization aim in additive noise disturbed condition, can be used for rebuilding target scene in the same manner The optimization aim of backscattering coefficient is：

Formula is meant that expressed by (10), is meetingConstraints under, solution obtain making Tr (X)+ λ||X||₁Minimum matrix X.

Wherein, B is a linear operator, i.e.,：

Step C：Using compression phase recovery algorithms, the optimization aim to rebuilding target scene backscattering coefficient is asked Solution, estimates the backscattering coefficient of target scene；

The step includes：

Sub-step C1：For above-mentioned different situations, it is determined that reconstruction target scene backscattering coefficient optimization aim it is equal It is Semidefinite Programming, it is possible to use solved based on the compression phase recovery algorithms of convex optimization, thus obtain estimating for matrix X Meter

Sub-step C2：To Matrix EstimationSingular value decomposition is carried out, i.e.,：

Sub-step C3：By Matrix EstimationThe square root of eigenvalue of maximumWith its characteristic vectorIt is multiplied, thus To the estimation of target scene backscattering coefficientI.e.：

Wherein,For homographyEigenvalueCharacteristic vector.

Step D：Judgment matrix is estimatedOrderWhether 1 is equal or approximately equal to, i.e.,If Meet, thenThere is no deviation or deviation very little between x, can directly by the estimation of target scene backscattering coefficientAs Final target scene backscattering coefficient, it is not necessary to be corrected, flow process terminates, realizes sparse microwave imaging；Otherwise, i.e., when Matrix EstimationOrderCompare with 1 when differing greatly,Deviation between x just can not be ignored, and it is right now to needCarry out offset correction, execution step E；

Wherein, reconstruction precisions of the τ according to required by backscattering coefficient x real to target scene is determined.If τ Value is too small, can make the probability increase that step E is performed, so as to increase the amount of calculation of whole scheme；If τ values are excessive, can Can causeDeviation between x becomes big, reduces reconstruction precision.In the present embodiment, τ=10^-2.In other realities of the present invention Apply in example, τ can be taken less than 10^-1Arithmetic number.

Step E：The reconstruction deviation of correction target scene backscattering coefficient.

To reduce because of Matrix EstimationOrderIt is the vector estimation caused by 1 condition to be unsatisfactory for orderWith target field Deviation between the real backscattering coefficient x of scape, using estimation of the change of scale to target scene backscattering coefficientEnter Row offset correction is processed, and obtains the target scene backscattering coefficient after offset correctionFor：

So as to realize sparse microwave imaging.

According to above-mentioned specific embodiment, below by emulation experiment, the application advantage of the present embodiment methods described is entered Row checking.In emulation experiment, according to synthetic aperture radar sub-aperture image model and the systematic parameter for pre-setting, obtain by The Stepped frequency radar echo-signal that reference target scene is generated, then adds error phase in Stepped frequency radar echo-signal, Obtain emulation experiment radar return data to be used.

In emulation experiment 1, the systematic parameter for pre-setting as shown in table 1, is utilized respectively the tradition based on matched filtering Imaging method, the sparse microwave imaging method based on hard -threshold iterative algorithm and the method for the invention process identical radar and return Wave number evidence, rebuilds to the backscattering coefficient of reference target scene, compares their imaging results.

Systematic parameter of the table 1 for emulation experiment 1

Fig. 2A～Fig. 2 D are to process radar return data of the identical with phase error using different imaging methods, right The result rebuild by reference target scene backscattering coefficient.Wherein, Fig. 2A is reference target scene；Fig. 2 B are based on matching The imaging results of the conventional imaging method of filtering；Fig. 2 C are the imaging of the sparse microwave imaging method based on hard -threshold iterative algorithm As a result；Fig. 2 D are the imaging results of the sparse microwave imaging method recovered based on compression phase.

Fig. 2 B, Fig. 2 C, Fig. 2 D and Fig. 2A are compared, it is known that the method for the present embodiment can directly using with phase place The radar return data of error, correctly reconstruct the backscattering coefficient of reference target scene, and the biography based on matched filtering System imaging method cannot but obtain the above results with the sparse microwave imaging method based on hard -threshold iterative algorithm.

In emulation experiment 2, the systematic parameter for pre-setting as shown in table 2, is believed in radar echo intensity to be dealt with In the case of number amount identical, sparse microwave imaging method based on PhaseLifi algorithms and of the present invention is utilized respectively Method, rebuilds to the backscattering coefficient of target scene, compares their reconstruction precision.

Systematic parameter of the table 2 for emulation experiment 2

When Fig. 3 is 0.16 for target scene degree of rarefication, in the case of the different down-sampled rates of correspondence, based on PhaseLift The sparse microwave imaging method reconstruction precision (curve (a)) of algorithm and the present embodiment methods described reconstruction precision (curve (b)) Comparative result.As shown in figure 3, when the strong scattering center distribution in target scene has openness, to be dealt with In the case of radar echo intensity signal data amount identical, reconstruction of the method for the invention to target scene backscattering coefficient Precision is higher than the sparse microwave imaging method based on PhaseLift algorithms.

So far, the present embodiment has been described in detail already in connection with accompanying drawing.According to above description, those skilled in the art The present invention should be had based on the sparse microwave imaging method that compression phase recovers and clearly be recognized.

Additionally, the above-mentioned definition to each element and method is not limited in the various concrete structures mentioned in embodiment, shape Shape or mode, those of ordinary skill in the art can be simply changed or be replaced to which.

In sum, the present invention utilizes radar echo intensity signal, rebuilds the backscattering coefficient of target scene, realizes micro- Ripple is imaged, and cannot accurately compensate institute caused negative shadow to imaging results because of radar return data phase error so as to avoid Ring.Meanwhile, when the strong scattering center distribution in target scene has openness, compare based on the dilute of general phase recovery Thin microwave imaging method, in the case of radar echo intensity signal data amount identical to be dealt with, the present invention is to target field The reconstruction precision of scape backscattering coefficient is higher.

Particular embodiments described above, has been carried out to the purpose of the present invention, technical scheme and beneficial effect further in detail Describe bright, the be should be understood that specific embodiment that the foregoing is only the present invention in detail, be not limited to the present invention, it is all Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements done etc., should be included in the guarantor of the present invention Within the scope of shield.

Claims (8)

1. it is a kind of based on compression phase recover sparse microwave imaging method, it is characterised in that include：

Step A：According to the original radar return data of observed object scene, radar echo intensity signal generation model is built；

Wherein, when original radar return data only exist phase error, the radar echo intensity signal generation mould of step A Type is：

B=| Ax |²

$\begin{array}{cc}{b}_i=|<x,a_i>{|}^2=a_i{\mathrm{xx}}^H{a}_i^H,& i=1,...,N\end{array}$

Wherein,For radar echo intensity signal, b_iFor i-th element of vectorial b；Be with without phase place The corresponding sparse microwave imaging system observing matrix of radar return data y of error,For sparse microwave imaging system The vector that i-th row element of observing matrix A is constituted；For the backscattering coefficient of target scene；

Step B：Using radar echo intensity signal generation model, it is determined that rebuilding the optimization mesh of target scene backscattering coefficient Mark；And

Step C：Using the compression phase recovery algorithms based on convex optimization, the optimization mesh to rebuilding target scene backscattering coefficient Mark is solved, and estimates the backscattering coefficient of target scene.

2. it is according to claim 1 based on compression phase recover sparse microwave imaging method, it is characterised in that the step In rapid B, the optimization aim for rebuilding target scene backscattering coefficient is：

$\begin{array}{ccccc}\underset{X}{min}& Tr\left(X\right)+\mathrm{\&lambda;}\left|\right|X|{|}_1,& s.t.& b_i=Tr\left({\mathrm{\&Phi;}}_{i}X\right),& i=1,...,N\end{array}$

Wherein,It is a positive semidefinite matrix,λ>0 is for the mark Tr (X) in matrix X With l₁- norm | | X₁| | between adjustment parameter.

3. it is a kind of based on compression phase recover sparse microwave imaging method, it is characterised in that include：

Step A：According to the original radar return data of observed object scene, radar echo intensity signal generation model is built；

Wherein, when original radar return data have phase error and radar echo intensity signal is subject to additive noise to disturb, The radar echo intensity signal generation model of step A is：

B=| Ax |²+e

b_i=|<x,a_i>|²+e_i, i=1 ..., N

Wherein,For radar echo intensity signal, b_iFor i-th element of vectorial b；Be with without phase place The corresponding sparse microwave imaging system observing matrix of radar return data y of error,For sparse microwave imaging system The vector that i-th row element of observing matrix A is constituted；For the backscattering coefficient of target scene；To be attached to Additive noise on radar echo intensity signal, and the l of vector e₂- norm meets | | e | |₂≤ ε, e_iFor i-th yuan of vectorial e Element；

Step B：Using radar echo intensity signal generation model, it is determined that rebuilding the optimization mesh of target scene backscattering coefficient Mark；And

Step C：Using the compression phase recovery algorithms based on convex optimization, the optimization mesh to rebuilding target scene backscattering coefficient Mark is solved, and estimates the backscattering coefficient of target scene.

4. it is according to claim 3 based on compression phase recover sparse microwave imaging method, it is characterised in that the step In rapid B, the optimization aim for rebuilding target scene backscattering coefficient is：

$\begin{array}{cccc}\underset{X}{min}& Tr\left(X\right)+\mathrm{\&lambda;}\left|\right|X|{|}_1,& s.t.& \left|\right|B\left(X\right)-b|{|}_2^2\&le;\mathrm{\&epsiv;}\end{array}$

Wherein,It is a positive semidefinite matrix；λ>0 be for the mark Tr (X) in matrix X with l₁- norm | | X | |₁Between adjustment parameter；B is a linear operator, i.e.,

5. according to claim 2 or 4 based on compression phase recover sparse microwave imaging method, it is characterised in that institute Stating step C includes：

Sub-step C1：Using the compression phase recovery algorithms based on convex optimization, to rebuilding the excellent of target scene backscattering coefficient Change target to be solved, obtain the estimation of matrix X

Sub-step C2：To Matrix EstimationSingular value decomposition is carried out, i.e.,：

$\hat{X}=\underset{k=1}{\overset{n}{\&Sigma;}}{\widehat{\mathrm{\&lambda;}}}_k{\hat{u}}_k{\hat{u}}_k^H,{\widehat{\mathrm{\&lambda;}}}_1\&GreaterEqual;...\&GreaterEqual;{\widehat{\mathrm{\&lambda;}}}_n\&GreaterEqual;0$

Sub-step C3：By Matrix EstimationThe square root of eigenvalue of maximumWith its characteristic vectorIt is multiplied, thus obtains target The estimation of scene backscattering coefficientI.e.：

$\hat{x}=\sqrt{{\widehat{\mathrm{\&lambda;}}}_1}{\hat{u}}_1$

Wherein,For homographyEigenvalueCharacteristic vector.

6. it is according to claim 5 based on compression phase recover sparse microwave imaging method, it is characterised in that the step Also include after rapid C：

Step D：Judgment matrix is estimatedOrderWhether meetIf meeting, by target scene The estimation of backscattering coefficientUsed as final target scene backscattering coefficient, flow process terminates, and realizes sparse microwave imaging； Otherwise, execution step E；

Step E：The reconstruction deviation of correction target scene backscattering coefficient, realizes sparse microwave imaging.

7. it is according to claim 6 based on compression phase recover sparse microwave imaging method, it is characterised in that the step In rapid D, reconstruction precisions of the τ according to required by backscattering coefficient x real to target scene is determined.

8. it is according to claim 6 based on compression phase recover sparse microwave imaging method, it is characterised in that the step Rapid E includes：

Using estimation of the change of scale to target scene backscattering coefficientOffset correction process is carried out, after obtaining offset correction Target scene backscattering coefficient

${\hat{x}}_{debias}=\sqrt{{\mathrm{\&Sigma;}}_{k=1}^N{\widehat{\mathrm{\&lambda;}}}_k}\hat{x}/\left|\right|\hat{x}|{|}_2.$