CN103969636A - Landmine target discrimination method with sparse time frequency representation conducted by means of echo reconstitution - Google Patents

Abstract

The invention belongs to the ground penetrating synthetic aperture radar signal processing field, and particularly relates to a landmine target discrimination method with sparse time frequency representation conducted by means of echo reconstitution. The method comprises the steps of acquiring the image of an area-of-interest in a GP-SAR image, and conducting two-dimensional Fourier transform on the area-of-interest to acquire the wavenumber domain image of the area-of-interest; calculating the target frequency response estimated value, changing along with the angle of incidence, in the wavenumber domain image according to the relation between frequency and the angle of incidence in a front and lateral view strip radar wavenumber domain, and conducting echo reconstitution according to the target frequency response estimated value; introducing a sparse atom group, conducting sparse time frequency representation on the reconstituted echo, and extracting a characteristic vector; initializing linear judgment descriminator parameters, introducing multiple training samples, and obtaining final linear judgment descriminator parameters through calculation; discriminating whether a landmine target exists in the area-of-interest according to the extracted characteristic vector and the obtained final linear judgment descriminator parameters.

Description

A kind of land mine target discrimination method that utilizes reconstruct echo to carry out sparse time-frequency representation

Technical field

The invention belongs to GP-SAR (earth's surface penetrates synthetic-aperture radar: Ground Penetrate SyntheticAperture Radar) signal process field, be specifically related to a kind of land mine target discrimination method that utilizes reconstruct echo to carry out sparse time-frequency representation.

Background technology

GP-SAR has good soil and vegetation penetration capacity, is widely used in the detection of the shallow earth's surface targets such as land mine.Due to the existence of clutter doughtily, and the decay of soil to signal, shallow embedding, a little less than the land mine target echo response on earth's surface is compared other target and wanted, causes conventional signal processing method can not effectively solve the test problems of land mine target in GP-SAR image.In order to remove a large amount of false-alarms in land mine target detection figure, need to take effective land mine target discrimination method.In land mine target discrimination method, extracting land mine target, to be different from the feature of other target and clutter most important, and most algorithm is only paid close attention to land mine target time domain or frequency domain character in a certain respect, and practicality is inadequate.Sun Yi-jun in 2005 and Li Jian (Sun Yi-jun, and Li Jian, Landmine detection using forward-looking ground penetrating radar[C] .Proceedingsof SPIE, 2005, 5794:1089-1097.Sun Yi-jun, and Li Jian, Plastic Landmine DetectionUsing Time-Frequency Analysis for Forward-Looking Ground Penetrating Radar[C] .Proceedings of SPIE, 2005, 5089:851-862.) based on vehicle-mounted test platform, propose the one-dimensional distance hatching line of land mine target to carry out time-frequency conversion, utilize time-frequency combination feature wherein to differentiate, obtain good identification result.Shi Y F (Shi Y F in 2011, Song Q, Jin T, et al..Landmine detectionbased on two-dimension time-frequency feature[J] .Signal Processing, 2011,27 (12): 1898-1903.) again the former subbase of the Time-frequency Decomposition in the method is improved, extract more accurate time-frequency characteristics, further improve and differentiate performance.

In modern war environment, antitank mine field often adopts the mode of the motor-driven layings of large area such as minelayer, rocket delivery mine and airborne dispensing minelaying, has very high emergentness and disguised, often easily causes soldier's Psychological phobia, hit army's morale, the quick propelling of sluggish armoured force.The GP-SAR mine-detecting technique of low latitude or aerial platform, not limited by landform, be not subject to whether minefield is that limit in enemy-occupied area, investigative range is large, detection efficiency is high, and owing to having avoided and the contacting of ground, minefield, has very high security, not only by become following fast, efficiently, the developing direction of shallow embedding minefield detection technology accurately, and there is important humanitarianism and Military Application meaning.Under vehicular platform, GP-SAR is nearer apart from land mine target, and (SCR:signal clutter ratio) is higher for land mine target signal to noise ratio in the GP-SAR image obtaining, and the time-frequency characteristics of one-dimensional distance hatching line, can accurately reflect land mine target property.But, when being mounted in low latitude or aerial platform, GP-SAR is far away apart from land mine target, when in the GP-SAR image obtaining, land mine target SCR is lower, affected by noise, the one-dimensional distance hatching line of choosing usually departs from land mine center, and then makes the feature of extracting based on one-dimensional distance hatching line time-frequency figure, separability is poor, cannot in the time that SCR is lower, meet the discriminating demand of land mine target.

Summary of the invention

The technical problem to be solved in the present invention be for existing GP-SAR land mine target discrimination method in the time that signal to noise ratio is lower, distinctive can meet the shortcoming of application demand, proposes a kind of land mine target discrimination method based on echo reconstruct.

In order to solve the problems of the technologies described above, the present invention adopts provides a kind of land mine target discrimination method that utilizes reconstruct echo to carry out sparse time-frequency representation, comprises the following steps:

(s1) obtain the area-of-interest (area-of-interest: Region of Interesting in GP-SAR image, be abbreviated as ROI) image, and described area-of-interest is carried out to two-dimensional Fourier transform, obtain the wavenumber domain image of area-of-interest.

(s2) according to the relation of positive side-looking band radar wave number field medium frequency and incident angle, calculate the target frequency response estimation value changing with incident angle in wavenumber domain image in described step (s1); And carry out echo reconstruct according to target frequency response estimation value;

(s3) introduce sparse former subbase, the echo of reconstruct in described step (s2) is carried out to sparse time-frequency representation processing, and extract eigenvector;

(s4) the linear judgement of initialization Discr. parameter, and introduce several training samples, calculate final linearity judgement Discr. parameter;

(s5) according to the final linear judgement Discr. parameter obtaining in the eigenvector extracting in described step (s3) and described step (s4), differentiate whether described area-of-interest exists land mine target.

The present invention can reach following technique effect: (1) data strong adaptability, easy to utilize.The present invention utilizes target two dimension wavenumber domain image and one dimension echo relation, the echo response of reconstruct particular orientation, and effectively clutter reduction, improves the accuracy of feature extraction, in SAR image is processed, has extensive data adaptability; In addition, the present invention joins together Discr. parameter training and the sparse time-frequency representation of echo in the time of training, preferred feature when acquisition can be used for the Discr. parameter of test, in when test based on criterion search characteristics, not only effectively improved the discriminating quality of land mine target, also can be other type clarification of objective extraction and differentiating provides a kind of new thinking.(2) the land mine target being applicable in the remote situation of low latitude or aerial platform is differentiated.Compared with vehicular platform, when being mounted in low latitude or aerial platform, GP-SAR is far away apart from land mine target, and a little less than target scattering echo, SCR is lower.Adopt the present invention not only can effectively suppress adjacent clutter, improve target scattering echoing characteristics, and the present invention is in the time utilizing sparse time-frequency representation to extract land mine feature, take into full account time domain two peak structure and the frequency concave point of land mine, simplified the search strategy of time-frequency dictionary Atom, not only can further eliminate the impact of noise, and reduce operand, simplify test and differentiated flow process, in the situation that SCR is lower, obtained good land mine target identification result.

The concrete principle of the present invention is described below:

The first step, obtains ROI image, and carries out two-dimensional Fourier transform.The ROI (area-of-interest: Region of Interesting) detecting in the SAR image that GP-SAR is obtained, carries out two-dimensional Fourier transform, obtains ROI wavenumber domain image.

If make the ROI image of f (r, x) for obtaining in SAR image, it is carried out to two-dimensional Fourier transform, can obtain its two-dimentional wavenumber domain image:

$\tilde{F}(k_r,k_x)=F_{r,x\→k_r,k_x}^2\left[f(r,x)\right]---\left(1\right)$

K in formula _r, k _xbe respectively oblique distance wave number and orientation wave number, r, x represent respectively oblique distance, position of orientation.

2007 annuities add that (gold adds at its PhD dissertation, " the theory and technology research of ultra broadband SAR shallow embedding target imaging and detection ", National University of Defense Technology's doctorate paper, 2007) middle proof, no matter adopt what imaging algorithm, positive side-looking stripmap SAR two dimension wavenumber domain image meet:

$\left\{\begin{array}{c}k=\frac{1}{2}\sqrt{k_x^2+k_r^2}\\ \mathrm{\θ}=\arctan (-\frac{k_x}{k_r})\end{array}\right.---\left(2\right)$

K=2 π f/c in formula, c is the light velocity, f is frequency.According to the difference of imaging algorithm, give the impact bringing only shows two-dimentional wavenumber domain Support difference.In order to facilitate follow-up discussion, suppose that the span of θ is $(-\frac{\mathrm{\π}}{2},\frac{\mathrm{\π}}{2}].$

Second step, the echo reconstruct that based target frequency response is estimated.According to the relation of positive side-looking stripmap SAR wavenumber domain medium frequency and incident angle, estimate the target frequency response changing with incident angle in ROI wavenumber domain image.Inverse Fourier transform is carried out in estimation to target frequency response in ROI wavenumber domain image, the target echo of the adjacent clutter impact that has been eliminated.Detailed step is as follows

(1) estimation of target frequency response

Can obtain according to (2) formula:

$\left\{\begin{array}{c}{k}_r=2k\cos \mathrm{\θ}=\frac{4\mathrm{\π}}{c}f\cos \mathrm{\θ}\\ k_x=2k\sin \mathrm{\θ}=\frac{4\mathrm{\π}}{c}f\sin \mathrm{\θ}\end{array}\right.---\left(3\right)$

According to (3) formula, can be by be mapped in f-θ territory, form the frequency domain response of target under each incident angle:

$S(f,\mathrm{\θ})=\tilde{F}(\frac{4\mathrm{\π}}{c}f\cos \mathrm{\θ},\frac{4\mathrm{\π}}{c}f\cos \mathrm{\θ})---\left(4\right)$

As θ=θ ₀=0 o'clock, S (f, θ ₀) be the frequency domain response of vertical synthetic aperture; The image S (f, θ) of all ROI is all got to θ=θ ₀=0, can ensure

$S(f,{\mathrm{\θ}}_0)=\tilde{F}(\frac{4\mathrm{\π}}{c}f,\frac{4\mathrm{\π}}{c}f)---\left(5\right)$

(5) formula is the estimation of target frequency response in ROI wavenumber domain image.

(2) echo reconstruct

(5) formula is carried out to inverse Fourier transform, can obtain the echo of reconstruct:

$\hat{s}(t,{\mathrm{\θ}}_0)=F_{f\→t}^{-1}\left[S(f,{\mathrm{\θ}}_0)\right]---\left(6\right)$

The 3rd step: the extraction of sparse time-frequency representation and eigenvector.Time domain based on land mine target and frequency domain character are selected sparse former subbase, utilize selected sparse former subbase, and the echo of reconstruct is carried out to sparse time-frequency representation.

(1) select sparse former subbase

Select Gabor atom:

$g_{\mathrm{\κ}}\left(t\right)=\frac{1}{\sqrt{a}}g\left(\frac{t-b}{a}\right)e^{\mathrm{j\ξt}}---\left(7\right)$

Wherein, g (t) represents Gauss function, and j is imaginary unit, and κ=(a, b, ξ) is time and frequency parameter; A is contraction-expansion factor, in order to regulate temporal resolution; B is shift factor, for adjusting atom site; And ξ is modulation factor, for regulating the displacement of atom on frequency domain.

(7) Fourier transform of formula is:

$G_{\mathrm{\κ}}\left(w\right)=\sqrt{a}G\left[a(w-\mathrm{\ξ})\right]e^{-j(w-\mathrm{\ξ})b}---\left(8\right)$

Convert parameter a in L formula (7) and formula (8), obtain L time-frequency atom, composition dictionary D.W is corresponding to the angular frequency of t.

(2) sparse time-frequency representation

Make (6) formula time domain echo for ? its Sparse Decomposition be

${\hat{s}}_0=\mathrm{D\β}---\left(9\right)$

Decomposable process is:

$\min {\left|\right|\mathrm{\β}\left|\right|}_{1}s.t.{\hat{s}}_0=\mathrm{D\β}---\left(10\right)$

In formula || || ₁represent 1-norm.β is sparse coefficient in dictionary D, in the time only having the individual nonzero coefficient of limit in β, explanation sparse in dictionary D, wherein, s.t. is the abbreviation of English subject to, represents to meet the mathematic sign of constraint condition, that is: meeting constraint condition under, solve min|| β || ₁, lower same herein.

(3) eigenvector extracting method

According to bimodal (the Jin T of land mine target time domain, Zhou Z M.Study of Subsurface MetallicLandmine2-Dimensional Electromagnetic Signature in Ground Penetrating SyntheticAperture Radar.Acta Electronica Sinica, 2006, 34 (12): 2246-2249) and bimodal (the Sun X K of frequency domain, Zhou Z M, Wang J.Scattering from Buried Metal Landmines.Journal ofMicrowaves, 2008, 24 (4): 5-9) structure, according to the match search of (10) formula, two atoms of each searching in time domain and frequency domain, obtain 12 features:

(a _i,b _i,ξ _i)，i＝1,2,3,4 (11)

On the basis of 12 features, select again b ₁, b ₂, ξ ₃, ξ ₄, obtain time domain Peak Separation feature E and frequency domain concave point feature F by its variation:

$\left\{\begin{array}{c}E=b_2-b_1\\ F=({\mathrm{\ξ}}_3+{\mathrm{\ξ}}_4)/2\end{array}\right.---\left(12\right)$

By an eigenvector v of this 14 feature compositions.

The 4th step, determines linear discriminant device parameter.

The ROI image of definition known target is training sample, and ROI image to be identified is test sample book, according to following two formulas, solves final Discr. parameter.

$C_i^n=\arg \min ({\left|\right|X_i-{\mathrm{D\α}}_i\left|\right|}_2+{\left|\right|y_i-C_i^{n-1}{v}_i^n\left|\right|}_2+{\left|\right|C_i^{n-1}\left|\right|}_2)s.t.{\left|\right|{\mathrm{\α}}_i\left|\right|}_0=4---\left(13\right)$

$v_i^n=\arg \min ({\left|\right|X_i-{\mathrm{D\α}}_i\left|\right|}_2+{\left|\right|y_i-C_i^n{v}_i^{n-1}\left|\right|}_2+{\left|\right|C_i^n\left|\right|}_2)s.t.{\left|\right|{\mathrm{\α}}_i\left|\right|}_0=4---\left(14\right)$

Wherein, X _irepresent i training sample; be i training sample, the linearity obtaining after the n time iteration judgement Discr. parameter vector; be i training sample, the eigenvector after the n time iteration.I training sample X _icorresponding label is y _i, y in the time that sample is land mine target _i=1, otherwise, y _i=-1; α _ifor X _isparse coefficient vector under dictionary D, n=1,2 ..., N; N is natural number.

Iteration detailed process is as follows: establishing training sample has M, i.e. i=1, and 2 ..., M;

Initialization, the vector that equals zero, by training sample X ₁the eigenvector extracting both substitutions (13) formula is calculated, obtained then, will substitution (14) formula, calculates the eigenvector after upgrading by eigenvector with substitution (13) formula, calculates the like, iteration calculates for N time

By training sample X ₂the eigenvector extracting by Discr. parameter vector with substitution (13) formula, calculates then, will substitution (14) formula, calculates the eigenvector after upgrading by eigenvector with substitution (13) formula, calculates the like, iteration calculates for N time

By above algorithm, travel through after M sample, obtain final Discr. parameter vector

The 5th step, the discrimination process of target.

Utilize the Discr. parameter vector obtaining above to test sample book X _tdifferentiate have:

Wherein, ν _trepresent test sample book X _teigenvector, work as judge X _tfor land mine target; When $f\left(X_t\right)=\mathrm{sgn}\left(C_M^N{v}_t\right)=-1,$ Judge X _tfor clutter.

From above process, the present invention carries out the simultaneously thunder target discriminating of sparse time-frequency representation to the echo of reconstruct, can be in the situation that signal to noise ratio be lower, obtain good land mine target identification result.This process can be differentiated software realization by land mine target, this software is made up of the two-dimensional Fourier transform of ROI image, the echo reconstruct that based target frequency response is estimated, three modules of judgement based on sparse time-frequency representation, respectively corresponding three steps of the present invention.

The present invention has taken into full account in low latitude or the remote situation of aerial platform the lower feature of land mine target SCR in GP-SAR image, propose to utilize reconstruct echo to carry out the land mine target discrimination method of sparse time-frequency representation, effectively improve the accuracy of feature extraction, simplify identification flow, in the situation that signal to noise ratio is lower, obtain good land mine target identification result.Adopt measured data, land mine target discrimination method of the present invention is tested, obtained good effect.

Brief description of the drawings

Fig. 1 is conventional GP-SAR land mine target discrimination method process flow diagram;

Fig. 2 is the land mine target discrimination method process flow diagram that utilizes reconstruct echo to carry out sparse time-frequency representation of the present invention;

Fig. 3 is that the ROI extracting in Fig. 1 flow process schemes apart from hatching line and CWD (Choi-WilliamsDistribution) thereof;

Fig. 4 is echo reconstruct and the result figure in sparse each stage of time-frequency representation in Fig. 2 flow process;

Fig. 5 is that measured data is differentiated and Fig. 2 flow process identification result operation of receiver curve (Receiver Operator Characteristic Curve, ROC) comparison diagram according to Fig. 1 flow process.

Embodiment

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

Fig. 1 is conventional GP-SAR land mine target discrimination method process flow diagram.Be divided into two parts of training and testing.Part of detecting flow process comprises that ROI is apart from hatching line selection, time-frequency representation (comprising feature extraction), three parts of discriminating (wherein time-frequency representation method has Short Time Fourier Transform, CWD etc. conventionally).Training department's point flow process comprises that the ROI identical with part of detecting is apart from hatching line selection, two parts of time-frequency representation (comprising feature extraction), adds Discr. training part, and the Discr. that its function is mainly part of detecting provides parameter.In training module, three parts series connection, without feedback, differentiates based on linear decision rule, in the time that Discr. is trained, only adjusts Discr. parameter according to input training characteristics.When test, feature extraction is irrelevant with discriminating.

Fig. 2 is the land mine target discrimination method process flow diagram that utilizes reconstruct echo to carry out sparse time-frequency representation of the present invention.Wherein Fig. 2-1 is the process flow diagram of echo reconstructed module, comprises that two-dimensional Fourier transform (2D-FFT), target frequency response are estimated, three parts are estimated in target echo response.Fig. 2-2 are general flow chart, are divided into two parts of training and testing.Part of detecting flow process comprises echo reconstruct, the sparse time-frequency representation based on criterion, three parts of differentiation.Training department's point flow process comprises the echo reconstruct part identical with part of detecting, adds sparse time-frequency representation (comprising feature extraction) and two parts of Discr. training, and the Discr. that its function is mainly part of detecting provides parameter.In training module, in sparse time-frequency representation (comprising feature extraction), two modules of Discr. training, there is feedback branch, time Discr. parameter training and the sparse time-frequency representation of echo are joined together in training, by iteration preferred eigenvector when acquisition can be used for the Discr. parameter of test.In the time of test, sparse time-frequency representation, based on criterion, is searched for the feature of sparse time-frequency representation according to Discr. parameter.

Fig. 3 is that the ROI that extracts in Fig. 1 flow process is apart from hatching line and CWD distribution plan thereof.In ROI section, be (a) distance hatching line corresponding to maximal value, (b) for to depart from distance hatching line corresponding to maximal value-2 pixel, and (c) for departing from distance hatching line corresponding to 2 pixels of maximal value.Fig. 3-2, Fig. 3-3, Fig. 3-4 are respectively (a) (b) (c) corresponding CWD distribution.Can find out, near its time-frequency representation difference of distance hatching line maximal value is obvious.Because ROI center generally forms by methods such as gray scale maximal value, centers of gravity, be difficult to accomplish completely accurately, be difficult to positive goal practical center, therefore, this algorithm is easily affected by noise, and under noise situations, target scattering characteristics cannot accurately reflect, thereby can predict the reduction of its discriminating performance.

Fig. 4 is echo reconstruct and the result figure in sparse each stage of time-frequency representation in Fig. 2 process flow diagram.The ROI of Fig. 4-1 for comprising target; The wavenumber domain image obtaining after the two-dimensional Fourier transform that Fig. 4-2 are Fig. 4-1, Fig. 4-3 figure is the image that Fig. 4-2 figure obtains to the mapping of frequency-orientation angular domain by wavenumber domain; And Fig. 4-4 are obtained to carrying out inverse Fourier transform along frequency by Fig. 4-3.In Fig. 4-4, can find out, the target echo after reconstruct has better consistance on each position angle, ensures the robustness of the time-frequency characteristics obtaining by it.Fig. 4-5 for position angle be the reconstruct echo of 0 o'clock target, the sparse time-frequency representation that Fig. 4-6 are Fig. 4-5.In Fig. 4-6, the sparse time-frequency image of target is by 4 atomic buildings, wherein each two of time domain and frequency domain, and correspond respectively to the bimodal of time-domain diagram picture and frequency domain figure picture.Utilize the target echo reconstructing method of ROI, energy realize target accurate description, carries out sparse time frequency analysis to it, can obtain good target signature.

Fig. 5 is that measured data is differentiated and Fig. 2 flow process identification result ROC comparison diagram according to Fig. 1 flow process.As can be drawn from Figure 5, the result that the more conventional identification algorithm of identification algorithm of the present invention is obtained in land mine target discrimination process.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (4)

1. utilize reconstruct echo to carry out a land mine target discrimination method for sparse time-frequency representation, it is characterized in that: comprise the following steps:

(s1) obtain the region of interest area image in GP-SAR image, and described area-of-interest is carried out to two-dimensional Fourier transform, obtain the wavenumber domain image of area-of-interest.

(s2) according to the relation of positive side-looking band radar wave number field medium frequency and incident angle, calculate the target frequency response estimation value changing with incident angle in wavenumber domain image in described step (s1); And carry out echo reconstruct according to target frequency response estimation value;

(s3) introduce sparse former subbase, the echo of reconstruct in described step (s2) is carried out to sparse time-frequency representation processing, and extract eigenvector;

(s4) the linear judgement of initialization Discr. parameter, and introduce several training samples, calculate final linearity judgement Discr. parameter;

(s5) according to the final linear judgement Discr. parameter obtaining in the eigenvector extracting in described step (s3) and described step (s4), differentiate whether described area-of-interest exists land mine target.

2. a kind of land mine target discrimination method that utilizes reconstruct echo to carry out sparse time-frequency representation as claimed in claim 1, is characterized in that: described step (s3) comprises the following steps:

(s31) select Gabor atom g _κ(t) be sparse former subbase, that is:

Wherein, g (t) represents Gauss function, and j is imaginary unit, and κ=(a, b, ξ) represents time and frequency parameter, and a is contraction-expansion factor, in order to regulate temporal resolution; B is shift factor, adjusts atom site; And ξ is modulation factor, represent the displacement on frequency domain;

The Fourier transform of described (7) formula is:

W is the angular frequency corresponding to the t moment, and a parameter change in formula (1) and formula (2) L time, obtains L Gabor atom, described L Gabor atom composition dictionary D;

(s32) echo described step (2) reconstruct being obtained carry out Its Sparse Decomposition, that is:

Solve β process:

Wherein, || || ₁represent to solve 1-norm, β is sparse coefficient in dictionary D, s.t. represents to meet the mathematic sign of constraint condition.

3. a kind of land mine target discrimination method that utilizes reconstruct echo to carry out sparse time-frequency representation as claimed in claim 2, it is characterized in that: the eigenvector of the extraction training sample in described step (s4) comprises the following steps: in time domain and frequency domain, search for respectively two atoms according to the matching relationship in described (10) formula, obtain 12 features:

(a _i,b _i,ξ _i)，i＝1,2,3,4 (5)，

Select b ₁, b ₂, ξ ₃, ξ ₄, calculate and obtain time domain Peak Separation feature E and frequency domain concave point feature F:

By an eigenvector v of the common composition of described 12 features, Peak Separation feature E and frequency domain concave point feature F.

4. a kind of land mine target discrimination method that utilizes reconstruct echo to carry out sparse time-frequency representation as claimed in claim 1, is characterized in that: the linear judgement Discr. parameter of obtaining in described step (s4) comprises the following steps:

The linear judgement of initialization Discr. parameter the vector that equals zero, by training sample X ₁the eigenvector extracting according to following two formulas:

s.t.||α _i|| ₀＝4

s.t.||α _i|| ₀＝4

Wherein, X _irepresent i training sample; be i training sample, the linearity obtaining after the n time iteration judgement Discr. parameter vector; be i training sample, the eigenvector after the n time iteration; I training sample X _icorresponding label is y _i, y in the time that sample is land mine target _i=1, otherwise, y _i=-1; α _ifor X _isparse coefficient vector under dictionary D, n=1,2 ..., N; N is natural number;

In the time that training sample has M, through N the interative computation of described (13) and (14) formula, obtain final Discr. parameter vector and be

(s1) obtain the ROI image f (r, x) in GP-SAR image, described ROI image f (r, x) is carried out to two-dimensional Fourier transform, obtain two-dimentional wavenumber domain image and be that is:

Wherein, k _rfor oblique distance wave number, k _xfor orientation wave number, r represents that oblique distance, x represent position of orientation;

(s2) estimating target frequency response values, will be mapped in f-θ territory, form the frequency domain response of target correspondence under incidence angle θ:

As θ=θ ₀=0 o'clock, the frequency domain response of vertical synthetic aperture was S (f, θ ₀), the image S (f, θ) of all ROI all gets θ=θ ₀=0,

That is:

(11) formula is carried out to inverse Fourier transform, can obtain the echo of reconstruct

。