CN104483671A - Sparse representation theory-based synthetic aperture radar imaging method - Google Patents

Abstract

The invention discloses a sparse representation theory-based synthetic aperture radar imaging method which is mainly used for solving the problem that the traditional sparse representation-based imaging method cannot process complicated scenes and has large loss. The sparse representation theory-based synthetic aperture radar imaging method comprises the following steps: 1, obtaining a ground scene echo matrix Y; 2, constructing a ground scene azimuth matrix R and a ground scene range basis matrix G; 3, obtaining a matrix relation according to the matrixes in the steps 1 and 2, Gaussian noise N and a scattering coefficient matrix F: Y=RFG+N; 4, constructing an optimization function f (F, V, Dx, Dy) under a total variation frame according to the matrix relation, an intermediate variable matrix V, a horizontal total variation matrix Dx, a vertical total variation matrix Dy and the matrixes in the steps 1 and 2; and 5, solving the optimization function to obtain the image of the ground scene. The sparse representation theory-based synthetic aperture radar imaging method is capable of realizing the high-resolution imaging of synthetic aperture radars, is high in imaging speed, and can be used for large-area topographic mapping.

Description

Based on the synthetic aperture radar image-forming method of sparse representation theory

Technical field

The invention belongs to Radar Technology field, specifically a kind of synthetic aperture radar image-forming method that effectively can process complicated large scene, can be used for large-scale terrain mapping, cartography, round-the-clock global reconnaissance.

Background technology

Synthetic-aperture radar SAR is a kind of imaging radar with high resolution, has round-the-clock, round-the-clock imaging capability, is widely used in military and civilian.The high-resolution of SAR, radial distance relies on broadband signal, and Range resolution unit can be narrowed down to sub-meter grade by the frequency band of hundreds of megahertz; Orientation then relies on Texas tower move, form very long linear array in space equivalently, and each echo is stored the ARRAY PROCESSING of doing to synthesize.

In SAR system, radar is scene transponder pulse earthward along course line, and receives the echo from this ground scene scattering, then utilizes focusing algorithm, as Range Doppler, Chirp Scaling process echo, reconstructs ground scene.Although this Measures compare is effective, need to utilize the sample frequency being greater than nyquist frequency to carry out digitized processing to echo, higher sample frequency is concerning a huge challenge beyond doubt the A/D converter of receiving end; The a large amount of sampled datas obtained of simultaneously sampling too increase the burden storing and transmit; The resolution limitations of the SAR image that classic method reconstructs out is in the bandwidth of SAR system signal, the bandwidth of signal can only be improved in order to improve resolution, so also increase the complexity of hardware, and coherent speckle noise, and secondary lobe artifact is also very serious on the impact of picture quality.

The sparse representation theory of emerging in large numbers in recent years is pointed out, if certain higher-dimension signal itself is sparse or is sparse under certain transform domain, with the incoherent observing matrix of transform domain, this signal can be projected on lower dimensional space by one, and realize high probability signal reconstruction by optimization method.The proposition of sparse representation theory is that the high-resolution imaging of synthetic-aperture radar provides possibility.Theoretical according to this, the people such as Vishal M.Patel propose a kind of formation method based on total variation rarefaction representation at document " Compressed Synthetic Aperture Radar.IEEEJournalofSelected Topicsin Signal Processing; Vol.4; NO.2; April 2010. ", scene vectorization is constructed observing matrix, and recycling receives the method that echo is reconstructed.Although this formation method carrying out imaging lower than under Nyquist sampling frequency, often can require a great deal of time, the imaging processing of real-time can not be reached, and imaging validity is poor, makes it can only process less scene.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of synthetic aperture radar image-forming method based on sparse representation theory, to realize directly being reconstructed ground complicated two-dimensional scene, high-resolutionly reduce imaging time in maintenance simultaneously.

For achieving the above object, technical scheme of the present invention comprises the steps:

(1) according to radar scene transponder pulse earthward obtain the echoed signal of ground scene

$y(t_a,\hat{t})=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{\mathrm{pq}}{w}_a(t_a-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_a-\frac{x_p}{v})}^2)w_r(\hat{t}-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{(\hat{t}-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\π}f}_c}{C}{R}_q)$

In formula, for the fast time, t _afor the slow time, f _cfor carrier frequency, γ is chirp rate, and v is carrier aircraft speed, and C is propagation velocity of electromagnetic wave, w _a() is orientation window function, w _r() is chirp pulse signal time window function, P be ground scene in orientation to discrete grid block number, Q be ground scene distance to discrete grid block number, p be ground scene in orientation to p discrete grid block, q be ground scene distance to q discrete grid block, f _pqbe the scattering coefficient of (p, q) individual grid place scattering point, R ₀for radar is to the vertical oblique distance at ground scene center, R _qfor radar is to distance to the vertical oblique distance of q discrete grid block, x _pfor orientation is to the x-axis coordinate of p discrete grid block;

(2) to echoed signal carry out two-dimensional discrete sampling, obtain following echo matrix Y:

Wherein, M be orientation to exomonental number, N is that in each pulse, distance is to sampling number; for echoed signal is in the sample value of (m, n) individual sampling instant, its expression is as follows:

$y(t_{a,m},{\hat{t}}_n)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{\mathrm{pq}}{w}_a(t_{a,m}-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_{a,m}-\frac{x_p}{v})}^2)w_r({\hat{t}}_n-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{({\hat{t}}_n-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\πR}}_q}{\mathrm{\λ}})$

In formula, λ is carrier wavelength, t _a,mbe m pulse, for fast time n-th sampling instant value;

(3) orientation of ground scene is constructed to basis matrix R:

Wherein, $r(t_{a,m},p)=w_a(t_{a,m}-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{\mathrm{\λ}{R}_0}{(t_{a,m}-\frac{x_p}{v})}^2);$

(4) distance of ground scene is constructed to basis matrix G:

Wherein, $g(q,{\hat{t}}_n)=w_r({\hat{t}}_n-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{({\hat{t}}_n-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\πR}}_q}{\mathrm{\λ}});$

(5) according to echo matrix Y, orientation to basis matrix R, distance to the scattering coefficient matrix F of basis matrix G and ground scene, build following matrix relationship formula:

Y＝RFG+N，

In formula, N is and the noise matrix of echo matrix Y with dimension, and the form of scattering coefficient matrix F is as follows:

Wherein, p=1,2 ..., P, q=1,2 ..., Q;

(6) according to the scattering coefficient matrix F of ground scene, intermediate variable matrix V is obtained, horizontal total variation matrix D _x, vertical total variation matrix D _y:

V＝F

D _x＝D _hF，

D _y＝FD _v

In formula, D _hfor horizontal total variation operator matrix, D _vfor vertical total variation operator matrix;

(7) parameter that the matrix relationship formula of step (5) and step (6) obtain is utilized, majorized function f (F, V, D under structure total variation framework _x, D _y):

$\underset{F,V,D_x,D_y}{\min }f(F,V,D_x,D_y)=\{{\left|\right|D_x\left|\right|}_1+{\left|\right|D_y\left|\right|}_1+\frac{\mathrm{\λ}}{2}{\left|\right|D_{h}V-D_x\left|\right|}_F^2+\frac{\mathrm{\λ}}{2}{\left|\right|{\mathrm{VD}}_v-D_y\left|\right|}_F^2+\frac{v}{2}{\left|\right|V-F\left|\right|}_F^2+\frac{\mathrm{\μ}}{2}{\left|\right|\mathrm{RFG}-Y\left|\right|}_F^2\},$

Wherein represent the operational symbol finding a function minimum value, λ is total variation penalty factor, and ν is scene scatters coefficient penalty factor, and μ is echo penalty factor, || || _frepresent the Frobenius norm asking matrix, || || ₁represent and be added again after each element of matrix is taken absolute value;

(8) use Split-Bregman method to majorized function f (F, V, the D in step (7) _x, D _y) carry out iterative, obtain the final iteration result F of ground scene scattering coefficient matrix F ^*;

(9) step (8) is obtained to the final iteration result F of ground scene scattering coefficient matrix F ^*delivery value, exports the image obtaining ground scene.

The present invention compared with prior art tool has the following advantages:

The first, the present invention, by doing total variation process to scene, then utilizes Split-Bregman method imaging processing, makes the scene of the method process complexity based on rarefaction representation become possibility.

Second, the present invention is directly reconstructed imaging to two-dimentional ground scene image, the observing matrix that the reconstructing method avoiding scene image vectorization produces is excessive, the problem that calculated amount sharply increases, there is large scene fast imaging, to image taking speed, the advantage of little scene real time imagery, requires that there is obvious advantage high application scenario.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the image that the present invention emulates the Harbor scene of use;

Fig. 3 is the image of the Harbor scene reconstructed by the inventive method;

Fig. 4 is the image that the present invention emulates the terraced fields scene of use.

Specific implementation method

Below in conjunction with accompanying drawing, the present invention is described in further detail.

With reference to Fig. 1, specific embodiment of the invention step is as follows:

Step 1: obtain discrete two-dimensional echo matrix Y.

(1a) carrier aircraft moves ahead along course, and chirp launched by radar earthward scene:

$s(t_a,\hat{t})=w_r\left(\hat{t}\right)\exp \left(\mathrm{j\π\γ}{\hat{t}}^2\right)\exp \left(j2\mathrm{\π}{f}_{c}t\right),$

In formula, f _cfor carrier frequency, γ is chirp rate, and t is full-time, for the fast time, t _afor the slow time, the pass of these three times is represent the time window function of chirp pulse signal, T _rit is the time of pulse persistance;

(1b) receive the echo-pulse of this scene, obtaining echoed signal is

$y(t_a,\hat{t})=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{\mathrm{pq}}{w}_a(t_a-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_a-\frac{x_p}{v})}^2)w_r(\hat{t}-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{(\hat{t}-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\π}f}_c}{C}{R}_q)$

In formula, v is carrier aircraft speed, and C is propagation velocity of electromagnetic wave, w _a() is orientation window function, w _r() is chirp pulse signal time window function, P be ground scene in orientation to discrete grid block number, Q be ground scene distance to discrete grid block number, p be ground scene in orientation to p discrete grid block, q be ground scene distance to q discrete grid block, f _pqbe the scattering coefficient of (p, q) individual grid place scattering point, R ₀for radar is to the vertical oblique distance at ground scene center, R _qfor radar is to distance to the vertical oblique distance of q discrete grid block, x _pfor orientation is to the x-axis coordinate of p discrete grid block;

(1c) by the echo of step (1b) ground scene carry out two-dimensional discrete sampling, obtain echo matrix Y:

Wherein M be orientation to exomonental number, N is that distance in each pulse is to sampling number; represent the sample value of (m, n) individual sampling instant of echo, its expression is as follows:

$y(t_{a,m},{\hat{t}}_n)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{\mathrm{pq}}{w}_a(t_{a,m}-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_{a,m}-\frac{x_p}{v})}^2)w_r({\hat{t}}_n-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{({\hat{t}}_n-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\πR}}_q}{\mathrm{\λ}})$

In formula, λ is carrier wavelength, t _a,mbe m pulse, for fast time n-th sampling instant value.

Step 2: the orientation of structure ground scene is to basis matrix R and distance to basis matrix G.

(2a) according to step 1 parameter, the orientation of structure ground scene is to gene polyadenylation signal r (t _a,m, p):

$r(t_{a,m},p)=w_a(t_{a,m}-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{\mathrm{\λ}{R}_0}{(t_{a,m}-\frac{x_p}{v})}^2),$

Wherein, t _a,mbe m pulse, p=1,2 ..., P, m=1,2 ..., M, w _a() is orientation window function, and v is carrier aircraft speed, and λ is carrier wavelength, R ₀for radar is to the vertical oblique distance at ground scene center, x _pfor orientation is to the x-axis coordinate of p discrete grid block;

(2b) according to orientation to gene polyadenylation signal r (t _a,m, p), obtain orientation to basis matrix R:

In formula, M be orientation to exomonental number, P be ground scene orientation to discrete grid block number;

(2c) according to step 1 parameter, the distance of structure ground scene is to gene polyadenylation signal

$g(q,{\hat{t}}_n)=w_r({\hat{t}}_n-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{({\hat{t}}_n-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\πR}}_q}{\mathrm{\λ}}),$

In formula, for fast time n-th sampling instant value, q=1,2 ..., Q, n=1,2 ..., N, γ are chirp rate, w _r() for chirp time window function, C be propagation velocity of electromagnetic wave, λ is carrier wavelength, R _qfor radar is to distance to the vertical oblique distance of q discrete grid block;

(2d) according to distance to gene polyadenylation signal obtain distance to basis matrix G:

Wherein, N be distance in each pulse to sampling number, Q be ground scene D distance to discrete grid block number.

Step 3: the echo matrix Y obtained according to step 1 and 2, orientation, to basis matrix R, distance to the scattering coefficient matrix F of basis matrix G and ground scene, build following matrix relationship formula:

Y＝RFG+N

In formula, N is and the noise matrix of echo matrix Y with dimension, and the form of scattering coefficient matrix F is as follows:

Wherein, p=1,2 ..., P, q=1,2 ..., Q.

Step 4: majorized function f (F, V, D under the matrix relationship formula structure total variation framework in the matrix variables obtained according to step 1 and 2 and step 3 _x, D _y).

(4a) according to the scattering coefficient matrix F of ground scene, intermediate variable matrix V is obtained, horizontal total variation matrix D _x, vertical total variation matrix D _y:

V＝F

D _x＝D _hF，

D _y＝FD _v

In formula, D _hfor horizontal total variation operator matrix, D _vfor vertical total variation operator matrix;

(4b) according to the matrix variables in step (4a), majorized function f (F, V, D under structure total variation framework _x, D _y):

$\underset{F,V,D_x,D_y}{\min }f(F,V,D_x,D_y)=\{{\left|\right|D_x\left|\right|}_1+{\left|\right|D_y\left|\right|}_1+\frac{\mathrm{\λ}}{2}{\left|\right|D_{h}V-D_x\left|\right|}_F^2+\frac{\mathrm{\λ}}{2}{\left|\right|{\mathrm{VD}}_v-D_y\left|\right|}_F^2+\frac{v}{2}{\left|\right|V-F\left|\right|}_F^2+\frac{\mathrm{\μ}}{2}{\left|\right|\mathrm{RFG}-Y\left|\right|}_F^2\},$

Wherein, represent the operational symbol finding a function minimum value, λ is total variation penalty factor, and ν is scene scatters coefficient penalty factor, and μ is echo penalty factor, || || _frepresent the Frobenius norm asking matrix, || || ₁represent and be added again after each element of matrix is taken absolute value.

Step 5: by Split-Bregman method to majorized function f (F, V, the D in step 4 _x, D _y) carry out iterative, obtain the image of the ground scene after imaging.

(5a) according to majorized function f (F, V _,d _x, D _y), obtain majorized function L (F, V, the D of Split-Bregman form _x, D _y):

$\underset{F,V,D_x,D_y}{\min }L(F,V,D_x,D_y)=\{{\left|\right|D_x\left|\right|}_1+{\left|\right|D_y\left|\right|}_1+\frac{\mathrm{\λ}}{2}{\left|\right|D_{h}V-D_x+B_x\left|\right|}_F^2+\frac{\mathrm{\λ}}{2}{\left|\right|{\mathrm{VD}}_v-D_y+B_y\left|\right|}_F^2+\frac{v}{2}{\left|\right|V-F+W\left|\right|}_F^2+\frac{\mathrm{\μ}}{2}{\left|\right|\mathrm{RFG}-Y\left|\right|}_F^2\}$

In formula, B _xfor horizontal total variation matrix auxiliary variable, B _yfor vertical total variation matrix auxiliary variable, W is scattering coefficient matrix auxiliary variable;

(5b) initialization: iterative steps k=0, scattering coefficient matrix F after kth time iteration ^kfor all 1's matrix, intermediate variable matrix V after kth time iteration ^kfor all 1's matrix, horizontal total variation matrix after kth time iteration for all 1's matrix, vertical total variation matrix after kth time iteration for all 1's matrix; Scattering coefficient matrix auxiliary variable W after kth time iteration ^kfor full 0 matrix, horizontal total variation matrix auxiliary variable after kth time iteration for full 0 matrix, vertical total variation matrix auxiliary variable after kth time iteration for full 0 matrix; Total variation penalty factor λ >0 is set, scene scatters coefficient penalty factor ν >0, echo penalty factor μ >0, stopping criterion for iteration ε=5 × 10 ^-4;

(5c) scattering coefficient matrix F after kth+1 iteration is obtained ^k+1;

(5c1) according to orientation to basis matrix R, distance to basis matrix G, obtain orientation to symmetric matrix Ψ, distance is to symmetric matrix Φ:

Ψ＝R ^TR，

Φ＝GG ^T

Wherein, () ^trepresenting matrix transposition;

(5c2) according to feature decomposition orientation to symmetric matrix Ψ, distance, to symmetric matrix Φ, obtains orientation to orthogonal matrix U _r, orientation is to diagonal matrix L _r, distance is to orthogonal matrix U _g, distance is to diagonal matrix L _g;

(5c3) according to echo matrix Y, orientation to basis matrix R, distance to basis matrix G, intermediate variable matrix V after kth time iteration ^k, scattering coefficient matrix auxiliary variable W after kth time iteration ^k, orientation is to orthogonal matrix U _r, distance is to orthogonal matrix U _g, orientation is to diagonal matrix L _r, distance is to diagonal matrix L _g, according to scattering coefficient companion matrix after following formula acquisition kth+1 iteration

In formula, p=1,2 ..., P, q=1,2 ..., Q;

(5c4) according to orientation to orthogonal matrix U _r, distance is to orthogonal matrix U _g, scattering coefficient companion matrix after kth+1 iteration according to scattering coefficient matrix F after following formula acquisition kth+1 iteration ^k+1:

(5d) intermediate variable matrix V after kth+1 iteration is obtained ^k+1;

(5d1) according to horizontal total variation operator matrix D _h, vertical total variation operator matrix D _v, obtain horizontal total variation matrix E, vertical total variation matrix Z:

$\begin{array}{c}E=D_h^T{D}_h\\ Z=D_v{D}_v^T\end{array};$

(5d2) according to feature decomposition horizontal total variation matrix E, vertical total variation matrix Z, obtains horizontal total variation orthogonal matrix U _x, horizontal total variation diagonal matrix L _x, vertical total variation orthogonal matrix U _y, vertical total variation diagonal matrix L _y;

(5d3) according to scattering coefficient matrix F after kth+1 iteration ^k+1, horizontal total variation operator matrix D _h, vertical total variation operator matrix D _v, scattering coefficient matrix auxiliary variable W after kth time iteration ^k, horizontal total variation matrix auxiliary variable after kth time iteration vertical total variation matrix auxiliary variable after kth time iteration horizontal total variation matrix after kth time iteration vertical total variation matrix after kth time iteration horizontal total variation orthogonal matrix U _x, vertical total variation orthogonal matrix U _y, horizontal total variation diagonal matrix L _x, vertical total variation diagonal matrix L _y, according to intermediate variable companion matrix after following formula acquisition kth+1 iteration

In formula, p=1,2 ..., P, q=1,2 ..., Q;

(5d4) according to horizontal total variation orthogonal matrix U _x, vertical total variation orthogonal matrix U _y, intermediate variable companion matrix after kth+1 iteration according to intermediate variable matrix V after following formula acquisition kth+1 iteration ^k+1:

(5e) according to intermediate variable matrix V after kth+1 iteration ^k+1, horizontal total variation matrix auxiliary variable after kth time iteration vertical total variation matrix auxiliary variable after kth time iteration according to horizontal total variation matrix after following formula acquisition kth+1 iteration vertical total variation matrix after kth+1 iteration

$\begin{array}{c}{\left(D_x^{k+1}\right)}_{p,q}=\mathrm{sign}\left({(D_h{V}^{k+1}+B_x^k)}_{p,q}\right)\max \left(\right|{(D_h{V}^{k+1}+B_x^k)}_{p,q}|-\frac{1}{\mathrm{\λ}},0)\\ {\left(D_y^{k+1}\right)}_{p,q}=\mathrm{sign}\left({(V^{k+1}{D}_v+B_y^k)}_{p,q}\right)\max \left(\right|{(V^{k+1}{D}_v+B_y^k)}_{p,q}|-\frac{1}{\mathrm{\λ}},0)\end{array},$

In formula, p=1,2 ..., P, q=1,2 ..., Q, D _hfor horizontal total variation operator matrix, D _vfor vertical total variation operator matrix, sign () is sign function;

(5f) according to intermediate variable matrix V after the above-mentioned kth obtained+1 iteration ^k+1, scattering coefficient matrix F after kth+1 iteration ^k+1, horizontal total variation matrix after kth+1 iteration vertical total variation matrix after kth+1 iteration horizontal total variation matrix auxiliary variable after kth time iteration vertical total variation matrix auxiliary variable after kth time iteration scattering coefficient matrix auxiliary variable W after kth time iteration ^k, according to scattering coefficient matrix auxiliary variable W after following formula acquisition kth+1 iteration ^k+1, horizontal total variation matrix auxiliary variable after kth+1 iteration vertical total variation matrix auxiliary variable after kth+1 iteration

W ^k+1＝W ^k+V ^k+1-F ^k+1

$B_x^{k+1}=B_x^k+D_h{V}^{k+1}-D_x^{k+1};$

$B_y^{k+1}=B_y^k+V^{k+1}{D}_v-D_y^{k+1}$

(5g) according to scattering coefficient matrix F after kth+1 iteration ^k+1, scattering coefficient matrix F after kth time iteration ^k, obtain square error M by following formula:

$M=\frac{{\left|\right|F^{k+1}-F^k\left|\right|}_F^2}{{\left|\right|F^k\left|\right|}_F^2},$

In formula, || || _frepresent the Frobenius norm asking matrix;

(5h) judge whether square error M≤ε sets up, perform step (5i) if set up; Otherwise make k=k+1, return step (5c) and continue iteration operation;

(5i) F is made ^*=F ^k+1, obtain the final iteration result F of ground scene scattering coefficient matrix F ^*;

(5j) to final iteration result F ^*delivery value, exports the image obtaining ground scene.

Effect of the present invention can be illustrated by following emulation experiment:

1. simulated conditions

(1a) operation platform configuration:

CPU:Intel (R) Core (TM) 2Duo CPU E4500@2.20GHz; Internal memory: 2GB (hundred million energy DDR2 667MHZ);

Operating system: Windows 7 Ultimate 32 SP1 operating systems; Simulation software: MATLAB R (2011b).

(1b) simulation parameter is arranged

Transmit employing linear FM signal, transmission signal parameters and experiment simulation optimum configurations as shown in table 1.

Table 1 transmission signal parameters and experiment simulation parameter

Parameter	Value
		Carrier frequency	f c＝10GHz
The linear FM signal duration	T r＝5μs
		Linear FM signal modulating bandwidth	B r＝37.5MHz
Carrier aircraft platform speed	v＝150m/s
		Antenna equivalent aperture	D＝4m
The vertical oblique distance of carrier aircraft and scene center	R 0＝20Km
		Pulse repetition rate	PRF＝300Hz
Sample frequency	f s＝225MHz

2. emulate content and result

Emulation 1, according to the simulation parameter of table 1, be the Harbor scene of 687 × 803 by synthetic-aperture radar to the size shown in Fig. 2, carry out detecting and obtaining echo, reconstruct the image of Harbor scene by the inventive method, result as shown in Figure 3.Image shows: the present invention can realize the high-resolution reconstruct to the complicated large scene in ground.

Emulation 2, according to the simulation parameter of table 1, emulation obtains the echo of different size terraced fields scenes as shown in Figure 4, wherein Fig. 4 (a) is the terraced fields scene of 64 × 64, Fig. 4 (b) is the terraced fields scene of 128 × 128, Fig. 4 (c) is the terraced fields scene of 256 × 256, and Fig. 4 (d) is the terraced fields scene of 512 × 512.

According to Fig. 4 (a), Fig. 4 (b), Fig. 4 (c), the echo of Fig. 4 (d), by the inventive method respectively to Fig. 4 (a), Fig. 4 (b), Fig. 4 (c), Fig. 4 (d) is reconstructed, and records corresponding reconstitution time loss, as shown in table 2.

The time loss of table 2 the inventive method reconstruct different size terraced fields scene

Terraced fields scene	Fig. 4 (a)	Fig. 4 (b)	Fig. 4 (c)	Fig. 4 (d)
					The size of scene	64×64	128×128	256×256	512×512
Time loss (s)	0.126	0.369	1.592	14.739

The time loss of different size terraced fields scene is reconstructed as can be seen from the inventive method of table 2, relative to the existing rarefaction representation algorithm by two-dimensional scene vectorization, method of the present invention accelerates the imaging time to scene greatly, achieve little scene real time imagery, the object of large scene fast imaging, has significant practicality.

Claims (5)

1., based on a synthetic aperture radar image-forming method for sparse representation theory, comprise the steps:

(1) according to radar scene transponder pulse earthward obtain the echoed signal of ground scene $y(t_a,\hat{t})=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{\mathrm{pq}}{w}_a(t_a-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_a-\frac{x_p}{v})}^2)w_r(\hat{t}-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{(\hat{t}-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\πf}}_c}{C}{R}_q)$

In formula, for the fast time, t _afor the slow time, f _cfor carrier frequency, γ is chirp rate, and v is carrier aircraft speed, and C is propagation velocity of electromagnetic wave, w _a() is orientation window function, w _r() is chirp pulse signal time window function, P be ground scene in orientation to discrete grid block number, Q be ground scene distance to discrete grid block number, p be ground scene in orientation to p discrete grid block, q be ground scene distance to q discrete grid block, f _pqbe the scattering coefficient of (p, q) individual grid place scattering point, R ₀for radar is to the vertical oblique distance at ground scene center, R _qfor radar is to distance to the vertical oblique distance of q discrete grid block, x _pfor orientation is to the x-axis coordinate of p discrete grid block;

(2) to echoed signal carry out two-dimensional discrete sampling, obtain following echo matrix Y:

Wherein, M be orientation to exomonental number, N is that in each pulse, distance is to sampling number; for echoed signal is in the sample value of (m, n) individual sampling instant, its expression is as follows:

$y(t_{a,m},{\hat{t}}_n)=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{f}_{\mathrm{pq}}{w}_a(t_{a,m}-\frac{x_p}{v})\exp (-j\frac{{2\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_{a,m}-\frac{x_p}{v})}^2)w_r({\hat{t}}_n-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{\left(\frac{{2R}_q}{C}\right)}^2\right)\exp (-j\frac{{4\mathrm{\πR}}_q}{\mathrm{\λ}})$

In formula, λ is carrier wavelength, t _a,mbe m pulse, for fast time n-th sampling instant value;

(3) orientation of ground scene is constructed to basis matrix R:

Wherein $r(t_{a,m},p)=w_a(t_{a,m}-\frac{x_p}{v})\exp (-j\frac{{\mathrm{\πv}}^2}{{\mathrm{\λR}}_0}{(t_{a,m}-\frac{x_p}{v})}^2);$

(4) distance of ground scene is constructed to basis matrix G:

Wherein, $g(q,{\hat{t}}_n)=w_r({\hat{t}}_n-\frac{{2R}_q}{C})\exp \left(\mathrm{j\π\γ}{({\hat{t}}_n-\frac{{2R}_q}{C})}^2\right)\exp (-j\frac{{4\mathrm{\πR}}_q}{\mathrm{\λ}});$

(5) according to echo matrix Y, orientation to basis matrix R, distance to the scattering coefficient matrix F of basis matrix G and ground scene, build following matrix relationship formula:

Y＝RFG+N，

In formula, N is and the noise matrix of echo matrix Y with dimension, and the form of scattering coefficient matrix F is as follows:

Wherein, p=1,2 ..., P, q=1,2 ..., Q;

(6) according to the scattering coefficient matrix F of ground scene, intermediate variable matrix V is obtained, horizontal total variation matrix D x, vertical total variation matrix D _y:

V＝F

D _x＝D _hF，

D _y＝FD _v

In formula, D _hfor horizontal total variation operator matrix, D _vfor vertical total variation operator matrix;

(7) parameter that the matrix relationship formula of step (5) and step (6) obtain is utilized, majorized function f (F, V, D under structure total variation framework _x, D _y):

$\underset{F,V,D_x,D_y}{\min }f(F,V,D_x,D_y)=\{{\left|\right|D_x\left|\right|}_1+{\left|\right|D_y\left|\right|}_1+\frac{\mathrm{\λ}}{2}{\left|\right|D_{h}V-D_x\left|\right|}_F^2+\frac{\mathrm{\λ}}{2}{\left|\right|{\mathrm{VD}}_v-D_y\left|\right|}_F^2+\frac{v}{2}{\left|\right|V-F\left|\right|}_F^2+\frac{\mathrm{\μ}}{2}{\left|\right|\mathrm{RFG}-Y\left|\right|}_F^2\},$

Wherein represent the operational symbol finding a function minimum value, λ is total variation penalty factor, and ν is scene scatters coefficient penalty factor, and μ is echo penalty factor, || || _frepresent the Frobenius norm asking matrix, || || ₁represent and be added again after each element of matrix is taken absolute value;

(8) use Split-Bregman method to majorized function f (F, V, the D in step (7) _x, D _y) carry out iterative, obtain the final iteration result F of ground scene scattering coefficient matrix F ^*;

(9) step (8) is obtained to the final iteration result F of ground scene scattering coefficient matrix F ^*delivery value, exports the image obtaining ground scene.

2. the synthetic aperture radar image-forming method based on sparse representation theory according to claim 1, wherein said step (1) radar scene transponder pulse earthward it is expressed as follows:

$s(t_a,\hat{t})=w_r\left(\hat{t}\right)\exp \left(\mathrm{j\π\γ}{\hat{t}}^2\right)\exp \left(j2\mathrm{\π}{f}_{c}t\right),$

In formula, f _cfor carrier frequency, γ is chirp rate, and t is full-time, for the fast time, t _afor the slow time, the pass of these three times is represent the time window function of chirp pulse signal, T _rit is the time of pulse persistance.

3. the synthetic aperture radar image-forming method based on sparse representation theory according to claim 1, wherein said step (8) uses Split-Bregman method to majorized function f (F, V, the D in step (7) _x, D _y) carry out iterative, carry out as follows:

(8a) according to majorized function f (F, V, D _x, D _y), obtain majorized function L (F, V, the D of Split-Bregman form _x, D _y):

$\underset{F,V,D_x,D_y}{\min }L(F,V,D_x,D_y)=\{{\left|\right|D_x\left|\right|}_1+{\left|\right|D_y\left|\right|}_1+\frac{\mathrm{\λ}}{2}{\left|\right|D_{h}V-D_x+B_x\left|\right|}_F^2+\frac{\mathrm{\λ}}{2}{\left|\right|{\mathrm{VD}}_v-D_y+B_y\left|\right|}_F^2+\frac{v}{2}{\left|\right|V-F+W\left|\right|}_F^2+\frac{\mathrm{\μ}}{2}{\left|\right|\mathrm{RFG}-Y\left|\right|}_F^2\},$

In formula, B _xfor horizontal total variation matrix auxiliary variable, B _yfor vertical total variation matrix auxiliary variable, W is scattering coefficient matrix auxiliary variable;

(8b) initialization iterative steps k=0, scattering coefficient matrix F after kth time iteration ^kfor all 1's matrix, intermediate variable matrix V after kth time iteration ^kfor all 1's matrix, horizontal total variation matrix after kth time iteration for all 1's matrix, vertical total variation matrix after kth time iteration for all 1's matrix; Scattering coefficient matrix auxiliary variable W after kth time iteration ^kfor full 0 matrix, horizontal total variation matrix auxiliary variable after kth time iteration for full 0 matrix, vertical total variation matrix auxiliary variable after kth time iteration for full 0 matrix; Total variation penalty factor λ >0 is set, scene scatters coefficient penalty factor ν >0, echo penalty factor μ >0, stopping criterion for iteration ε=5 × 10 ^-4;

(8c) scattering coefficient matrix F after kth+1 iteration is obtained ^k+1;

(8d) intermediate variable matrix V after kth+1 iteration is obtained ^k+1;

(8e) according to intermediate variable matrix V after kth+1 iteration ^k+1, horizontal total variation matrix auxiliary variable after kth time iteration vertical total variation matrix auxiliary variable after kth time iteration according to horizontal total variation matrix after following formula acquisition kth+1 iteration vertical total variation matrix after kth+1 iteration

$\begin{array}{c}{\left(D_x^{k+1}\right)}_{p,q}=\mathrm{sign}\left({(D_h{V}^{k+1}+B_x^k)}_{p,q}\right)\max \left(\right|{(D_h{V}^{k+1}+B_x^k)}_{p,q}|-\frac{1}{\mathrm{\λ}},0)\\ {\left(D_y^{k+1}\right)}_{p,q}=\mathrm{sign}\left({(V^{k+1}{D}_v+B_y^k)}_{p,q}\right)\max \left(\right|{(V^{k+1}{D}_v+B_y^k)}_{p,q}|-\frac{1}{\mathrm{\λ}},0)\end{array},$

In formula, p=1,2 ..., P, q=1,2 ..., Q, D _hfor horizontal total variation operator matrix, D _vfor vertical total variation operator matrix, sign () is sign function;

(8f) according to intermediate variable matrix V after kth+1 iteration ^k+1, scattering coefficient matrix F after kth+1 iteration ^k+1, horizontal total variation matrix after kth+1 iteration vertical total variation matrix after kth+1 iteration horizontal total variation matrix auxiliary variable after kth time iteration vertical total variation matrix auxiliary variable after kth time iteration scattering coefficient matrix auxiliary variable W after kth time iteration ^k, according to scattering coefficient matrix auxiliary variable W after following formula acquisition kth+1 iteration ^k+1, horizontal total variation matrix auxiliary variable after kth+1 iteration vertical total variation matrix auxiliary variable after kth+1 iteration

W ^k+1＝W ^k+V ^k+1-F ^k+1

$B_x^{k+1}=B_x^k+D_h{V}^{k+1}-D_x^{k+1};$

$B_y^{k+1}=B_y^k+V^{k+1}{D}_v-D_y^{k+1}$

(8g) according to scattering coefficient matrix F after kth+1 iteration ^k+1, scattering coefficient matrix F after kth time iteration ^k, obtain square error M by following formula:

$M=\frac{{\left|\right|F^{k+1}-F^k\left|\right|}_F^2}{{\left|\right|F^k\left|\right|}_F^2},$

In formula, || || _frepresent the Frobenius norm asking matrix;

(8h) judge whether square error M≤ε sets up, perform step (8i) if set up; Otherwise make k=k+1, return step (8c) and continue iteration operation, wherein ε is stopping criterion for iteration;

(8i) F is made ^*=F ^k+1, obtain the final iteration result F of ground scene scattering coefficient matrix F ^*.

4. the synthetic aperture radar image-forming method based on sparse representation theory according to claim 3, scattering coefficient matrix F after acquisition kth+1 iteration in wherein said step (8c) ^k+1, carry out in accordance with the following steps:

(8c1) according to orientation to basis matrix R, distance to basis matrix G, obtain orientation to symmetric matrix Ψ, distance is to symmetric matrix Φ:

Ψ＝R ^TR

，

Φ＝GG ^T

Wherein, () ^trepresenting matrix transposition;

(8c2) according to feature decomposition orientation to symmetric matrix Ψ, distance, to symmetric matrix Φ, obtains orientation to orthogonal matrix U _r, orientation is to diagonal matrix L _r, distance is to orthogonal matrix U _g, distance is to diagonal matrix L _g;

(8c3) according to echo matrix Y, orientation to basis matrix R, distance to basis matrix G, intermediate variable matrix V after kth time iteration ^k, scattering coefficient matrix auxiliary variable W after kth time iteration ^k, orientation is to orthogonal matrix U _r, distance is to orthogonal matrix U _g, orientation is to diagonal matrix L _r, distance is to diagonal matrix L _g, according to scattering coefficient companion matrix after following formula acquisition kth+1 iteration

In formula, p=1,2 ..., P, q=1,2 ..., Q;

(8c4) according to orientation to orthogonal matrix U _r, distance is to orthogonal matrix U _g, scattering coefficient companion matrix after kth+1 iteration according to scattering coefficient matrix F after following formula acquisition kth+1 iteration ^k+1:

5. the synthetic aperture radar image-forming method based on sparse representation theory according to claim 3, intermediate variable matrix V after acquisition kth+1 iteration in wherein said step (8d) ^k+1, carry out in accordance with the following steps:

(8d1) according to horizontal total variation operator matrix D _h, vertical total variation operator matrix D _v, obtain horizontal total variation matrix E, vertical total variation matrix Z:

$\begin{array}{c}E=D_h^T{D}_h\\ Z=D_v{D}_v^T\end{array},$

Wherein, () ^trepresenting matrix transposition;

(8d2) according to feature decomposition horizontal total variation matrix E, vertical total variation matrix Z, obtains horizontal total variation orthogonal matrix U _x, horizontal total variation diagonal matrix L _x, vertical total variation orthogonal matrix U _y, vertical total variation diagonal matrix L _y;

(8d3) according to scattering coefficient matrix F after kth+1 iteration ^k+1, horizontal total variation operator matrix D _h, vertical total variation operator matrix D _v, scattering coefficient matrix auxiliary variable W after kth time iteration ^k, horizontal total variation matrix auxiliary variable after kth time iteration vertical total variation matrix auxiliary variable after kth time iteration horizontal total variation matrix after kth time iteration vertical total variation matrix after kth time iteration horizontal total variation orthogonal matrix U _x, vertical total variation orthogonal matrix U _y, horizontal total variation diagonal matrix L _x, vertical total variation diagonal matrix L _y, according to intermediate variable companion matrix after following formula acquisition kth+1 iteration

In formula, p=1,2 ..., P, q=1,2 ..., Q;

(8d4) according to horizontal total variation orthogonal matrix U _x, vertical total variation orthogonal matrix U _y, intermediate variable companion matrix after kth+1 iteration according to intermediate variable matrix V after following formula acquisition kth+1 iteration ^k+1: