CN104714229A - Microwave gazing correlated imaging treatment method convenient in extracting of object contour - Google Patents

Abstract

The invention discloses a microwave gazing correlated imaging treatment method convenient in extracting of an object contour. The method comprises the following steps: establishing a microwave gazing correlated imaging linear model on the basis of an electromagnetic scattering theory and radar parameters; reconstructing a microwave gazing correlated imaging linear model by virtue of a total variation regularizing method so as to obtain a reconstructed target model of microwave gazing correlated imaging; and setting regularizing parameters and carrying out iterative inversion imaging so as to obtain a microwave gazing correlated inversed image which is stable and is high in definition. The method disclosed by the invention can be used for effectively solving the ill-posed problems of a random radiation field matrix; and the method is conducive to maintaining the edge characteristics of a target, and is especially suitable for an imaging scene which is clear in target outline and keeps a high contrast ratio with the surrounding environment.

Description

A kind of microwave being convenient to extract objective contour stares relevance imaging disposal route

Technical field

The present invention relates to microwave and stare relevance imaging field, particularly relate to a kind of microwave being convenient to extract objective contour and stare relevance imaging disposal route.

Background technology

It is that a kind of brand-new microwave stares relevance imaging system that microwave based on space-time bidimensional random radiation field stares relevance imaging.This novel imaging system forms scatter echo by the objectives interation in the radiation field of structure space-time bidimensional random variation and the gaze area of geo-stationary, the scatter echo received and radiation field information are made relevant treatment, obtains the high resolution radar picture of observation area internal object.This imaging system breaches the restriction of the antenna aperture of conventional radar imaging system, for round-the-clock, round-the-clock, high-resolution remote sensing of the earth are stared observation and provided a kind of new technological approaches.

Microwave based on space-time bidimensional random radiation field stares relevance imaging as a kind of new microwave imaging system, and its research work is still in the starting stage, also has many key issues to have to be solved.In systems in practice, the structure of space-time bidimensional radiation field is subject to random radiation unit number, random radiation actinal surface size, the restriction of the factors such as signal bandwidth, and the space-time bidimensional randomness that realize ideal is very difficult.Nonideal random radiation field is easy to the pathosis causing random radiation field observing matrix, makes the object inversion of microwave staring imaging become a non-well-posedness problem.

The general thoughts solved of non-well-posedness problem increases constraint condition to be translated into solving of a well-posed problem.But the constraint condition of often kind of conversion method has its specific aim, must depending on embody rule scene.So it is necessary that the microwave studied under different scene stares relevance imaging disposal route.

Summary of the invention

The object of this invention is to provide a kind of microwave being convenient to extract objective contour and stare relevance imaging disposal route, effectively can solve the pathosis problem of random radiation field matrix, be conducive to being stable into picture and maintain edge characteristic.

The object of the invention is to be achieved through the following technical solutions:

The microwave being convenient to extract objective contour stares a relevance imaging disposal route, and the method comprises:

Utilize Electromagnetic Scattering Theory and radar parameter to set up linear model that microwave stares relevance imaging;

Utilize total variation regularization method to stare the linear model reconstruct of relevance imaging to described microwave, obtain the object reconstruction model that microwave stares relevance imaging;

Setting regularization parameter carries out iterative inversion imaging, and acquisition is stablized high-resolution microwave and stared association inversion image.

Further, the linear model that described microwave stares relevance imaging is expressed as:

$S_r({\stackrel{\→}{r}}^{\′\′},t_m)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}[E^{\mathrm{rad}}({\stackrel{\′\′}{r}}_n,{\stackrel{\→}{r}}^{\′\′},t_m)\mathrm{\σ}\left({\stackrel{\→}{r}}_n\right)+Q\left(t_m\right)];$

Wherein, represent the locus of receiver, t _mrepresent the moment of reception m echo, m=1,2 ... M; represent the locus of the n-th imageable target in imaging region, n=1,2 ... N; expression is positioned at the receiver at place is at t _mthe Echo Rating that reception arrives; represent echo corresponding the space-time bidimensional random radiation field at place; represent place's target scattering coefficient; Q (t _m) represent t _mreception to echo in noise;

Write above-mentioned expression formula as matrix form equation:

Described matrix equation is abbreviated as:

b＝A·σ+Q；

Wherein, b is echoed signal, and A is that space-time bidimensional penetrates field matrix at random, and σ is imageable target function, and Q is noise.

Further, described space-time bidimensional random radiation field matrix A is space-time bidimensional random radiation field function discrete form, in rectangular coordinate system O-XYZ, random radiation source is positioned on plane D, its by L independently random radiation unit form, the antenna aperture planar central position of each random radiation unit is for being respectively

Imaging region is the region S in XOY two dimensional surface, represent two dimensional surface space, for the position vector of any point in imaging region, the vertical range between imaging region S and array plane D is z ₀, suppose that the pumping signal of i-th random radiation unit is f _i(t), then space-time bidimensional random radiation field function be expressed as:

$E^{\mathrm{rad}}(\stackrel{\→}{r},{\stackrel{\→}{r}}^{\′\′},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_i\left({\hat{R}}_i^{^}\right)F_r\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}{f}_i(t-\frac{R_i}{c});$

Wherein, c represents the light velocity, $R_i=|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}|,{\hat{R}}_i=\frac{\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}}{|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}|},R_r=|{\stackrel{\→}{r}}^{\′\′}-\stackrel{\→}{r}|,{\hat{R}}_r=\frac{{\stackrel{\→}{r}}^{\′\′}-\stackrel{\→}{r}}{|{\stackrel{\→}{r}}^{\′\′}-\stackrel{\→}{r}|},F_i\left({\hat{R}}_i\right)$ Be the radiation pattern function of i-th random radiation unit, for the radiation pattern function of receiver.

Further, described echoed signal b is time domain echoed signal discrete form, described time domain echoed signal be expressed as:

Wherein, represent the locus of receiver, t is the time, for space-time bidimensional random radiation field function, the noise in the echo that Q (t) receives for t.

Further, described imageable target function σ ∈ C ⁿfor scattering coefficient on imageable target face discrete form, the wherein discretize number of N imageable target, for the position vector of any point in imaging region.

Further, the described total variation regularization method that utilizes stares the linear model reconstruct of relevance imaging to described microwave, and the object reconstruction model that acquisition microwave stares relevance imaging comprises:

The linear model based on total variation regularization method microwave being stared relevance imaging changes solving of a well-posed problem into, obtains the object reconstruction model that microwave stares relevance imaging, is expressed as:

$\underset{\mathrm{\σ}}{\min }J\left(\mathrm{\σ}\right):J\left(\mathrm{\σ}\right)=\frac{1}{p}{\left|\right|b-\mathrm{A\σ}\left|\right|}_p^p+\frac{\mathrm{\α}}{q}{\left|\right|\sqrt{{\left(D_x\mathrm{\σ}\right)}^2+{\left(D_y\mathrm{\σ}\right)}^2}\left|\right|}_q^q;$

Wherein, J (σ) is optimization object function, || || _prepresent and l is asked to vector _pnorm, 1≤p≤2 in formula, 1≤q≤2, α is regularization parameter, for broad sense total variance regular function, D _x, D _yrepresent the discrete differential of x, y dimension to scattering coefficient distribution σ respectively.

Further, described setting regularization parameter carries out iterative inversion imaging, obtains to stablize high-resolution microwave and stare association inversion image and comprise:

By structure weighting matrix, above-mentioned microwave is stared the l of the total variation regularization of relevance imaging _pnorm problem is converted into equal l ₂norm problem:

$\underset{\mathrm{\σ}}{\min }{J}_1\left(\mathrm{\σ}\right):{J_1}^{\left(k\right)}\left(\mathrm{\σ}\right)=\frac{1}{2}{\left|\right|W_1^{\left(k\right)\frac{1}{2}}(b-\mathrm{A\σ})\left|\right|}_2^2+\frac{\mathrm{\α}}{2}{\left|\right|W_2^{\left(k\right)\frac{1}{2}}\left|\right|}_2^2;$

Wherein, J ₁(σ) be l ₂the optimization object function of norm problem, D is difference matrix, and subscript k represents kth time iterative process, weighting matrix for the Iterative Matrix constructed in kth time iterative process;

The value of setting p, q and regularization parameter, initialized target scene backscattering coefficient σ ⁽⁰⁾=(A ^ta+ α D ^td) ^-1a ^tb, iterations k=0;

Solve according to following iterative formula:

${\mathrm{\σ}}^{(k+1)}={(A^T{W}_1^{\left(k\right)}A+\mathrm{\α}{D}^T{W}_2^{\left(2\right)}D)}^{-1}{A}^T{W}_1^{\left(k\right)}b;$

Until k reaches greatest iteration number k _max, acquisition is stablized high-resolution microwave and is stared association inversion image

Further, described weighting matrix be expressed as:

$W_1^{\left(k\right)}=\mathrm{diag}\left({|b-\mathrm{A\σ}|}^{p-2}\right);$

Described weighting matrix be expressed as:

$W_2^{\left(k\right)}=\left(\begin{array}{cc}\mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{q-2}{2}}& 0\\ 0& \mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{q-2}{2}}\end{array}\right).$

As seen from the above technical solution provided by the invention, stare in relevance imaging at the microwave of space-time bidimensional random radiation field, when radiation field matrix is morbid state, the method based on total variation regularization is adopted to be changed into solving of a well-posed problem, this image processing method is conducive to the local edge keeping target, be conducive to the extraction of objective contour, the imaging scene that particularly suitable objective contour is clear and large with surrounding enviroment contrast.

Accompanying drawing explanation

In order to be illustrated more clearly in the technical scheme of the embodiment of the present invention, below the accompanying drawing used required in describing embodiment is briefly described, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawings can also be obtained according to these accompanying drawings.

A kind of being convenient to that Fig. 1 provides for the embodiment of the present invention extracts the process flow diagram that the microwave of objective contour stares relevance imaging disposal route;

The process flow diagram carrying out iterative inversion imaging that Fig. 2 provides for the embodiment of the present invention;

Fig. 3 stares relevance imaging scene schematic diagram for the microwave based on space-time bidimensional random radiation field that the embodiment of the present invention provides;

The radiation pattern during 10GHz that Fig. 4 provides for the embodiment of the present invention;

The emulation original image object module figure that Fig. 5 provides for the embodiment of the present invention.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, be clearly and completely described the technical scheme in the embodiment of the present invention, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on embodiments of the invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to protection scope of the present invention.

Embodiment

A kind of being convenient to that Fig. 1 provides for the embodiment of the present invention extracts the process flow diagram that the microwave of objective contour stares relevance imaging disposal route.As shown in Figure 1, the method mainly comprises the steps:

Step 11, utilize Electromagnetic Scattering Theory and radar parameter to set up linear model that microwave stares relevance imaging.

Step 12, utilize total variation regularization method to stare the linear model reconstruct of relevance imaging to described microwave, obtain microwave and stare the object reconstruction model of relevance imaging.

Step 13, setting regularization parameter carry out iterative inversion imaging, and acquisition is stablized high-resolution microwave and stared association inversion image.

For the ease of understanding, be described in detail for above-mentioned three steps below.

1, the linear model that microwave stares relevance imaging is set up.

In rectangular coordinate system O-XYZ, random radiation source is positioned on plane D, and it is made up of the individual independently random radiation unit of L, and the antenna aperture planar central position of each random radiation unit is for being respectively imaging region is the region S in XOY two dimensional surface, represent two dimensional surface space, for the position vector of any point in imaging region, the vertical range between imaging region S and array plane D is z ₀; Suppose that the pumping signal of i-th random radiation unit is f _i(t), when not considering polarization, the incident field distribution that it is formed on imaging region S can be expressed as with scalar form:

$E_i^{\mathrm{inc}}(\stackrel{\→}{r},t)=\frac{F_i\left({\hat{R}}_i\right)}{4\mathrm{\π}{R}_i}{f}_i(t-\frac{R_i}{c})---\left(1\right)$

Wherein, c represents the light velocity, it is the radiation pattern function of i-th random radiation unit;

The then incident field distribution that formed in imaging region S of L random radiation unit the superposition of the far region radiation field that each random radiation unit is formed can be expressed as:

$E^{\mathrm{inc}}(\stackrel{\→}{r},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{E}_i^{\mathrm{inc}}(\stackrel{\→}{r},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_i\left({\hat{R}}_i\right)}{4\mathrm{\π}{R}_i}{f}_i(t-\frac{R_i}{c})---\left(2\right)$

According to Electromagnetic Scattering Theory, the incident field on imaging region S with after objectives interation the scattered field that place is formed can be expressed as:

$E^{\mathrm{sca}}({\stackrel{\→}{r}}^{\′\′},t)=\underset{S}{\∫\∫}\frac{E^{\mathrm{inc}}(\stackrel{\→}{r},t)\mathrm{\σ}\left(\stackrel{\→}{r}\right)}{4\mathrm{\π}{R}_r}d\stackrel{\→}{r}=\underset{S}{\∫\∫}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_i\left({\hat{R}}_i\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}{f}_i(t-\frac{R_i}{c})\mathrm{\σ}\left(\stackrel{\→}{r}\right)d\stackrel{\→}{r}---\left(3\right)$

Wherein, for the scattering coefficient of imaging region S internal object distributes.Then be positioned at the echoed signal that the receiver at place receives can be expressed as:

$S_r({\stackrel{\→}{r}}^{\′\′},t)=\underset{S}{\∫\∫}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_i\left(\stackrel{^^}{R_i}\right)F_r\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}{f}_i(t-\frac{R_i}{c})\mathrm{\σ}\left(\stackrel{\→}{r}\right)d\stackrel{\→}{r}+Q\left(t\right)---\left(4\right)$

Wherein, for the radiation pattern function of receiver, the noise in the echo that Q (t) receives for t.

Definition space-time bidimensional random radiation field function for

$E^{\mathrm{rad}}(\stackrel{\→}{r},{\stackrel{\→}{r}}^{\′\′},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_i\left({\hat{R}}_i^{^}\right)F_r\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}{f}_i(t-\frac{R_i}{c})---\left(5\right)$

The echoed signal that then receiver receives can be expressed as further:

Sliding-model control is carried out to above formula, then can obtain as Linear Model with Side:

$S_r({\stackrel{\→}{r}}^{\′\′},t_m)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}[E^{\mathrm{rad}}({\stackrel{\′\′}{r}}_n,{\stackrel{\→}{r}}^{\′\′},t_m)\mathrm{\σ}\left({\stackrel{\→}{r}}_n\right)+Q\left(t_m\right)];$

Wherein, represent the locus of receiver, t _mrepresent the moment of reception m echo, m=1,2 ... M; represent the locus of the n-th imageable target in imaging region, n=1,2 ... N; expression is positioned at the receiver at place is at t _mthe Echo Rating that reception arrives; represent echo corresponding the space-time bidimensional random radiation field at place; represent place's target scattering coefficient; Q (t _m) represent t _mreception to echo in noise;

Write above-mentioned expression formula as matrix form equation:

Described matrix equation is abbreviated as:

b＝A·σ+Q； (7)

Wherein, b is echoed signal, and A is that space-time bidimensional penetrates field matrix at random, and σ is imageable target function, and Q is noise.

In above formula, described echoed signal b ∈ C ^m, C represents complex number space, C ^mfor M ties up complex number space, it is time domain echoed signal discrete form, imageable target function σ ∈ C ⁿfor scattering coefficient on imageable target face discrete form, space-time bidimensional random radiation field matrix A ∈ C ^{m × N}for space-time bidimensional radiation field function discrete form, n ∈ C ^mfor the discrete form of noise.

2, the linear model reconstruct of relevance imaging is stared based on the microwave of total variation regularization method.

The linear model of above-mentioned association staring imaging in actual applications, structure due to space-time bidimensional random radiation field is subject to the restriction of the conditions such as radiation element number of array and signal bandwidth, make the conditional number of radiation field observing matrix larger, namely radiation field observing matrix is ill-condition matrix, and Scattering data result is affected by noise larger.Adopt the method based on total variation regularization to be changed into solving of a well-posed problem in the embodiment of the present invention, obtain stablizing high-resolution microwave and stare association inversion image.

Specifically, the linear model based on total variance (TV) regularization method microwave being stared relevance imaging changes solving of a well-posed problem into, obtains the object reconstruction model that microwave stares relevance imaging, is expressed as:

$\underset{\mathrm{\σ}}{\min }J\left(\mathrm{\σ}\right):J\left(\mathrm{\σ}\right)=\frac{1}{p}{\left|\right|b-\mathrm{A\σ}\left|\right|}_p^p+\frac{\mathrm{\α}}{q}{\left|\right|\sqrt{{\left(D_x\mathrm{\σ}\right)}^2+{\left(D_y\mathrm{\σ}\right)}^2}\left|\right|}_q^q;---\left(8\right)$

Wherein, J (σ) is optimization object function, || || _prepresent and l is asked to vector _pnorm, subscript p represents l _pthe p power of norm,

In imaging process, make discretize stress and strain model to imaging region, the discrete grid block number that (x, y) ties up is respectively (N _x, N _y), then grid adds up to N=N _x× N _y, net point coordinate is { (x _i, y _j) | x _i=i Δ x, y _j=j Δ y, i=1 ..., N _x, j=1 ..., N _y, then the discrete differential of x, y dimension of scattering system distribution σ can be expressed as:

$\left\{\begin{array}{c}{D}_x\mathrm{\σ}(x_i,y_i)=\left\{\begin{array}{cc}\frac{\mathrm{\σ}(x_{i+1},y_j)-\mathrm{\σ}(x_i,y_j)}{\mathrm{\Δx}}& ,i\≤N_x\\ 0& ,i=N_x\end{array}\right.\\ D_y\mathrm{\σ}(x_i,y_i)=\left\{\begin{array}{cc}\frac{\mathrm{\σ}(x_i,y_{j+1})-\mathrm{\σ}(x_i,y_j)}{\mathrm{\Δy}}& ,i\≤N_y\\ 0& ,i=N_y\end{array}\right.\end{array}\right.---\left(9\right)$

The Generalized Solving Method model that described microwave stares the total variation regularization of relevance imaging is a l _pleast norm problem, adopts weighted iteration least-squares algorithm to solve.By structure weighting matrix, can by above-mentioned l _pnorm problem is converted into equal l ₂norm problem:

$\underset{\mathrm{\σ}}{\min }{J}_1\left(\mathrm{\σ}\right):{J_1}^{\left(k\right)}\left(\mathrm{\σ}\right)=\frac{1}{2}{\left|\right|W_1^{\left(k\right)\frac{1}{2}}(b-\mathrm{A\σ})\left|\right|}_2^2+\frac{\mathrm{\α}}{2}{\left|\right|W_2^{\left(k\right)\frac{1}{2}}\left|\right|}_2^2;---\left(10\right)$

Wherein, J ₁(σ) be l ₂the optimization object function of norm problem, subscript k represents kth time iterative process, and difference matrix D is

$D=\left(\begin{array}{c}{D}_x\\ D_y\end{array}\right)---\left(11\right)$

Weighting matrix be expressed as:

$W_1^{\left(k\right)}=\mathrm{diag}\left({|b-\mathrm{A\σ}|}^{p-2}\right);---12$

Described weighting matrix be expressed as:

$W_2^{\left(k\right)}=\left(\begin{array}{cc}\mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{q-2}{2}}& 0\\ 0& \mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{q-2}{2}}\end{array}\right).---\left(13\right)$

3, iterative inversion imaging.

Described microwave stares the l after the Generalized Solving Method model conversation of the total variation regularization of relevance imaging ₂norm problem solving, its iterative step as shown in Figure 2, mainly comprises the steps:

1) value and the regularization parameter of p, q is set, initialized target scene backscattering coefficient σ ⁽⁰⁾=(A ^ta+ α D ^td) ^-1a ^tb, iterations k=0.

2) weighting matrix is calculated with

3) solve according to following iterative formula: ${\mathrm{\σ}}^{(k+1)}={(A^T{W}_1^{\left(k\right)}A+\mathrm{\α}{D}^T{W}_2^{\left(k\right)}D)}^{-1}{A}^T{W}_1^{\left(k\right)}b;$

4) k=k+1 is made, until k reaches greatest iteration number k _max.

5) obtain and stablize high-resolution microwave and stare association inversion image

Exemplary, below in conjunction with the scene shown in accompanying drawing 3, principle of the present invention is described in detail.

Simulating scenes as shown in Figure 3, the spacing between transmitting-receiving array plane and staring imaging plane is z ₀=100m, space-time bidimensional random radiation source is made up of L=25 random radiation source unit, and the emitting antenna of each radiating element is equidistantly arranged by 5 × 5 on plane D, the total cun of d that radiation actinal surface X ties up _xfor the size d of 1.5m, Y dimension _yfor 1.5m, aperture centre coordinate is (0,0, z ₀).Staring imaging region is two-dimentional X0Y plane, and area size is 40m × 40m, is divided into the image-generating unit of 80 × 80, image-generating unit separation delta x=Δ y=0.5m.The center carrier frequence that each transmitter is launched is 10GHz, and signal bandwidth is 1GHz, and adopt random frequency hopping pulse signal form, then the pumping signal of i-th random radiation unit is f _it () can be expressed as

$f_i\left(t\right)=\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\mathrm{rect}\left(\frac{t-m{T}_r}{\mathrm{\τ}}\right)\exp [j2\mathrm{\π}{f}_{\mathrm{im}}(t-m{T}_r)+j{\mathrm{\φ}}_m+j2\mathrm{\π}{f}_{0}t];---\left(14\right)$

Wherein, τ is the duration of pulse, T _rfor the pulse repetition time, in emulation, get τ=500ns, T _r=1500ns, M are the pulse number launched, f _im, φ _imbe respectively modulation frequency when i-th radiating element launches m pulse and initial phase, wherein f _imvalue be random selecting in the bandwidth range of 1GHz, φ _imvalue be random selecting within the scope of 0 ~ 2 π, f ₀carrier frequency centered by=10GHz, rect (t) is rectangular window function, and it is defined as

$\mathrm{rect}\left(t\right)=\left\{\begin{array}{c}\mathrm{1,0}\≤t\≤\mathrm{\τ}\\ 0,t>\mathrm{\τ}\end{array}\right.;---\left(15\right)$

The incident field distribution that then L radiating element is formed on imaging region S is expressed as:

$E^{\mathrm{inc}}(\stackrel{\→}{r},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\left\{\begin{array}{c}\mathrm{rect}\left(\frac{t-m{T}_r-R_i/c}{\mathrm{\τ}}\right)\frac{F_{\mathrm{im}}\left({\hat{R}}_i\right)}{4\mathrm{\π}{R}_i}\\ \·\exp [j2\mathrm{\π}{f}_{\mathrm{im}}(t-m{T}_r{R}_i/c)+j{\mathrm{\φ}}_{\mathrm{im}}+j2\mathrm{\π}{f}_{0}t]\end{array}\right\};---\left(16\right)$

Wherein it is the radiation pattern function corresponding when launching m pulse of i-th random radiation unit, as shown in Figure 4, which show the directional diagram of adopted electromagnetic horn antenna when 10GH, wherein left figure is depicted as E face directional diagram, its 3dB beam angle is 13.5 °, right figure is depicted as H face directional diagram, and its 3dB beam angle is 15.25 °.

When receiver is positioned at place, and when receiving antenna is identical with emitting antenna, the echoed signal received can be expressed as:

$S_r({\stackrel{\→}{r}}^{\′\′},t)=\underset{S}{\∫\∫}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\left\{\begin{array}{c}\mathrm{rect}\left(\frac{t-m{T}_r-(R_i+R_r)/c}{\mathrm{\τ}}\right)\frac{F_{\mathrm{im}}\left({\hat{R}}_i^{^}\right)F_{\mathrm{im}}\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}\\ \·\exp [j2\mathrm{\π}{f}_{\mathrm{im}}(t-m{T}_r-(R_i+R_r)/c)+j{\mathrm{\φ}}_{\mathrm{im}}+j2\mathrm{\π}{f}_{0}t]\end{array}\right\}\mathrm{\σ}\left(\stackrel{\→}{r}\right)d\stackrel{\→}{r}+Q\left(t\right);---\left(17\right)$

Space-time bidimensional random radiation field function is expressed as:

$E^{\mathrm{rad}}(\stackrel{\→}{r},{\stackrel{\→}{r}}^{\′\′},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\left\{\begin{array}{c}\mathrm{rect}\left(\frac{t-m{T}_r-(R_i+R_r)/c}{\mathrm{\τ}}\right)\frac{F_{\mathrm{im}}\left({\hat{R}}_i^{^}\right)F_{\mathrm{im}}\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}\\ \·\exp [j2f_{\mathrm{im}}(t-m{T}_r-(R_i+R_r)/c)+j{\mathrm{\φ}}_{\mathrm{im}}+j2f_0]\end{array}\right\};---\left(18\right)$

Within m recurrence interval, get the Echo Rating in moment as a sample, then can obtain following linear equation after sliding-model control:

$S_r({\stackrel{\→}{r}}^{\′\′},t_m)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}[E^{\mathrm{rad}}({\stackrel{\→}{r}}_n,{\stackrel{\→}{t}}^{\′\′},t_m)\mathrm{\σ}\left({\stackrel{\→}{r}}_n\right)+n\left(t_m\right)];---\left(19\right)$

Wherein,

$E^{\mathrm{rad}}(\stackrel{\→}{r},{\stackrel{\→}{r}}^{\′\′},t_m)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_{\mathrm{im}}\left({\hat{R}}_i^{^}\right)F_{\mathrm{im}}\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}\exp [j2\mathrm{\π}{f}_{\mathrm{im}}(\frac{\mathrm{\τ}}{2}+\frac{2z_0-(R_i+R_r)}{c})+j{\mathrm{\φ}}_{\mathrm{im}}+j2\mathrm{\π}{f}_0{t}_m];---\left(20\right)$

Determine p=2 when getting, during q=1, the total variation regularization model that microwave stares relevance imaging is following optimization problem

$\underset{\mathrm{\σ}}{\min }J\left(\mathrm{\σ}\right):J\left(\mathrm{\σ}\right)=\frac{1}{2}{\left|\right|b-\mathrm{A\σ}\left|\right|}_2^2+\mathrm{\α}{\left|\right|\sqrt{{\left(D_x\mathrm{\σ}\right)}^2+{\left(D_y\mathrm{\σ}\right)}^2}\left|\right|}_1^1;---\left(21\right)$

By structure weighting matrix, above-mentioned optimization problem can be converted into equal l ₂during norm, weighting matrix for:

$W_1^{\left(k\right)}=\mathrm{diag}\left({|b-\mathrm{A\σ}|}^{p-2}\right)=I;---\left(22\right)$

Weighting matrix for:

$W_2^{\left(k\right)}=\left(\begin{array}{cc}\mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{-1}{2}}& 0\\ 0& \mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{-1}{2}}\end{array}\right);---\left(23\right)$

L after then transforming ₂norm optimization problem is:

$\underset{\mathrm{\σ}}{\min }{J}_1\left(\mathrm{\σ}\right):{J_1}^{\left(k\right)}\left(\mathrm{\σ}\right)=\frac{1}{2}{\left|\right|(b-\mathrm{A\σ})\left|\right|}_2^2+\frac{\mathrm{\α}}{2}{\left|\right|W_2^{\left(k\right)\frac{1}{2}}\mathrm{D\σ}\left|\right|}_2^2;---\left(24\right)$

Its iterative formula is:

${\mathrm{\σ}}^{(k+1)}={(A^{T}A+\mathrm{\α}{D}^T{W}_2^{\left(k\right)}D)}^{-1}{A}^{T}b;---\left(25\right)$

Such scheme is utilized to carry out emulation experiment to the object module figure shown in accompanying drawing 5; When getting sample number M=6000, when echo signal to noise ratio (S/N ratio) is 20dB, adopt traditional back-projection algorithm completely can not imaging; When adopting traditional truncated singular value decomposition (TSVD) method and Tikhonov regularization to carry out inversion imaging, but can both carry out imaging object edge there is ambiguity; And adopting the inverting based on total variation regularization provided by the present invention, imaging that it can not only be stable well remains the local edge of target simultaneously, thus provides convenience for the extraction of objective contour information.

The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (8)

1. the microwave being convenient to extract objective contour stares a relevance imaging disposal route, and it is characterized in that, the method comprises:

Utilize Electromagnetic Scattering Theory and radar parameter to set up linear model that microwave stares relevance imaging;

Utilize total variation regularization method to stare the linear model reconstruct of relevance imaging to described microwave, obtain the object reconstruction model that microwave stares relevance imaging;

Setting regularization parameter carries out iterative inversion imaging, and acquisition is stablized high-resolution microwave and stared association inversion image.

2. method according to claim 1, is characterized in that, the linear model that described microwave stares relevance imaging is expressed as:

$S_r({\stackrel{\→}{r}}^{\′\′},t_m)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}[E^{\mathrm{rad}}({\stackrel{\→}{r}}_n,{\stackrel{\→}{r}}^{\′\′},t_m)\mathrm{\σ}\left({\stackrel{\→}{r}}_n\right)+Q\left(t_m\right)];$

Wherein, represent the locus of receiver, t _mrepresent the moment of reception m echo, m=1,2 ... M; represent the locus of the n-th imageable target in imaging region, n=1,2 ... N; expression is positioned at the receiver at place is at t _mthe Echo Rating that reception arrives; represent echo corresponding the space-time bidimensional random radiation field at place; represent place's target scattering coefficient; Q (t _m) represent t _mreception to echo in noise;

Write above-mentioned expression formula as matrix form equation:

Described matrix equation is abbreviated as:

b＝A·σ+Q；

Wherein, b is echoed signal, and A is that space-time bidimensional penetrates field matrix at random, and σ is imageable target function, and Q is noise.

3. method according to claim 2, is characterized in that,

Described space-time bidimensional random radiation field matrix A is space-time bidimensional random radiation field function discrete form, in rectangular coordinate system O-XYZ, random radiation source is positioned on plane D, its by L independently random radiation unit form, the antenna aperture planar central position of each random radiation unit is for being respectively

Imaging region is the region S in XOY two dimensional surface, represent two dimensional surface space, for the position vector of any point in imaging region, the vertical range between imaging region S and array plane D is z ₀, suppose that the pumping signal of i-th random radiation unit is f _i(t), then space-time bidimensional random radiation field function be expressed as:

$E^{\mathrm{rad}}(\stackrel{\→}{r},{\stackrel{\→}{r}}^{\′\′},t)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{F_i\left({\hat{R}}_i^{^}\right)F_r\left(R_r\right)}{{\left(4\mathrm{\π}\right)}^2{R}_i{R}_r}{f}_i(t-\frac{R_i}{c});$

Wherein, c represents the light velocity, $R_i=|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}|,{\hat{R}}_i=\frac{\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}}{|\stackrel{\→}{r}-{\stackrel{\→}{r}}^{\′}|},R_r=|{\stackrel{\→}{r}}^{\′\′}-\stackrel{\→}{r}|,{\hat{R}}_r=\frac{{\stackrel{\→}{r}}^{\′\′}-\stackrel{\→}{r}}{|{\stackrel{\→}{r}}^{\′\′}-\stackrel{\→}{r}|},$ be the radiation pattern function of i-th random radiation unit, for the radiation pattern function of receiver.

4. method according to Claims 2 or 3, is characterized in that,

Described echoed signal b is time domain echoed signal discrete form, described time domain echoed signal be expressed as:

Wherein, represent the locus of receiver, t is the time, for space-time bidimensional random radiation field function, the noise in the echo that Q (t) receives for t.

5. method according to Claims 2 or 3, is characterized in that,

Described imageable target function σ ∈ C ⁿfor scattering coefficient on imageable target face discrete form, the wherein discretize number of N imageable target, for the position vector of any point in imaging region.

6. method according to claim 1 and 2, is characterized in that, the described total variation regularization method that utilizes stares the linear model reconstruct of relevance imaging to described microwave, and the object reconstruction model that acquisition microwave stares relevance imaging comprises:

The linear model based on total variation regularization method microwave being stared relevance imaging changes solving of a well-posed problem into, obtains the object reconstruction model that microwave stares relevance imaging, is expressed as:

$\underset{\mathrm{\σ}}{\min }J\left(\mathrm{\σ}\right):J\left(\mathrm{\σ}\right)=\frac{1}{p}{\left|\right|b-\mathrm{A\σ}\left|\right|}_p^p+\frac{\mathrm{\α}}{q}{\left|\right|\sqrt{{\left(D_x\mathrm{\σ}\right)}^2+{\left(D_y\mathrm{\σ}\right)}^2}\left|\right|}_q^q;$

Wherein, J (σ) is optimization object function, || || _prepresent and l is asked to vector _pnorm, 1≤p≤2 in formula, 1≤q≤2, α is regularization parameter, for broad sense total variance regular function, D _x, D _yrepresent the discrete differential of x, y dimension to scattering coefficient distribution σ respectively.

7. method according to claim 6, is characterized in that, described setting regularization parameter carries out iterative inversion imaging, obtains to stablize high-resolution microwave and stare association inversion image and comprise:

By structure weighting matrix, above-mentioned microwave is stared the l of the total variation regularization of relevance imaging _pnorm problem is converted into equal l ₂norm problem:

$\underset{\mathrm{\σ}}{\min }{J}_1\left(\mathrm{\σ}\right):{J_1}^{\left(k\right)}\left(\mathrm{\σ}\right)=\frac{1}{2}{\left|\right|{W_1}^{\left(k\right)\frac{1}{2}}(b-\mathrm{A\σ})\left|\right|}_2^2+\frac{\mathrm{\α}}{2}{\left|\right|{W_2}^{\left(k\right)\frac{1}{2}}\mathrm{D\σ}\left|\right|}_2^2;$

Wherein, J ₁(σ) be l ₂the optimization object function of norm problem, D is difference matrix, and subscript k represents kth time iterative process, weighting matrix W ₁ ^(k), W ₂ ^(k)for the Iterative Matrix constructed in kth time iterative process;

The value of setting p, q and regularization parameter, initialized target scene backscattering coefficient σ ⁽⁰⁾=(A ^ta+ α D ^td) ^-1a ^tb, iterations k=0;

Solve according to following iterative formula:

${\mathrm{\σ}}^{(k+1)}={(A^T{W_1}^{\left(k\right)}A+\mathrm{\α}{D}^T{W_2}^{\left(k\right)}D)}^{-1}{A}^T{W_1}^{\left(k\right)}b;$

Until k reaches greatest iteration number k _max, acquisition is stablized high-resolution microwave and is stared association inversion image

8. method according to claim 7, is characterized in that,

Described weighting matrix W ₁ ^(k)be expressed as:

${W_1}^{\left(k\right)}=\mathrm{diag}\left({|b-\mathrm{A\σ}|}^{p-2}\right);$

Described weighting matrix W ₂ ^(k)be expressed as:

${W_2}^{\left(k\right)}=\left(\begin{array}{cc}\mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{q-2}{2}}& 0\\ 0& \mathrm{diag}{({\left(D_x{\mathrm{\σ}}^{\left(k\right)}\right)}^2+{\left(D_y{\mathrm{\σ}}^{\left(k\right)}\right)}^2)}^{\frac{q-2}{2}}\end{array}\right).$