CN104182753A - Target scattering center extraction method by combining image segmentation with subspace matching pursuit - Google Patents

Abstract

The invention discloses a target scattering center extraction method by combining image segmentation with subspace matching pursuit, and mainly solves a problem of inaccurate parameter estimation caused by a big coupling degree between a scattering center category discrimination error and a scattering center of a traditional attribute scattering center method. The implementation processes of the target scattering center extraction method comprises the following steps: 1) on the basis of an attribute scattering center model, constructing a redundant dictionary of an attribute scattering center; 2) on the basis of target frequency domain observation data, combining a threshold segmentation image segmentation method with a subspace matching pursuit method to solve sparse representation observed by a target in a frequency domain; and 3) according to the redundant dictionary of the attribute scattering center and the sparse representation observed by the target in the frequency domain, extracting a target attribute scattering center parameter. A target attribute scattering center can be effectively extracted, the geometric dimensions of the target and important components thereof can be precisely estimated, and the invention can be used for the classification and identification of a radar target.

Description

Combining image is cut apart the target scattering center extracting method of following the trail of with Subspace Matching

Technical field

The invention belongs to Radar Technology field, relate to a kind of target scattering center extracting method, can be used for the physical dimension of estimating target and vitals thereof, for target classification identification provides important characteristic information.

Background technology

Synthetic-aperture radar SAR is a kind of active microwave imaging sensor, utilize respectively distance to pulse compression technique and orientation to complex art realize higher spatial resolution.SAR has round-the-clock, round-the-clock feature of scouting, and the information that provides optical sensor not provide.Rely on its unique advantage, SAR has become a kind of indispensable military surveillance and civil remote sensing.

When radar is operated in high frequency region, the electromagnetic scattering sum that total electromagnetic scattering of target can Approximate Equivalent is a plurality of locally scattered sources, these locally scattered sources are just called scattering center.At present for extracting the model of target scattering center, be mainly divided into three kinds: ideal point scattering center model, damped expoential model, and attribute scattering center model.Wherein attribute scattering center model meets the scattering properties of SAR target most, and the attribute scattering center that it is described has abundant geometric meaning and physical significance.

The attribute scattering center model parameterized model that is applicable to High Resolution SAR view data that to be Michael J.Gerry in 1999 and Lee C.Potter propose based on geometric theory of diffraction and physical optics theory.See [M.J.Gerry, L.C.Potter, I.J.Gupta, and A.van der Merwe, A parametric model for synthetic aperture radar measurements[J] .IEEE Transactions on Antennas and Propagation, 1999, Vol.47, NO.7, pp.1179-1188].This model has not only been described positional information and the strength information of scattering center, has also described the physical dimension of scattering center, and the dependence of scattering center to frequency and orientation, and can be finally inversed by thus the geometry of target.Attribute scattering center model, than point scattering model and damped expoential model, comprises the abundanter feature that can be used for target classification identification.

The feature extraction of attribute scattering center is in fact a process of estimating each scattering center parameter from target echo data.Because the scattering center information that attribute scattering center model comprises is more, cause model structure complexity and parameter dimension higher, increased the complicacy of model parameter estimation.Existing method is mainly divided into two kinds, is respectively scattering centers extraction and the scattering centers extraction based on frequency domain data based on image area.Scattering centers extraction method based on image area has the advantages that to reduce the degree of coupling between scattering center, but has the problem that model order is selected and scattering center structured sort is differentiated.The problem that scattering centers extraction method based on frequency domain data has avoided model mismatch and scattering center classification to differentiate, but helpless for the strong coupling between adjacent scattering center.

Summary of the invention

The object of the invention is to propose a kind of combining image and cut apart the target scattering center extracting method of following the trail of with Subspace Matching, to solve the degree of coupling between model mismatch in existing method, scattering center classification differentiation mistake and scattering center, cause greatly the inaccurate problem of parameter estimation.

Technical scheme of the present invention is achieved in that

One. technical thought

In the radar return of high frequency region, the approximate backscattering echo stack of regarding as by a small amount of strong scattering center of target scattering echo is produced, by solving target at the rarefaction representation of frequency field, extract the scattering center feature of target.Consider that attribute scattering center parameter space dimension is higher, scattering centers extraction process computation complexity is large, adopts based on Subspace Matching and follows the trail of the set according to a preliminary estimate of obtaining objective attribute target attribute scattering center parameter; For the degree of coupling between scattering center, cause greatly the inaccurate problem of parameter estimation, by utilizing the method that image is cut apart to reduce the degree of coupling between scattering center.

Two. technical scheme

According to above-mentioned thinking performing step of the present invention, comprise as follows:

(1) extract original image I ₀in local maximum region, obtain target image I ₁; To target image I ₁cut apart, obtain the contour area R of target, use contour area R to original image I ₀carry out mask process, obtain target and be communicated with support area image I ₂, to being communicated with, support area image I ₂by two-dimensional Fourier transform, obtain the frequency domain observation signal s of target;

(2) determine the location sets Θ of scattering center ₁community set Θ with scattering center ₂;

2a) according to the nonzero element position in contour area R, obtain scattering center apart from the span X of dimension coordinate parameter x and the span Y of scattering center azimuth dimension coordinate parameters y, determine the location sets of scattering center: Θ ₁=(x, y) | x ∈ X, y ∈ Y};

2b) by the span of scattering center azimuth dimension coordinate parameters y, determined the span L of scattering center length parameter L; Orientation angular domain by radar return data recording is determined scattering center position angle span Φ; By the centre frequency of radar return data recording, determine scattering center orientation dependent factor γ span Γ; The frequency dependent factor-alpha span of setting scattering center be Λ=1 ,-0.5,0,0.5,1}; The final community set Θ that determines scattering center ₂: ${\mathrm{\Θ}}_2=\left\{(L,\stackrel{\‾}{\mathrm{\φ}},\mathrm{\α},\mathrm{\γ})\right|L\∈L,\stackrel{\‾}{\mathrm{\φ}}\∈\mathrm{\Φ},\mathrm{\α}\∈\mathrm{\Λ},\mathrm{\γ}\∈\mathrm{\Γ}\};$

(3) according to described location sets Θ ₁with community set Θ ₂, utilize attribute scattering center model to build respectively positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary

(4) by above-mentioned location sets Θ ₁, community set Θ ₂, positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary utilize Subspace Matching back tracking method to obtain the Θ of set according to a preliminary estimate of objective attribute target attribute scattering center parameter ₀;

(5) to gathering according to a preliminary estimate Θ ₀be optimized, obtain the characteristic set Θ ' of objective attribute target attribute scattering center:

5.1) make iteration set Θ equal to gather according to a preliminary estimate Θ ₀, note Θ={ θ ₁..., θ _i..., θ _p, θ wherein _ithe i group parameter in Θ, 1≤i≤p, p is that in iteration set Θ, parameter is always organized number, makes cache set Θ ₃equal to gather according to a preliminary estimate Θ ₀, sub-iterations q=1, makes splitting factor ξ=0.1;

5.2) from iteration set Θ, remove q group parameter, obtain sub-iteration set Θ ' _qfor:

Θ' _q＝{θ ₁,...,θ _q-1,θ _q+1,...,θ _p}；

5.3) according to sub-iteration set Θ ' _q, utilize attribute scattering center model to build sub-iteration dictionary D' _q;

5.4) by sub-iteration dictionary D' _q, obtain residual frequency domain vector d _rfor:

d _r＝(I-((D' _q) ^H·D' _q) ^-1(D' _q) ^H)s

Wherein () ^-1expression is to matrix inversion, () ^hexpression is carried out conjugate transpose to matrix, and I is unit matrix;

5.5) utilize above calculation of parameter surplus correlation matrix C':

$C^{\′}=D_1{(x,y|{\mathrm{\Θ}}_1)}^H\·\mathrm{diag}\left(d_r\right)\·D_2(L,\stackrel{\‾}{\mathrm{\φ}},\mathrm{\α},\mathrm{\γ}|{\mathrm{\Θ}}_2)$

Wherein diag () represents diagonalization operation;

5.6) according to line number n' and columns m' that in surplus correlation matrix C', mould value greatest member is corresponding, obtain local dictionary D ₀; D ₀=D ₁(n ') * D ₂(m '), wherein, * is dot product symbol, representing matrix correspondence position multiplies each other, D ₁(n ') represents positional information dictionary D ₁(x, y| Θ ₁) in n' dictionary atom, D ₂(m ') represents attribute information dictionary in m' dictionary atom;

5.7) by local dictionary D ₀with residual frequency domain vector d _r, by two-dimentional inverse Fourier transform, obtain respectively local tomography matrix I _dwith residual imaging array I _r:

I _D＝ifft2(reshape(D ₀,f _n,φ _n))，

I _r＝ifft2(reshape(d _r,f _n,φ _n))，

Wherein, ifft2 () represents two-dimentional inverse Fourier transform, and reshape () is matrix dimensionality transformation operator, f _nthe distance dimension sampling number of radar image, φ _nit is the azimuth dimension sampling number of radar image;

5.8) by local tomography matrix I _dthe maximum norm value of middle element and splitting factor ξ, determine segmentation threshold M _ξ: M _ξ=ξ max (I _d), wherein max () represents to get maximum norm value;

5.9) by local tomography matrix I _dmiddle intensity is more than or equal to segmentation threshold M _ξelement put 1, be less than segmentation threshold M _ξelement set to 0, obtain threshold matrix I _f;

5.10) by threshold matrix I _fwith residual imaging array I _r, by two-dimensional Fourier transform, obtain splitting signal F _s: F _s=vec (fft2 (I _f* I _r)), wherein fft2 represents two-dimensional Fourier transform, vec represents column vectorization operation;

5.11) by above calculation of parameter, cut apart correlation matrix C ":

$C^{\′\′}=D_1{(x,y|{\mathrm{\Θ}}_1)}^H\·\mathrm{diag}\left(F_s\right)\·D_2(L,\stackrel{\‾}{\mathrm{\φ}},\mathrm{\α},\mathrm{\γ}|{\mathrm{\Θ}}_2)$

5.12) find out and cut apart correlation matrix C " the line number n that mould value greatest member is corresponding " and columns m ", obtain one group of partitioning parameters ${\mathrm{\θ}}_q^{\′\′}(x,y,L,\stackrel{\‾}{\mathrm{\φ}},\mathrm{\α},\mathrm{\γ})=[{\mathrm{\Θ}}_1\left(n^{\′\′}\right),{\mathrm{\Θ}}_2\left(m^{\′\′}\right)],$ Θ wherein ₁(n ") represents location sets Θ ₁in n " group parameter, Θ ₂(m ") represents community set Θ ₂in m " group parameter;

5.13) use partitioning parameters upgrade q group parameter in iteration set Θ, ${\mathrm{\θ}}_q={\mathrm{\θ}}_q^{\′\′}(x,y,L,\stackrel{\‾}{\mathrm{\φ}},\mathrm{\α},\mathrm{\γ});$

5.14) judge whether q < p sets up, if set up, make q=q+1, return to step 5.2); If be false, establish q=1, execution step 5.15);

5.15) judgement Θ ₃whether=Θ sets up, if be false, makes Θ ₃=Θ, returns to step 5.2); If set up, iteration set Θ is now exactly the characteristic set Θ ' of objective attribute target attribute scattering center, i.e. Θ '=Θ.

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

1. avoided model mismatch and classification misjudgement:

The present invention is based on attribute scattering center model and build redundant dictionary, frequency domain observation data from target, by solving target at the rarefaction representation of frequency domain observation, extract the attribute scattering center parameter of target, solved model mismatch and classification discrimination in scattering centers extraction process.

2. improved the accuracy of extracting attribute scattering center parameter:

The present invention has utilized the image area information of target, combining image dividing method sum of subspace match tracing method is extracted objective attribute target attribute scattering center parameter, solved because the degree of coupling between scattering center causes greatly the incorrect problem of parameter extraction, improved the accuracy of estimation of attribute scattering center parameter.

3. can obtain the precise geometrical size characteristic of target and vitals thereof:

Because the inventive method can effectively be extracted objective attribute target attribute scattering center parameter, so the present invention, according to the attribute scattering center parameter sets of extracting, can obtain the precise geometrical size characteristic of target and vitals thereof.

Accompanying drawing explanation

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

Fig. 2 is the original radar image of T72 tank in MSTAR database.

Embodiment

One, know-why

High Resolution SAR Images is the two-dimensional scattering image of target, can be similar to regard as to be produced by the backscattering echo sum at a small amount of strong scattering center.The model that extracts at present target scattering center is mainly divided into three kinds: ideal point scattering center model, damped expoential model, and attribute scattering center model.Wherein attribute scattering center model meets the scattering properties of SAR target most, positional information and the strength information of scattering center have not only been described, also describe the physical dimension of scattering center, and the dependence of scattering center to frequency and orientation, and can be finally inversed by thus the geometry of target.Attribute scattering center model, than point scattering model and damped expoential model, comprises the abundanter feature that can be used for target classification identification.The attribute scattering center that it is described has abundant geometric meaning and physical significance.

Known according to attribute scattering center model, in target, i scattering center frequency-orientation two dimension echoed signal is:

$\begin{array}{c}{E}_i(f,\mathrm{\&phi;};{\mathrm{\&theta;}}_i)=A_i\&CenterDot;{\left(j\frac{f}{f_c}\right)}^{{\mathrm{\&alpha;}}_i}\exp \left(\frac{-j4\mathrm{\&pi;f}}{c}(x_i\cos \mathrm{\&phi;}+y_i\sin \mathrm{\&phi;})\right)\&CenterDot;\\ \sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_i\sin (\mathrm{\&phi;}-{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_i)\right)\exp (-2\mathrm{\&pi;f}{\mathrm{\&gamma;}}_i\sin \mathrm{\&phi;})\end{array}$

Wherein, i represents scattering center sequence number, and f is radar emission signal frequency, and φ is radar bearing angle, and exp () is natural exponential function, and sin c () is Sinc function, and c is the light velocity, θ _ithe parameter vector that represents i scattering center, comprises a _ifor the scattering strength of scattering center, x _ifor apart from dimension coordinate, y _ifor azimuth dimension coordinate, L _ifor the length of distributed scattering center azimuth dimension, for the position angle of distributed scattering center, α _ifor the frequency dependent factor, general α _i∈ 1 ,-0.5,0,0.5,1}, γ _iorientation dependent factor for local formula scattering center.

By the echoed signal sum of each scattering center, can form target frequency-orientation two dimension echoed signal:

$E(f,\mathrm{\&phi;};\mathrm{\&Theta;})=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{E}_i(f,\mathrm{\&phi;};{\mathrm{\&theta;}}_i),{\mathrm{\&Theta;}}^T=[{\mathrm{\&theta;}}_1^T,...,{\mathrm{\&theta;}}_i^T,...,{\mathrm{\&theta;}}_M^T]$

Wherein i represents scattering center sequence number, E _i(f, φ; θ _i) be the echoed signal of i scattering center, M is scattering center number, Θ represents M scattering center parameter matrix, () ^trepresent matrix transpose operation;

Target echo signal is expressed with matrix form, and its expression formula is:

s＝D(Θ)σ+n

Wherein s is target echo signal E (f, φ; Column vector Θ), D (Θ) is dictionary corresponding to scattering center parameter matrix Θ, and σ is scattering coefficient vector, and n represents noise.

In radar return, because most energy of target scattering field are only contributed by a small amount of strong scattering center, therefore explanation radar return has very strong sparse property at the parameter space of attribute scattering center.Sparse property according to radar return at the parameter space of attribute scattering center, by solving the rarefaction representation of observation data s, and the set of scattering center parameter estimation, can estimating target and the geometries characteristic of vitals by scattering center parameter sets.

Two, performing step

With reference to Fig. 1, performing step of the present invention is as follows:

Step 1, obtains the frequency domain observation signal s of target.

From MSTAR database, extract T72 tank original image I ₀, as shown in Figure 2; Extract original image I ₀in local maximum region, obtain target image I ₁; To target image I ₁cut apart, obtain the contour area R of target, use contour area R to original image I ₀carry out mask process, obtain target and be communicated with support area image I ₂, to being communicated with, support area image I ₂by two-dimensional Fourier transform, obtain the frequency domain observation signal s of target.

Step 2, determines the location sets Θ of target scattering center ₁community set Θ with scattering center ₂.

2a) according to the nonzero element position in contour area R, obtain scattering center apart from the span X of dimension coordinate parameter x and the span Y of scattering center azimuth dimension coordinate parameters y, determine the location sets of scattering center: Θ ₁=(x, y) | and x ∈ X, y ∈ Y},

For example, when radar image data is open MSTAR measured data, according to the nonzero element position in contour area R, can obtain scattering center apart from the span X={x|-2.0700≤x≤1.2937} of dimension coordinate parameter x, span Y={y|-6.5000≤y≤3.1200} of scattering center azimuth dimension coordinate parameters y, so the location sets Θ of scattering center ₁=(x, y) | x ∈ X, y ∈ Y};

2b) by the span of scattering center azimuth dimension coordinate parameters y, determined the span L of scattering center length parameter L; Orientation angular domain by radar return data recording is determined scattering center position angle span Φ; By the centre frequency of radar return data recording, determine scattering center orientation dependent factor γ span Γ; The frequency dependent factor-alpha span of setting scattering center be Λ=1 ,-0.5,0,0.5,1}; The final community set Θ that determines scattering center ₂: ${\mathrm{\&Theta;}}_2=\left\{(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;})\right|L\&Element;L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}\&Element;\mathrm{\&Phi;},\mathrm{\&alpha;}\&Element;\mathrm{\&Lambda;},\mathrm{\&gamma;}\&Element;\mathrm{\&Gamma;}\},$

For example, when radar image data is open MSTAR measured data, span L={L|0≤L≤9.88} of scattering center length parameter L, scattering center position angle span scattering center orientation dependent factor γ span Γ=and γ | 0≤γ≤1.0417e-9}, frequency dependent factor-alpha span is that Λ={ 1 ,-0.5,0,0.5,1}, so the community set of scattering center ${\mathrm{\&Theta;}}_2=\left\{(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;})\right|L\&Element;L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}\&Element;\mathrm{\&Phi;},\mathrm{\&alpha;}\&Element;\mathrm{\&Lambda;},\mathrm{\&gamma;}\&Element;\mathrm{\&Gamma;}\}.$

Step 3, according to described location sets Θ ₁with community set Θ ₂, utilize attribute scattering center model to build respectively positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary

3a) input position set Θ ₁with community set Θ ₂;

3b) by location sets Θ ₁with community set Θ ₂, produce respectively position atom d _w(f, φ) and attribute atom d' _l(f, φ);

$d_w(f,\mathrm{\&phi;})=\mathrm{vec}\left(\exp \left(\frac{-j4\mathrm{\&pi;f}}{c}(x_w\cos \mathrm{\&phi;}+y_w\sin \mathrm{\&phi;})\right)\right),w=1,...,N_1$

$\begin{array}{c}{d}_l^{\&prime;}(f,\mathrm{\&phi;})=\mathrm{vec}({\left(j\frac{f}{f_c}\right)}^{{\mathrm{\&alpha;}}_l}\&CenterDot;\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_l\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_l})\right)\&CenterDot;\exp (-2\mathrm{\&pi;f}{\mathrm{\&gamma;}}_l\sin \mathrm{\&phi;}))\\ l=1,...,N_2\end{array},$

Wherein, vec () represents column vectorization operation, N ₁represent location sets Θ ₁parameter always organize number, N ₂represent community set Θ ₂parameter always organize number, exp () is natural exponential function, sin c () is Sinc function, (x _w, y _w) be location sets Θ ₁w group parameter, for community set Θ ₂l group parameter, f is radar emission signal frequency, f _cfor radar emission signal center frequency, φ is radar beam position angle, and c is the light velocity;

3c) by position atom d _w(f, φ) and attribute atom d' _l(f, φ), obtains normalized position atom with normalized attribute atom for: ${\hat{d}}_w=\frac{d_w(f,\mathrm{\&phi;})}{{\left|\right|d_w(f,\mathrm{\&phi;})\left|\right|}_2},{\hat{d}}_l^{\&prime;}=\frac{d_l^{\&prime;}(f,\mathrm{\&phi;})}{{\left|\right|d_l^{\&prime;}(f,\mathrm{\&phi;})\left|\right|}_2},$ Wherein, || || ₂be 2 norm operators;

3d) by normalized position atom with normalized attribute atom build respectively positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary for:

$D_1(x,y|{\mathrm{\&Theta;}}_1)=[{\hat{d}}_1,...,{\hat{d}}_w,...,{\hat{d}}_{N_1}]$

$D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2)=[{\hat{d}}_1^{\&prime;},...,{\hat{d}}_l^{\&prime;},...,{\hat{d}}_{N_2}^{\&prime;}].$

Step 4, by above-mentioned location sets Θ ₁, community set Θ ₂, positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary utilize Subspace Matching back tracking method to obtain the Θ of set according to a preliminary estimate of objective attribute target attribute scattering center parameter ₀.

4a) degree of rarefication of hypothetical target attribute scattering center is N, signal margin r is initialized as to frequency domain observation signal s, by redundant set Θ ' ₀with interim set Θ " ₀be initialized as sky, by interim dictionary D " (Θ " ₀) be initialized as sky, establishing reconstruct energy error constraint factor is ε, ε is communicated with and is supported area image I by target ₂signal to noise ratio (S/N ratio) determine;

4b) utilize above calculation of parameter correlation matrix:

$C=D_1{(x,y|{\mathrm{\&Theta;}}_1)}^H\&CenterDot;\mathrm{diag}\left(r\right)\&CenterDot;D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2),$

Wherein diag () represents diagonalization operation, () ^hexpression is carried out conjugate transpose to matrix;

The corresponding redundant row manifold of K element of 4c) finding out mould value maximum in correlation matrix C closes n and redundant columns manifold is closed m, K=2 * N wherein, n={n ₁..., n _u...., n _k, m={m ₁..., m _u...., m _k, n _uand m _urespectively that in correlation matrix C, element is arranged line number and the columns of rear u element from big to small by mould value;

4d) by redundant row number vector n, redundant columns number vector m, gather Θ temporarily " ₀with interim dictionary D " (Θ " ₀), obtain redundant set Θ ' ₀with redundant dictionary D'(Θ ' ₀):

Θ' ₀＝{(Θ ₁(n _u)，Θ ₂(m _u))|n _u∈n,m _u∈m}∪Θ″ ₀，

D'(Θ' ₀)＝{D ₁(n _u)·*D ₂(m _u)|n _u∈n,m _u∈m}∪D″(Θ″ ₀)，

Wherein, ∪ represents to get union, Θ ₁(n _u) expression location sets Θ ₁in n _ugroup parameter, Θ ₂(m _u) expression community set Θ ₂in m _ugroup parameter, D ₁(n _u) expression positional information dictionary D ₁(x, y| Θ ₁) in n _uindividual dictionary atom, D ₂(m _u) expression attribute information dictionary in m _uindividual dictionary atom;

4e) by redundant dictionary D'(Θ ' ₀) calculating redundancy coefficient vector: σ=pinv (D'(Θ ' ₀)) s, find out corresponding interim line number set: the n ' of N element of mould value maximum in redundancy coefficient vector σ=n ' ₁..., n ' _v...., n ' _n, wherein pinv () represents pseudoinverse, n ' _vit is the line number of v the element of element after arranging from big to small by mould value in coefficient vector σ;

4f), by interim line number set n ', obtain gathering Θ " temporarily ₀with interim dictionary D " (Θ " ₀):

Θ″ ₀＝{Θ' ₀(n _v)|n _v∈n′}，

D″(Θ″ ₀)＝{D′(n _v)|n _v∈n′}，

Θ ' wherein ₀(n _v) expression redundant set Θ ' ₀in n _vgroup parameter, D ' (n _v) expression redundant dictionary D'(Θ ' ₀) in n _vindividual dictionary atom;

4g) by interim dictionary D " (Θ " ₀), obtain reconstruction signal for:

$\hat{s}\left({\mathrm{\&Theta;}}_0^{\&prime;\&prime;}\right)=D^{\&prime;\&prime;}\left({\mathrm{\&Theta;}}_0^{\&prime;\&prime;}\right)\&CenterDot;\mathrm{pinv}\left(D^{\&prime;\&prime;}\left({\mathrm{\&Theta;}}_0^{\&prime;\&prime;}\right)\right)\&CenterDot;s;$

4h) by reconstruction signal update signal surplus r is:

4i) judgement || r|| ₂whether≤ε sets up, if be false, returns to step 4b); If set up, interim set Θ now " ₀be exactly to gather according to a preliminary estimate Θ ₀, i.e. Θ ₀=Θ " ₀.

Step 5, to gathering according to a preliminary estimate Θ ₀be optimized, obtain the characteristic set Θ ' of objective attribute target attribute scattering center.

5.1) make iteration set Θ equal to gather according to a preliminary estimate Θ ₀, note Θ={ θ ₁..., θ _i..., θ _p, θ wherein _ithe i group parameter in Θ, 1≤i≤p, p is that in iteration set Θ, parameter is always organized number, makes cache set Θ ₃equal to gather according to a preliminary estimate Θ ₀, sub-iterations q=1, makes splitting factor ξ=0.1;

5.2) from iteration set Θ, remove q group parameter, obtain sub-iteration set Θ ' _qfor:

Θ' _q＝{θ ₁,...,θ _q-1,θ _q+1,...,θ _p}；

5.3) according to sub-iteration set Θ ' _q, utilize attribute scattering center model to build sub-iteration dictionary D' _q;

5.3.1) input sub-iteration set Θ ' _q;

5.3.2) by sub-iteration set Θ ' _q, produce sub-iteration atom

$\begin{array}{c}{d}_t^0(f,\mathrm{\&phi;})=\mathrm{vec}({\left(j\frac{f}{f_c}\right)}^{{\mathrm{\&alpha;}}_t}\&CenterDot;\exp (\frac{-j4\mathrm{\&pi;f}}{c}(x_t\cos \mathrm{\&phi;}+y_t\sin \mathrm{\&phi;}))\&CenterDot;\\ \sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_t\sin (\mathrm{\&phi;}-{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_t)\right)\&CenterDot;\exp (-2\mathrm{\&pi;f}{\mathrm{\&gamma;}}_t\sin \mathrm{\&phi;}))\end{array},$

Wherein for sub-iteration set Θ ' _qt group parameter, 1≤t≤N ₃, N ₃sub-iteration set Θ ' _qparameter always organize number;

5.3.3) by sub-iteration atom obtain normalized sub-iteration atom for:

${\hat{d}}_t^0=\frac{d_t^0(f,\mathrm{\&phi;})}{{\left|\right|d_t^0(f,\mathrm{\&phi;})\left|\right|}_2};$

5.3.4) by normalized sub-iteration atom build sub-iteration dictionary D' _qfor:

$D_q^{\&prime;}=[{\hat{d}}_1^0,...,{\hat{d}}_t^0,...,{\hat{d}}_{N_3}^0];$

5.4) by sub-iteration dictionary D' _q, obtain residual frequency domain vector d _rfor:

d _r＝(I-((D' _q) ^H·D' _q) ^-1(D' _q) ^H)s，

Wherein () ^-1expression is to matrix inversion, () ^hexpression is carried out conjugate transpose to matrix, and I is unit matrix;

5.5) utilize above calculation of parameter surplus correlation matrix C':

$C^{\&prime;}=D_1{(x,y|{\mathrm{\&Theta;}}_1)}^H\&CenterDot;\mathrm{diag}\left(d_r\right)\&CenterDot;D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2)$

Wherein diag () represents diagonalization operation;

5.6) according to line number n' and columns m' that in surplus correlation matrix C', mould value greatest member is corresponding, obtain local dictionary D ₀; D ₀=D ₁(n ') * D ₂(m '), wherein, * is dot product symbol, representing matrix correspondence position multiplies each other, D ₁(n ') represents positional information dictionary D ₁(x, y| Θ ₁) in n' dictionary atom, D ₂(m ') represents attribute information dictionary in m' dictionary atom;

5.7) by local dictionary D ₀with residual frequency domain vector d _r, by two-dimentional inverse Fourier transform, obtain respectively local tomography matrix I _dwith residual imaging array I _r:

I _D＝ifft2(reshape(D ₀,f _n,φ _n))，

I _r＝ifft2(reshape(d _r,f _n,φ _n))，

Wherein, ifft2 () represents two-dimentional inverse Fourier transform, and reshape () is matrix dimensionality transformation operator, f _nthe distance dimension sampling number of radar image, φ _nit is the azimuth dimension sampling number of radar image;

5.8) by local tomography matrix I _dthe maximum norm value of middle element and splitting factor ξ, determine segmentation threshold M _ξ: M _ξ=ξ max (I _d), wherein max () represents to get maximum norm value;

5.9) by local tomography matrix I _dmiddle intensity is more than or equal to segmentation threshold M _ξelement put 1, be less than segmentation threshold M _ξelement set to 0, obtain threshold matrix I _f;

5.10) by threshold matrix I _fwith residual imaging array I _r, by two-dimensional Fourier transform, obtain splitting signal F _s: F _s=vec (fft2 (I _f* I _r)), wherein fft2 represents two-dimensional Fourier transform, vec represents column vectorization operation;

5.11) by above calculation of parameter, cut apart correlation matrix C ":

$C^{\&prime;\&prime;}=D_1{(x,y|{\mathrm{\&Theta;}}_1)}^H\&CenterDot;\mathrm{diag}\left(F_s\right)\&CenterDot;D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2);$

5.12) find out and cut apart correlation matrix C " the line number n that mould value greatest member is corresponding " and columns m ", obtain one group of partitioning parameters: ${\mathrm{\&theta;}}_q^{\&prime;\&prime;}(x,y,L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;})=[{\mathrm{\&Theta;}}_1\left(n^{\&prime;\&prime;}\right),{\mathrm{\&Theta;}}_2\left(m^{\&prime;\&prime;}\right)],$ Θ wherein ₁(n ") represents location sets Θ ₁in n " group parameter, Θ ₂(m ") represents community set Θ ₂in m " group parameter;

5.13) use partitioning parameters upgrade q group parameter in iteration set Θ, ${\mathrm{\&theta;}}_q={\mathrm{\&theta;}}_q^{\&prime;\&prime;}(x,y,L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;});$

5.14) judge whether q < p sets up, if set up, make q=q+1, return to step 5.2); If be false, establish q=1, execution step 5.15);

5.15) judgement Θ ₃whether=Θ sets up, if be false, makes Θ ₃=Θ, returns to step 5.2); If set up, iteration set Θ is now exactly the characteristic set Θ ' of objective attribute target attribute scattering center, i.e. Θ '=Θ.

Effect of the present invention further illustrates by the experiment of following measured data:

1) experiment scene:

Testing measured data used is that disclosed MSTAR data centralization position angle is that 80.774185 ° of angles of pitch are the synthetic-aperture radar SAR data of the T72 tank of 15 °, the centre frequency f of radar _c=9.599GHz, bandwidth B=591MHz.T72 tank true geometric is of a size of: the long 6.41m of car body, and overall width 3.52m, gun barrel is long 6.155 meters, gun barrel 9.445 meters of vehicle body overall lengths forward time.

2) experiment content:

For position angle, be that 80.774185 ° of angles of pitch are the T72 tank MSTAR data of 15 °, utilize the present invention to extract the parameter sets of objective attribute target attribute scattering center, as shown in Table 1 and Table 2.

Table 1 the inventive method is processed T72 gun barrel scattering center parameter

Table 2 the inventive method is processed T72 tank volume scattering Center Parameter

3) interpretation:

The space length of scattering center 1 and scattering center 2 end points in reckoner 1, can obtain the gun barrel total length that the present invention estimates T72 is 5.98 meters,

The space length of scattering center 3 and scattering center 4 end points in reckoner 2, can obtain the tank body length that the present invention estimates T72 is 5.98 meters,

The space length of scattering center 2 and scattering center 3 in reckoner 1 and table 2, can obtain the tank body width that the present invention estimates T72 is 3.36 meters; The space length of scattering center 1 and scattering center 4 end points in reckoner 1 and table 2, can obtain the overall length that the present invention estimates T72 tank is 9.22 meters,

True geometric size in conjunction with T72 tank is known, and the target that the inventive method is estimated and the physical dimension relative error of vitals thereof are in 6.7%.

Experimental result explanation, the present invention can solve by the degree of coupling between scattering center and cause greatly the incorrect problem of parameter estimation, can effectively accurately extract objective attribute target attribute scattering center feature, the objective attribute target attribute scattering center feature that the present invention extracts can be used for the physical dimension of accurate estimating target and vitals thereof.

Claims (4)

1. combining image is cut apart a target scattering center extracting method of following the trail of with Subspace Matching, comprises the steps:

(1) extract original image I ₀in local maximum region, obtain target image I ₁; To target image I ₁cut apart, obtain the contour area R of target, use contour area R to original image I ₀carry out mask process, obtain target and be communicated with support area image I ₂, to being communicated with, support area image I ₂by two-dimensional Fourier transform, obtain the frequency domain observation signal s of target;

(2) determine the location sets Θ of scattering center ₁community set Θ with scattering center ₂;

2a) according to the nonzero element position in contour area R, obtain scattering center apart from the span X of dimension coordinate parameter x and the span Y of scattering center azimuth dimension coordinate parameters y, determine the location sets of scattering center: Θ ₁=(x, y) | x ∈ X, y ∈ Y};

2b) by the span of scattering center azimuth dimension coordinate parameters y, determined the span L of scattering center length parameter L; Orientation angular domain by radar return data recording is determined scattering center position angle span Φ; By the centre frequency of radar return data recording, determine scattering center orientation dependent factor γ span Γ; The frequency dependent factor-alpha span of setting scattering center be Λ=1 ,-0.5,0,0.5,1}; The final community set Θ that determines scattering center ₂:

${\mathrm{\&Theta;}}_2=\left\{(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;})\right|L\&Element;L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}\&Element;\mathrm{\&Phi;},\mathrm{\&alpha;}\&Element;\mathrm{\&Lambda;},\mathrm{\&gamma;}\&Element;\mathrm{\&Gamma;}\};$

(3) according to described location sets Θ ₁with community set Θ ₂, utilize attribute scattering center model to build respectively positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary

(4) by above-mentioned location sets Θ ₁, community set Θ ₂, positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary utilize Subspace Matching back tracking method to obtain the Θ of set according to a preliminary estimate of objective attribute target attribute scattering center parameter ₀;

(5) to gathering according to a preliminary estimate Θ ₀be optimized, obtain the characteristic set Θ ' of objective attribute target attribute scattering center:

5.1) make iteration set Θ equal to gather according to a preliminary estimate Θ ₀, note Θ={ θ ₁..., θ _i..., θ _p, θ wherein _ithe i group parameter in Θ, 1≤i≤p, p is that in iteration set Θ, parameter is always organized number, makes cache set Θ ₃equal to gather according to a preliminary estimate Θ ₀, sub-iterations q=1, makes splitting factor ξ=0.1;

5.2) from iteration set Θ, remove q group parameter, obtain sub-iteration set Θ ' _qfor:

Θ' _q＝{θ ₁,...,θ _q-1,θ _q+1,...,θ _p}；

5.3) according to sub-iteration set Θ ' _q, utilize attribute scattering center model to build sub-iteration dictionary D' _q;

5.4) by sub-iteration dictionary D' _q, obtain residual frequency domain vector d _rfor:

d _r＝(I-((D' _q) ^H·D' _q) ^-1(D' _q) ^H）s

Wherein () ^-1expression is to matrix inversion, () ^hexpression is carried out conjugate transpose to matrix, and I is unit matrix;

5.5) utilize above calculation of parameter surplus correlation matrix C':

$C^{\&prime;}=D_1{(x,y|{\mathrm{\&Theta;}}_1)}^H\&CenterDot;\mathrm{diag}\left(d_r\right)\&CenterDot;D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2)$

Wherein diag () represents diagonalization operation;

5.6) according to line number n' and columns m' that in surplus correlation matrix C', mould value greatest member is corresponding, obtain local dictionary D ₀; D ₀=D ₁(n ') * D ₂(m '), wherein, * is dot product symbol, representing matrix correspondence position multiplies each other, D ₁(n ') represents positional information dictionary D ₁(x, y| Θ ₁) in n' dictionary atom, D ₂(m ') represents attribute information dictionary in m' dictionary atom;

5.7) by local dictionary D ₀with residual frequency domain vector d _r, by two-dimentional inverse Fourier transform, obtain respectively local tomography matrix I _dwith residual imaging array I _r:

I _D＝ifft2(reshape(D ₀,f _n,φ _n))，

I _r＝ifft2(reshape(d _r,f _n,φ _n))，

Wherein, ifft2 () represents two-dimentional inverse Fourier transform, and reshape () is matrix dimensionality transformation operator, f _nthe distance dimension sampling number of radar image, φ _nit is the azimuth dimension sampling number of radar image;

5.8) by local tomography matrix I _dthe maximum norm value of middle element and splitting factor ξ, determine segmentation threshold M _ξ: M _ξ=ξ max (I _d), wherein max () represents to get maximum norm value;

5.9) by local tomography matrix I _dmiddle intensity is more than or equal to segmentation threshold M _ξelement put 1, be less than segmentation threshold M _ξelement set to 0, obtain threshold matrix I _f;

5.10) by threshold matrix I _fwith residual imaging array I _r, by two-dimensional Fourier transform, obtain splitting signal F _s: F _s=vec (fft2 (I _f* I _r)), wherein fft2 represents two-dimensional Fourier transform, vec represents column vectorization operation;

5.11) by above calculation of parameter, cut apart correlation matrix C ":

$C^{\&prime;\&prime;}=D_1{(x,y|{\mathrm{\&Theta;}}_1)}^H\&CenterDot;\mathrm{diag}\left(F_s\right)\&CenterDot;D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2)$

5.12) find out and cut apart correlation matrix C " the line number n that mould value greatest member is corresponding " and columns m ", obtain one group of partitioning parameters Θ wherein ₁(n ") represents location sets Θ ₁in n " group parameter, Θ ₂(m ") represents community set Θ ₂in m " group parameter;

5.13) use partitioning parameters upgrade q group parameter in iteration set Θ, ${\mathrm{\&theta;}}_q={\mathrm{\&theta;}}_q^{\&prime;\&prime;}(x,y,L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;});$

5.14) judge whether q < p sets up, if set up, make q=q+1, return to step 5.2); If be false, establish q=1, execution step 5.15);

5.15) judgement Θ ₃whether=Θ sets up, if be false, makes Θ ₃=Θ, returns to step 5.2); If set up, iteration set Θ is now exactly the characteristic set Θ ' of objective attribute target attribute scattering center, i.e. Θ '=Θ.

2. method according to claim 1, wherein step (3) described according to location sets Θ ₁with community set Θ ₂, utilize attribute scattering center model to build respectively positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary carry out as follows:

3a) input position set Θ ₁with community set Θ ₂;

3b) by location sets Θ ₁with community set Θ ₂, produce respectively position atom d _w(f, φ) and attribute atom d' _l(f, φ);

$d_w(f,\mathrm{\&phi;})=\mathrm{vec}\left(\exp \left(\frac{-j4\mathrm{\&pi;f}}{c}(x_w\cos \mathrm{\&phi;}+y_w\sin \mathrm{\&phi;})\right)\right),w=1,...,N_1$

$\begin{array}{c}{d}_l^{\&prime;}(f,\mathrm{\&phi;})=\mathrm{vec}({\left(j\frac{f}{f_c}\right)}^{{\mathrm{\&alpha;}}_l}\&CenterDot;\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_l\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_l})\right)\&CenterDot;\exp (-2\mathrm{\&pi;f}{\mathrm{\&gamma;}}_l\sin \mathrm{\&phi;}))\\ l=1,...,N_2\end{array}$

Wherein, vec () represents column vectorization operation, N ₁represent location sets Θ ₁parameter always organize number, N ₂represent community set Θ ₂parameter always organize number, exp () is natural exponential function, sin c () is Sinc function, (x _w, y _w) be location sets Θ ₁w group parameter, for community set Θ ₂l group parameter, f is radar emission signal frequency, f _cfor radar emission signal center frequency, φ is radar beam position angle, and c is the light velocity;

3c) by position atom d _w(f, φ) and attribute atom d' _l(f, φ), obtains normalized position atom with normalized attribute atom for: ${\hat{d}}_w=\frac{d_w(f,\mathrm{\&phi;})}{{\left|\right|d_w(f,\mathrm{\&phi;})\left|\right|}_2},{\hat{d}}_l^{\&prime;}=\frac{d_l^{\&prime;}(f,\mathrm{\&phi;})}{{\left|\right|d_l^{\&prime;}(f,\mathrm{\&phi;})\left|\right|}_2},$ Wherein, || || ₂be 2 norm operators;

3d) by normalized position atom with normalized attribute atom build respectively positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary for:

$D_1(x,y|{\mathrm{\&Theta;}}_1)=[{\hat{d}}_1,...,{\hat{d}}_w,...,{\hat{d}}_{N_1}]$

$D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2)=[{\hat{d}}_1^{\&prime;},...,{\hat{d}}_l^{\&prime;},...,{\hat{d}}_{N_2}^{\&prime;}].$

3. method according to claim 1, wherein step (4) described by above-mentioned location sets Θ ₁, community set Θ ₂, positional information dictionary D ₁(x, y| Θ ₁) and attribute information dictionary utilize Subspace Matching back tracking method to obtain the Θ of set according to a preliminary estimate of objective attribute target attribute scattering center parameter ₀, carry out as follows:

4a) degree of rarefication of hypothetical target attribute scattering center is N, signal margin r is initialized as to frequency domain observation signal s, by redundant set Θ ' ₀with interim set Θ " ₀be initialized as sky, by interim dictionary D " (Θ " ₀) be initialized as sky, establishing reconstruct energy error constraint factor is ε, ε is communicated with and is supported area image I by target ₂signal to noise ratio (S/N ratio) determine;

4b) utilize above calculation of parameter correlation matrix: $C=D_1{(x,y|{\mathrm{\&Theta;}}_1)}^H\&CenterDot;\mathrm{diag}\left(r\right)\&CenterDot;D_2(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}},\mathrm{\&alpha;},\mathrm{\&gamma;}|{\mathrm{\&Theta;}}_2);$

The corresponding redundant row manifold of K element of 4c) finding out mould value maximum in correlation matrix C closes n and redundant columns manifold is closed m, K=2 * N wherein, n={n ₁..., n _u...., n _k, m={m ₁..., m _u...., m _k, n _uand m _urespectively that in correlation matrix C, element is arranged line number and the columns of rear u element from big to small by mould value;

4d) by redundant row number vector n, redundant columns number vector m, gather Θ temporarily " ₀with interim dictionary D " (Θ " ₀), obtain redundant set Θ ' ₀with redundant dictionary D'(Θ ' ₀):

Θ' ₀＝{(Θ ₁(n _u)，Θ ₂(m _u))|n _u∈n,m _u∈m}∪Θ″ ₀，

D'(Θ' ₀)＝{D ₁(n _u)·*D ₂(m _u)|n _u∈n,m _u∈m}∪D″(Θ″ ₀)，

Wherein, ∪ represents to get union, Θ ₁(n _u) expression location sets Θ ₁in n _ugroup parameter, Θ ₂(m _u) expression community set Θ ₂in m _ugroup parameter, D ₁(n _u) expression positional information dictionary D ₁(x, y| Θ ₁) in n _uindividual dictionary atom, D ₂(m _u) expression attribute information dictionary in m _uindividual dictionary atom;

4e) by redundant dictionary D'(Θ ' ₀) calculating redundancy coefficient vector: σ=pinv (D'(Θ ' ₀)) s, find out corresponding interim line number set: the n ' of N element of mould value maximum in redundancy coefficient vector σ=n ' ₁..., n ' _v...., n ' _n, wherein pinv () represents pseudoinverse, n ' _vit is the line number of v the element of element after arranging from big to small by mould value in coefficient vector σ;

4f), by interim line number set n ', obtain gathering Θ " temporarily ₀with interim dictionary D " (Θ " ₀):

Θ″ ₀＝{Θ' ₀(n _v)|n _v∈n′}，D″(Θ″ ₀)＝{D′(n _v)|n _v∈n′}，

Θ ' wherein ₀(n _v) expression redundant set Θ ' ₀in n _vgroup parameter, D ' (n _v) expression redundant dictionary D'(Θ ' ₀) in n _vindividual dictionary atom;

4g) by interim dictionary D " (Θ " ₀), obtain reconstruction signal for: $\hat{s}\left({\mathrm{\&Theta;}}_0^{\&prime;\&prime;}\right)=D^{\&prime;\&prime;}\left({\mathrm{\&Theta;}}_0^{\&prime;\&prime;}\right)\&CenterDot;\mathrm{pinv}\left(D^{\&prime;\&prime;}\left({\mathrm{\&Theta;}}_0^{\&prime;\&prime;}\right)\right)\&CenterDot;s;$

4h) by reconstruction signal update signal surplus r is:

4i) judgement || r|| ₂whether≤ε sets up, if be false, returns to step 4b); If set up, interim set Θ now " ₀be exactly to gather according to a preliminary estimate Θ ₀, i.e. Θ ₀=Θ " ₀.

4. method according to claim 1, wherein step 5.3) described according to sub-iteration set Θ ' _q, utilize attribute scattering center model to build sub-iteration dictionary D' _q, carry out as follows:

5.3.1) input sub-iteration set Θ ' _q;

5.3.2) by sub-iteration set Θ ' _q, produce sub-iteration atom

$\begin{array}{c}{d}_t^0(f,\mathrm{\&phi;})=\mathrm{vec}({\left(j\frac{f}{f_c}\right)}^{{\mathrm{\&alpha;}}_t}\&CenterDot;\exp (\frac{-j4\mathrm{\&pi;f}}{c}(x_t\cos \mathrm{\&phi;}+y_t\sin \mathrm{\&phi;}))\&CenterDot;\\ \sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_t\sin (\mathrm{\&phi;}-{\stackrel{\&OverBar;}{\mathrm{\&phi;}}}_t)\right)\&CenterDot;\exp (-2\mathrm{\&pi;f}{\mathrm{\&gamma;}}_t\sin \mathrm{\&phi;}))\end{array},$

Wherein for sub-iteration set Θ ' _qt group parameter, 1≤t≤N ₃, N ₃sub-iteration set Θ ' _qparameter always organize number;

5.3.3) by sub-iteration atom obtain normalized sub-iteration atom for:

5.3.4) by normalized sub-iteration atom build sub-iteration dictionary D' _qfor: