CN104459654A - Space correlation polarization SAR clutter image simulation method based on inverse transformation method - Google Patents

Abstract

The invention provides a space correlation polarization SAR clutter image simulation method based on an inverse transformation method. According to the technical scheme, the method comprises the step one of simulation of coherent speckle images of Wishart distribution, the step two of simulation of texture images of space correlation Fisher distribution, and the step three of generation of polarization SAR clutter images of space correlation KummerU distribution. Simulated coherent speckles and texture are multiplied to obtain simulated polarization SAR clutter images. The method has the advantages that the polarization SAR clutter images complying with KummerU distribution can be simulated; KummerU distribution can represent the statistical property of the polarization SAR clutter images and especially the high-resolution polarization SAR clutter images better, and the method can be applied to simulation of a large number of the polarization SAR clutter images based on a statistical method.

Description

Based on the space correlation polarization SAR clutter image emulation mode of inverse transformation method

Technical field

The present invention relates to imaging radar clutter image simulation technical field, more particularly, relate to a kind of polarization SAR (SyntheticAperture Radar, synthetic-aperture radar) clutter image emulation mode.

Background technology

SAR is a kind of active microwave imaging sensor, has round-the-clock, round-the-clock imaging capability.Polarization SAR is a kind of New System SAR, can work under multiple different polarization combination mode simultaneously.Compared with conventional SAR image, Polarimetric SAR Image comprises the information of target more horn of plenty, and this makes Polarimetric SAR Image be widely applied in a lot of military and civilian field.

Polarimetric SAR Image emulation has very important effect to Polarimetric SAR Image decipher, usually can be divided into two large classes.First kind method simulates whole polarization SAR imaging system, and it lays particular emphasis on the emulation of the polarization SAR original signal to dissimilar target especially man-made target, is obtained the Polarimetric SAR Image of emulation by imaging processing.The method needs the electromagnetic scattering attribute first knowing a large amount of different target, and complexity is high and calculated amount is large.Equations of The Second Kind method directly (comprises PDF (Probability Density Function from the statistical property of Polarimetric SAR Image itself, probability density function) and ACC (Auto-Correlation Coefficient, coefficient of autocorrelation)) set out, emulation possesses the image with actual Polarimetric SAR Image similar statistics characteristic, it lays particular emphasis on the emulation of polarization SAR clutter image, has simple advantage.The polarization SAR clutter image related in the present invention, refers to the Polarimetric SAR Image reflected to form as ocean, meadow and the woods etc. by natural feature on a map.

Inverse transformation method is a kind of polarization SAR clutter image emulation mode of highly versatile.Polarization SAR clutter image emulation based on inverse transformation method comprises two key issues, namely first key issue is that the statistical distribution pattern of polarization SAR clutter image is set up, and second key issue is the calculating of the Inverse distribution function of corresponding distribution and obeys the associated texture Computer image genration of respective texture distribution.Mainly distribute as the statistical distribution pattern of polarization SAR clutter image using K in existing polarization SAR clutter image emulation mode at present.But K distribution cannot meet the demand of the polarization SAR clutter image of high resolving power especially very high resolution being carried out to accurate count description very well.The proposition of KummerU distribution meets the demand of Current high resolution polarization SAR clutter image accurate count modeling to a great extent, and can deteriorate to classical K distribution under certain parameter condition, has broad application prospects.Therefore, study that to be distributed as the polarization SAR clutter image emulation mode of statistical distribution pattern with KummerU very valuable for the intelligent decipher of Polarimetric SAR Image.

Summary of the invention

The present invention, in order to effectively solve polarization SAR clutter image simulation problems, provides a kind of space correlation polarization SAR clutter image emulation mode based on inverse transformation method.This method can emulate the space correlation polarization SAR clutter image of obeying KummerU distribution, effectively meets the demand of high resolving power polarization SAR clutter image emulation.

Basic ideas of the present invention are, because polarization SAR clutter image can be analyzed to the product of coherent spot component and texture component, therefore under the polarization SAR clutter image simulation parameter arranged, first by simulating this two components respectively, then two components are multiplied process, obtain the polarization SAR clutter image of emulation.

Technical scheme of the present invention is: a kind of space correlation polarization SAR clutter image emulation mode based on inverse transformation method, specifically comprises the steps:

The first step: the coherent spot image simulation of multiple Wishart distribution

Known polarization SAR measuring image comprises a certain atural object classification to be emulated, and therefrom selects M the pixel that such atural object is corresponding, usual M >=100, utilizes following method to produce covariance matrix C:

$C=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{C}_i^{\′}$

Wherein C' _ibe that R × R corresponding to i-th pixel ties up polarization covariance matrix, i=1,2 ..., M, R are the dimension of polarization SAR Scattering of Vector, C' _ivalue utilize polarization SAR measuring image to obtain;

Calculate all eigenvalue λ of C ₁, λ ₂..., λ _rand corresponding unit character vector p ₁, p ₂..., p _r, for convenience, remember 0 < λ ₁≤ λ ₂≤ ... ,≤λ _r;

Make C _s=U Λ ^1/2, wherein Λ=diag{ λ ₁, λ ₂..., λ _r, U=[p ₁, p ₂..., p _r];

Each location of pixels (n of the polarization SAR clutter image that correspondence is to be emulated ₁, n ₂), 1≤n ₁≤ N ₁, 1≤n ₂≤ N ₂, the coherent spot covariance matrix Y obeying multiple Wishart distribution is produced according to following method ^(L)(n ₁, n ₂):

First produce L R and tie up complex vector Y _l(n ₁, n ₂)=C _s[η ₁+ j η ₂, η ₃+ j η ₄..., η _2R-1+ j η _2R] _l ^t, l=1,2 ..., L, wherein η ₁, η ₂, η ₃, η ₄..., η _2R-1, η _2Rfor mutual statistical independently average to be 0 variance be 0.5 Gaussian distributed random variable, L > R be polarization SAR clutter image to be emulated look number, be a positive integer, determine as required;

The matrix that coherent spot image simulation is corresponding $Y^{\left(L\right)}(n_1,n_2)=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{Y}_l(n_1,n_2)Y_l{(n_1,n_2)}^H.$

Second step: space correlation Fisher distribution texture image emulation

Producing a width size is N ₁× N ₂the Gaussian distribution image G of obedience average to be 0 variance the be statistical iteration of 1 ₁(n ₁, n ₂), 1≤n ₁≤ N ₁, 1≤n ₂≤ N ₂.

According to the actual requirements, the autocorrelation function ρ of texture component is set _t(d ₁, d ₂) value, d ₁and d ₂to represent respectively in texture image any two location of pixels in orientation to distance range difference upwards, d ₁=-D ₁, (-D ₁+ 1) ..., (D ₁-1), D ₁; d ₂=-D ₂, (-D ₂+ 1) ..., (D ₂-1), D ₂; D ₁and D ₂represent respectively orientation to distance maximum auto-correlation distance upwards, be positive integer, determine according to actual conditions.

According to following equation solution function ρ _g(d ₁, d ₂) value:

Wherein with for two form parameters of Fisher distribution, be arithmetic number, determine according to actual conditions, represent that degree of freedom is the inverse function of F function.

Utilize following formula computer memory correlated Gaussian distributed image G ₂(n ₁, n ₂):

$G_2(n_1.n_2)=\mathrm{IFFT}(\sqrt{\mathrm{FFT}\left({\mathrm{\&rho;}}_G(d_1,d_2)\right)}\&CenterDot;\mathrm{FFT}\left(G_1(n_1,n_2)\right))$

Wherein FFT and IFFT represents two-dimensional Fourier transform and inverse transformation thereof respectively.

To G ₂(n ₁, n ₂) carry out following nonlinear transformation:

$U(n_1,n_2)=\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_{-\&infin;}^{G_2(n_1,n_2)}\exp \{-\frac{1}{2}{t}^2\}\mathrm{dt},1\&le;n_1\&le;N_1,1\&le;n_2\&le;N_2$

Then U (n ₁, n ₂) be a width size be N ₁× N ₂the upper equally distributed space correlation image in obedience interval [0,1].

To U (n ₁, n ₂) carry out following nonlinear transformation:

Then T (n ₁, n ₂) be a width size be in theory N ₁× N ₂autocorrelation function be ρ _t, obey unit average Fisher distribute texture image.

3rd step: the polarization SAR clutter image that space correlation KummerU distributes generates

Corresponding each location of pixels (n ₁, n ₂), according to following formula structure complex matrix:

Z ^(L)(n ₁,n ₂)＝T(n ₁,n ₂)·Y ^(L)(n ₁,n ₂),1≤n ₁≤N ₁,1≤n ₂≤N ₂(6)

Then Z ^(L)(n ₁, n ₂) be a width size be N ₁× N ₂the emulation polarization SAR clutter image of obedience KummerU distribution, the complex conjugate symmetry matrix of the corresponding R × R of its each location of pixels.

The invention has the beneficial effects as follows: the polarization SAR clutter image of obeying KummerU distribution can be emulated.Because KummerU distribution is for the K distribution of classics, better can characterize the statistical property of polarization SAR clutter image especially high resolving power polarization SAR clutter image, thus the inventive method is had wide range of applications, the assessment of the Polarimetric SAR Image decipher algorithm of a large amount of Corpus--based Method method can be applied to.

Accompanying drawing explanation

Fig. 1 is polarization SAR clutter image emulation mode process flow diagram of the present invention;

Fig. 2 is the simulation result utilizing the first step of the present invention to obtain;

Fig. 3 is the simulation result utilizing second step of the present invention to obtain;

Fig. 4 is the simulation result utilizing the present invention to obtain.

Embodiment

Below in conjunction with accompanying drawing, space correlation polarization SAR clutter image emulation mode provided by the invention is described in detail.

Fig. 1 is the process flow diagram of polarization SAR clutter image emulation mode of the present invention.The first step of this flow process is the coherent spot image simulation that multiple Wishart distributes.First coherent spot component image is looked according to the polarization covariance matrix emulation L of known Polarimetric SAR Image.Second step is the emulation of space correlation Fisher distribution texture image.Based on the random average produced to be 0 variance be 1 Gaussian distribution image, obtain the texture image that the unit average Fisher that obeys space correlation distributes.3rd step is that the polarization SAR clutter image that space correlation KummerU distributes generates.Because Polarimetric SAR Image can be analyzed to the product of coherent spot and texture, therefore by the process that to be multiplied with texture to the coherent spot of emulation, obtain the polarization SAR clutter image of emulation.

Fig. 2 to Fig. 4 is the result of carrying out emulation experiment.Atural object classification to be emulated in emulation experiment is the woods, depending on several L=4, and image size N ₁=N ₂the optimum configurations of=200, Fisher distribution is with , D ₁=5 and D ₂=5.Utilize measured data, the dimension R=3 of polarization SAR Scattering of Vector, the covariance matrix C tried to achieve is:

$C=\left[\begin{array}{ccc}0.0485& 0.0045-j0.0015& 0.0070+j0.0035\\ 0.0045+J0.0015& 0.0300& 0.0004+j0.0028\\ 0.0070-j0.0035& 0.0004-j0.0028& 0.0622\end{array}\right].$

Fig. 2 is the simulation result utilizing the first step of the present invention to obtain, be respectively the image of simulation dry spot in three passages, based on the polarization characteristic of measured data, Fig. 2 (a), Fig. 2 (c) and Fig. 2 (e) are respectively the image of simulation dry spot in HH, HV and VV passage.Fig. 2 (b), Fig. 2 (d) and Fig. 2 (f) are respectively the image histogram of simulation dry spot in HH, HV and VV passage (circle represents histogram value) and corresponding theoretical PDF (solid line representation theory PDF value), as can be seen from the figure, the image histogram of coherent spot component in each passage of emulation and theoretical PDF very identical, thus demonstrate the validity of coherent spot component image emulation mode.

Fig. 3 is the simulation result utilizing second step of the present invention to obtain.The texture component image (intensity) that the unit average Fisher that Fig. 3 (a) is emulation distributes.The histogram (circle represents histogram value) that Fig. 3 (b) is this texture component image and corresponding theoretical PDF (solid line representation theory PDF value).The autocorrelation function ρ of the actual autocorrelation function (dotted line represents) that Fig. 3 (c) is texture component image and setting _t(solid line represents).In this experiment, the autocorrelation function ρ of texture component _t(d ₁, d ₂) utilize anisotropic Gaussian function to set, its expression formula is:

${\mathrm{\&rho;}}_T(d_1,d_2)=\exp \{-\frac{1}{2}(\frac{{(d_1\cos \mathrm{\&theta;}+d_2\sin \mathrm{\&theta;})}^2}{{\mathrm{\&sigma;}}_1^2}+\frac{{(-d_1\sin \mathrm{\&theta;}+d_2\cos \mathrm{\&theta;})}^2}{{\mathrm{\&theta;}}_2^2})\}---\left(1\right)$

Wherein σ ₁and σ ₂for two standard deviation criteria of this function, θ is the angle parameter of this function, determines according to actual needs, σ in this experiment ₁=2, σ ₂=3, θ=π/6.From result, the histogram PDF theoretical with it ten points of the texture component image of emulation coincide, the autocorrelation function of actual autocorrelation function and the setting of the texture component image of emulation is also very identical, thus demonstrates the validity of the texture image emulation mode of space correlation unit average Fisher distribution.

Fig. 4 is the simulation result utilizing the present invention to obtain.Fig. 4 (a), Fig. 4 (c) and Fig. 4 (e) are respectively the image in HH, HV and VV passage utilizing the present invention to obtain, and Fig. 4 (b), Fig. 4 (d) and Fig. 4 (f) are respectively the image histogram (circle represents histogram value) in HH, HV and VV passage and corresponding theoretical PDF (solid line representation theory PDF value) that utilize the present invention to obtain.From result, the polarization SAR clutter image of emulation histogram in each channel and corresponding theoretical PDF ten points coincide, thus demonstrate the validity of the space correlation polarization SAR clutter image emulation mode that KummerU of the present invention distributes.

Claims (1)

1., based on a space correlation polarization SAR clutter image emulation mode for inverse transformation method, SAR refers to synthetic-aperture radar, it is characterized in that, comprises the steps:

The first step, the coherent spot image simulation of multiple Wishart distribution:

Known polarization SAR measuring image comprises a certain atural object classification to be emulated, and therefrom selects M the pixel that such atural object is corresponding, M >=100, utilizes following method to produce covariance matrix C:

$C=\frac{1}{M}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{C}_i^{\&prime;}$

Wherein C' _ibe that R × R corresponding to i-th pixel ties up polarization covariance matrix, i=1,2 ..., M, R are the dimension of polarization SAR Scattering of Vector, C' _ivalue utilize known polarization SAR measuring image to obtain;

Calculate all eigenvalue λ of C ₁, λ ₂..., λ _rand corresponding unit character vector p ₁, p ₂..., p _r, remember 0 < λ ₁≤ λ ₂≤ ... ,≤λ _r;

Make C _s=U Λ ^1/2, wherein Λ=diag{ λ ₁, λ ₂..., λ _r, U=[p ₁, p ₂..., p _r];

To each location of pixels (n of polarization SAR clutter image ₁, n ₂), 1≤n ₁≤ N ₁, 1≤n ₂≤ N ₂, the coherent spot covariance matrix Y obeying multiple Wishart distribution is produced according to following method ^(L)(n ₁, n ₂):

First produce L R and tie up complex vector Y _l(n ₁, n ₂)=C _s[η ₁+ j η ₂, η ₃+ j η ₄..., η _2R-1+ j η _2R] _l ^t, l=1,2 ..., L, wherein η ₁, η ₂, η ₃, η ₄..., η _2R-1, η _2Rfor mutual statistical independently average to be 0 variance be 0.5 Gaussian distributed random variable, L > R be polarization SAR clutter image to be emulated look number, be a positive integer, determine as required;

The matrix that then coherent spot image simulation is corresponding $Y^{\left(L\right)}(n_1,n_2)=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{Y}_l(n_1,n_2)Y_l{(n_1,n_2)}^H;$

Second step, the emulation of space correlation Fisher distribution texture image:

Producing a width size is N ₁× N ₂the Gaussian distribution image G of obedience average to be 0 variance the be statistical iteration of 1 ₁(n ₁, n ₂);

According to the actual requirements, the autocorrelation function ρ of texture component is set _t(d ₁, d ₂) value, d ₁and d ₂to represent respectively in texture image any two location of pixels in orientation to distance range difference upwards, d ₁=-D ₁, (-D ₁+ 1) ..., (D ₁-1), D ₁; d ₂=-D ₂, (-D ₂+ 1) ..., (D ₂-1), D ₂; D ₁and D ₂represent respectively orientation to distance maximum auto-correlation distance upwards, be positive integer, determine according to actual conditions;

According to following equation solution function ρ _g(d ₁, d ₂) value:

Wherein with for two form parameters of Fisher distribution, be arithmetic number, determine according to actual conditions, represent that degree of freedom is the inverse function of F function;

Utilize following formula computer memory correlated Gaussian distributed image G ₂(n ₁, n ₂):

$G_2(n_1,n_2)=\mathrm{IFFT}(\sqrt{\mathrm{FFT}\left({\mathrm{\&rho;}}_G(d_1,d_2)\right)}\&CenterDot;\mathrm{FFT}\left(G_1(n_1,n_2)\right))$

Wherein FFT and IFFT represents two-dimensional Fourier transform and inverse transformation thereof respectively;

To G ₂(n ₁, n ₂) carry out following nonlinear transformation, obtain space correlation image U (n ₁, n ₂):

$U(n_1,n_2)=\frac{1}{\sqrt{2\mathrm{\&pi;}}}{\&Integral;}_{-\&infin;}^{G_2(n_1,n_2)}\exp \{-\frac{1}{2}{t}^2\}\mathrm{dt};$

To U (n ₁, n ₂) carry out following nonlinear transformation, obtain texture image T (n ₁, n ₂):

3rd step, the polarization SAR clutter image that space correlation KummerU distributes generates:

Corresponding each location of pixels (n ₁, n ₂), according to following formula structure complex matrix:

Z ^(L)(n ₁,n ₂)＝T(n ₁,n ₂)·Y ^(L)(n ₁,n ₂)

Then Z ^(L)(n ₁, n ₂) space correlation polarization SAR clutter image for obtaining.