CN102024253A - Method for generating SAR (specific absorption rate) image statistic distribution in self-adaption way - Google Patents

Abstract

The invention discloses a method for generating SAR (specific absorption rate) image statistic distribution in a self-adaption way, which relates to synthetic aperture radar image processing technology. On the base of the theoretical basis that any probability distribution not far from Gaussian distribution can perform approximation fitting through the standard Gaussian distribution with same mean value variance with the probability distribution, by using the self statistical property of an SAR image, the invention carries out variable substitute and other treatments on a Chebyshev-Hermite polynomial which is most applicable to frequency statistics to obtain an Edgeworth expanded formula so as to complete self-adaptation fitting for the statistical distribution of the SAR images. The invention solves the disadvantages of artificially appointing image distribution according to experience in the SAR image application and failing to change distribution types with the change of imaging conditions, and has great benefit for improving the precision of follow-up image processing steps.

Description

A kind of self-adaptation generates the method that the SAR image statistics distributes

Technical field

The present invention relates to the synthetic aperture radar (SAR) technical field of image processing, is that a kind of statistical property self-adaptation according to SAR image itself generates the method that the SAR image statistics distributes.

Background technology

Each pixel in the SAR image all is synthetic by the backward scattered echo coherence stack of the many small bins in ground, is a plurality of stochastic distribution aggregation of variable.And the SAR image that comprises certain zone is the distributed areas that a large amount of pixels are formed, i.e. distribution objectives.Distribution objectives also comprise a large amount of scatterers, general very not outstanding strong scattering body, the distribution of its signal echo data is more even, it has been generally acknowledged that certain statistical property is obeyed in the distribution of data, can be described promptly so-called Clutter Model with certain probability Distribution Model.Scene is very complicated to electromagnetic scattering process, and echoed signal is usually by many physics and geometrical factor decisions such as incident wave frequency, polarization mode, incident angle, target size, shape and structure, target dielectric properties; Quantization operation after imaging processing process and the imaging, contrast adjustment and resampling etc. also can have influence in various degree to the statistical property of SAR image.

Clutter data for different SAR scenes, the distributed model that is suitable for is different, for certain given SAR clutter data, selects the model of a given SAR picture amplitude the most close (intensity) data in the multi-model of comforming, this selection depends on practical experience, has certain randomness; Further be that Clutter Model can change because of variations such as wavelength, incident angle, resolution, even Same Scene, gained distributes and also is not quite similar under the different condition, and the method that all similar scene fixed single clutters are distributed does not have adaptivity.More than these factors all will reduce the precision of works of treatment such as the follow-up SAR image object that distributes based on image statistics detects, the SAR image classification is cut apart.If can find a kind of method, will improve the accuracy of SAR Flame Image Process greatly according to SAR image self statistical property self-adaptation match SAR image distribution.The method that does not also have self-adaptation match SAR image distribution at present both at home and abroad.

Summary of the invention

The objective of the invention is to solve people need artificial specify image distribution pattern in using the application of synthetic aperture radar (SAR) image distribution problem, a kind of method of self-adaptation match SAR image statistics distribution is provided, improves the degree of accuracy of follow-up SAR Flame Image Process.

In order to achieve the above object, technical solution of the present invention is:

A kind of self-adaptation generates the method that the SAR image statistics distributes, and it all approaches match by the standard Gaussian distribution that equates with its mean variance to any one from the not far probability distribution of Gaussian distribution; It comprises step:

Step 1: import the SAR image X under the big or small arbitrarily scene arbitrarily of a width of cloth, calculate its average

And variance

Obtain the basic statistical property of image;

Step 2: the gray-scale value to each pixel in the image carries out standardization, and its expression formula is:

Be beneficial to further processing;

Step 3: according to the gray-scale value of SAR image after the standardization obtain image one to Fourth-order moment: μ ₁' μ ₂' μ ₃' μ ₄', its expression formula is:

μ ₁′＝E[X]

${{\mathrm{\μ}}_2}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^2{m}_i}{n}$

${{\mathrm{\μ}}_3}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^3{m}_i}{n};$

${{\mathrm{\μ}}_4}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^4{m}_i}{n}$

Step 4: 3 rank and the 4 rank semi-invariant k that calculate image ₃, k ₄:

k ₃＝μ ₃′-3μ ₂′μ ₁′+2μ ₁′ ³

k ₄＝μ ₄′-4μ ₃′μ ₁′-3μ ₂′ ²+12μ ₂′μ ₁′ ²-6μ ₁′ ⁴；

Step 5: calculate the polynomial coefficient H of Chebyshev-Hermite by each rank semi-invariant of gained in the step 4 ₃(x), H ₄(x), H ₆(x), simulate Edgeworh exhibition formula, obtain statistical distribution functions:

$f_X\left(x\right)=(1+\frac{k_3}{6}{H}_3\left(x\right)+\frac{k_4}{24}{H}_4\left(x\right)+\frac{k_3^2}{72}{H}_6\left(x\right))\mathrm{\α}\left(x\right)$

Wherein

Be the standard Gaussian distribution, x is a function argument, and π is a circular constant constant 3.141592653589793, and e is a constant 2.718281828459, is the end of natural logarithm.

The method that described SAR image statistics distributes, its described Edgeworh exhibition formula is EdgeworhA class expansion.

Good effect of the present invention: method for transformation of the present invention, by the statistical nature of SAR image itself, do not need in advance that the people is not influenced by various image-forming conditions for making any hypothesis, can self-adaptation match SAR image distribution.

Description of drawings

Fig. 1 generates the method flow synoptic diagram that the SAR image statistics distributes for a kind of self-adaptation of the present invention.

Embodiment

A kind of self-adaptation of the present invention generates the method that the SAR image statistics distributes, can make a specific distribution roughly near a known distribution by changing variable in theory, its theoretical foundation be can be used for representing a certain unknown distribution with polynomial expression and a distribution commonly used.The distribution of widespread usage was exactly a Gaussian distribution during the SAR image statistics distributed, and can be by approaching match with the equal standard Gaussian distribution of its mean variance, so propose to use the method that Edgeworth exhibition formula self-adaptation generates the distribution of SAR image statistics from the not far probability distribution of Gaussian distribution to any one.

By mathematics and physical field a large amount of put into practice expansion (such as the Taylor expansion) or the expansion of trigonometric function (such as the fourier expansion formula) that we know that function can effectively be expressed as to be made up of each time of variable power, but they all not too are applicable to the frequency statistics function, and we introduce the Chebyshev-Hermite polynomial expression thus.

The Chebyshev-Hermite polynomial expression is defined as:

(-D) ^rα(x)＝H _r(x)α(x) (1)

H wherein ₀=1, α (x) is a standardized normal distribution,

Adopt the Taylor rule to obtain to (1):

$H_r\left(x\right)=x^r-\frac{r^{\left[2\right]}}{2\·1!}{x}^{r-2}+\frac{r^{\left[4\right]}}{2^2\·2!}{x}^{r-4}-\frac{r^{\left[6\right]}}{2^3\·3!}{x}^{r-6}+...---\left(2\right)$

Ten rank polynomial expressions are before the institute:

H ₀＝1

H ₁＝x

H ₂＝x ²-1

H ₃＝x ³-3x

H ₄＝x ⁴-6x ²+3 (3)

H ₅＝x ⁵-10x ³+15x

H ₆＝x ⁶-15x ⁴+45x ²-15

Consider H _r(x) Fourier of α (x) changes, and we have:

${(-1)}^r\sqrt{2\mathrm{\π}}{H}_r\left(t\right)\mathrm{\α}\left(t\right)={\∫}_{-\∞}^{\∞}{i}^r{x}^r\frac{e^{\mathrm{itx}}}{\sqrt{2\mathrm{\π}}}{e}^{-\frac{1}{2}{x}^2}\mathrm{dx}---\left(4\right)$

Opposite, can obtain:

$x^r\mathrm{\α}\left(x\right)=\frac{1}{2\mathrm{\π}}{\∫}_{-\∞}^{\∞}{i}^r{e}^{-\mathrm{itx}}\sqrt{2\mathrm{\π}}{H}_r\left(t\right)\mathrm{\α}\left(t\right)\mathrm{dt}---\left(5\right)$

Exchange x and t:

$\sqrt{2\mathrm{\π}}{(-i)}^r{t}^r\mathrm{\α}\left(t\right)={\∫}_{-\∞}^{\∞}{e}^{-\mathrm{itx}}{H}_r\left(x\right)\mathrm{\α}\left(x\right)\mathrm{dx}---\left(6\right)$

Get H thus _r(x) conversion of α (x) is exactly

Consider expression formula exp (k _rD ^r) α (x), wherein

k _rBe r rank semi-invariant, its fundamental function is:

${\∫}_{-\∞}^{\∞}{e}^{\mathrm{itx}}\exp \left(k_r{D}^r\right)\mathrm{\α}\left(x\right)\mathrm{dx}=\sqrt{2\mathrm{\π}}\mathrm{\α}\left(t\right)\exp \left\{\left(k_r{(-\mathrm{it})}^r\right)\right\}---\left(7\right)$

Approximate think be expressed as:

$\exp (-\frac{k_1-a}{1!}D+\frac{k_2-b}{2!}{D}^2-\frac{k_3}{3!}{D}^3+\frac{k_4}{4!}{D}^4...)\mathrm{\α}\left(x\right)---\left(8\right)$

After passing through a series of simplification and standardization again, obtain Edgeworth exhibition formula from following formula and be:

$f\left(x\right)=\exp \{-k_3\frac{D^3}{3!}+k_4\frac{D^4}{4!}-...\}\mathrm{\α}\left(x\right)---\left(9\right)$

For practical application, we use Edgeworth category-A expansion:

$f_X\left(x\right)=(1+\frac{k_3}{6}{H}_3\left(x\right)+\frac{k_4}{24}{H}_4\left(x\right)+\frac{k_3^2}{72}{H}_6\left(x\right))\mathrm{\α}\left(x\right)---\left(10\right)$

Can draw by above derivation: can be from the not far probability distribution of Gaussian distribution by approaching match with the equal standard Gaussian distribution of its mean variance to any one.In view of Gaussian distribution is the statistical distribution pattern of a most basic SAR image, so the method has feasibility.

As shown in Figure 1, a kind of self-adaptation of the present invention generates the method that the SAR image statistics distributes, and comprising:

Step 1: import a width of cloth SAR image X, obtain average and variance:

Average $E\left[X\right]=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{x_i{m}_i}{n}$

Variance $D\left[X\right]=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{(x_i-E[X\left]\right)}^2{m}_i}{n}$

X wherein _iBe grey scale pixel value, m _iFor grey scale pixel value is x _iNumber of pixels, n is the total number of pixels of image, L is a grey, ∑ for the summation symbol.

Step 2: the pixel value to each pixel in the image carries out standardization:

$x_i=\frac{x_i-E\left[X\right]}{\sqrt{D\left[X\right]}}$

Step 3: obtain image one to Fourth-order moment:

μ ₁′＝E[X]

${{\mathrm{\μ}}_2}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^2{m}_i}{n}$

${{\mathrm{\μ}}_3}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^3{m}_i}{n}$

${{\mathrm{\μ}}_4}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^4{m}_i}{n}$

Step 4: 3 rank and the 4 rank semi-invariant k that calculate image ₃, k ₄:

k ₃＝μ ₃′-3μ ₂′μ ₁′+2μ ₁′ ³

k ₄＝μ ₄′-4μ ₃′μ ₁′-3μ ₂′ ²+12μ ₂′μ ₁′ ²-6μ ₁′ ⁴

Step 5: get the polynomial coefficient of Chebyshev-Hermite by each rank semi-invariant, simulate Edgeworh exhibition formula, obtain statistical distribution functions:

H ₀＝1

H ₁＝x

H ₂＝x ²-1

H ₃＝x ³-3x

H ₄＝x ⁴-6x ²+3

H ₅＝x ⁵-10x ³+15x

H ₆＝x ⁶-15x ⁴+45x ²-15

$f_X\left(x\right)=(1+\frac{k_3}{6}{H}_3\left(x\right)+\frac{k_4}{24}{H}_4\left(x\right)+\frac{k_3^2}{72}{H}_6\left(x\right))\mathrm{\α}\left(x\right)$

Wherein

Be the standard Gaussian distribution, π is a circular constant, gets 3.1415926 during calculating, and e is the end of natural logarithm, approximates 2.71828 greatly.

Claims (2)

1. a self-adaptation generates the method that the SAR image statistics distributes, and it is characterized in that, can both be by approaching match with the equal standard Gaussian distribution of its mean variance from the not far probability distribution of Gaussian distribution to any one; It comprises step:

Step 1: import the SAR image X under the big or small arbitrarily scene arbitrarily of a width of cloth, calculate its average

And variance Obtain the basic statistical property of image;

Step 2: the gray-scale value to each pixel in the image carries out standardization, and its expression formula is:

Be beneficial to further processing;

Step 3: according to the gray-scale value of SAR image after the standardization obtain image one to Fourth-order moment: μ ₁' μ ₂' μ ₃' μ ₄', its expression formula is:

μ ₁′＝E[X]

${{\mathrm{\μ}}_2}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^2{m}_i}{n}$

${{\mathrm{\μ}}_3}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^3{m}_i}{n};$

${{\mathrm{\μ}}_4}^{\′}=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\frac{{x_i}^4{m}_i}{n}$

Step 4: 3 rank and the 4 rank semi-invariant k that calculate image ₃, k ₄:

k ₃＝μ ₃′-3μ ₂′μ ₁′+2μ ₁′ ³

k ₄＝μ ₄′-4μ ₃′μ ₁′-3μ ₂′ ²+12μ ₂′μ ₁′ ²-6μ ₁′ ⁴；

Step 5: calculate the polynomial coefficient H of Chebyshev-Hermite by each rank semi-invariant of gained in the step 4 ₃(x), H ₄(x), H ₆(x), simulate Edgeworh exhibition formula, obtain statistical distribution functions:

$f_X\left(x\right)=(1+\frac{k_3}{6}{H}_3\left(x\right)+\frac{k_4}{24}{H}_4\left(x\right)+\frac{k_3^2}{72}{H}_6\left(x\right))\mathrm{\α}\left(x\right)$

Wherein

Be the standard Gaussian distribution, x is a function argument, and π is a circular constant constant 3.141592653589793, and e is a constant 2.718281828459, is the end of natural logarithm.

2. the method that SAR image statistics as claimed in claim 1 distributes is characterized in that described Edgeworh exhibition formula is an Edgeworh category-A expansion.

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