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SAR Image: common distribution when fitting clutter

2022-07-18 07:55:00 【Xuan yanru Liu】

Record fitting SAR The commonly used distribution type of image clutter

Distribution type PDF explain CDF
Normal distribution f ( x ) = 1 2 π σ e − ( x − μ ) 2 2 σ 2 f(x)=\frac{1}{\sqrt{2 \pi}σ}e^{-\frac{(x-μ)^2}{2σ^2}} f(x)=2π​σ1​e−2σ2(x−μ)2​ μ by all value , σ 2 \mu Is the mean , \sigma^2 μ by all value ,σ2 Is variance F ( x ) = ∫ − ∞ x f ( t ) d t F(x)=\int_{-∞}^{x}f(t)dt F(x)=∫−∞x​f(t)dt
Lognormal distribution f ( x ) = 1 x 2 π σ e − ( l o g ( x ) − μ ) 2 2 σ 2 , x > 0 f(x)=\frac{1}{x\sqrt{2 \pi}σ}e^{-\frac{(log(x)-μ)^2}{2σ^2}},x>0 f(x)=x2π​σ1​e−2σ2(log(x)−μ)2​,x>0 ditto F ( x ) = ∫ 0 x f ( t ) d t F(x)=\int_{0}^{x}f(t)dt F(x)=∫0x​f(t)dt
Rayleigh distribution f ( x ) = x σ 2 e x p { − x 2 2 σ 2 } f(x)=\frac{x}{\sigma^2}exp\{\frac{-x^2}{2\sigma^2}\} f(x)=σ2x​exp{ 2σ2−x2​} σ \sigma σ As the standard deviation F ( x ) = 1 − e − x 2 2 b 2 F(x)=1-e^{\frac{-x^2}{2b^2}} F(x)=1−e2b2−x2​
weibull Distribution f ( x ) = λ v ( x v ) λ − 1 e ( − x v ) λ f(x)=\frac{\lambda}{v}(\frac{x}{v})^{\lambda-1}e^{(-\frac{x}{v})^\lambda} f(x)=vλ​(vx​)λ−1e(−vx​)λ λ \lambda λ For shape parameters , v v v It is a scale parameter F ( x ) = 1 − e ( − x v ) λ F(x)=1-e^{(-\frac{x}{v})^\lambda} F(x)=1−e(−vx​)λ
gamma Distribution f ( x ) = λ v Γ ( v ) x v − 1 e − λ x f(x)=\frac{\lambda^v}{\Gamma(v)}x^{v-1}e^{-\lambda x} f(x)=Γ(v)λv​xv−1e−λx λ \lambda λ For shape parameters , v v v It is a scale parameter , Γ ( ) \Gamma() Γ() by gamma function F ( x ) = Γ ( λ x , v ) F(x)=\Gamma(\lambda x,v) F(x)=Γ(λx,v)
K K K Distribution f ( x ) = 2 v Γ ( λ ) ( x 2 v ) λ K λ − 1 ( x λ ) , x > 0 f(x)=\frac{2}{v\Gamma(\lambda)}(\frac{x}{2v})^{\lambda}K_{\lambda-1}(\frac{x}{\lambda}),x>0 f(x)=vΓ(λ)2​(2vx​)λKλ−1​(λx​),x>0 λ \lambda λ For shape parameters , v v v It is a scale parameter F ( x ) = ∫ 0 x f ( t ) d t F(x)=\int_{0}^{x}f(t)dt F(x)=∫0x​f(t)dt
G 0 G^0 G0 Distribution f ( x ) = 2 n n Γ ( n − λ ) x 2 n − 1 v λ Γ ( n ) Γ ( − λ ) ( v + n x 2 ) ( n − λ ) , − λ , v , n , x > 0 f(x)=\frac{2n^n\Gamma(n-\lambda)x^{2n-1}}{v^{\lambda}\Gamma(n)\Gamma(-\lambda)(v+nx^2)^(n-\lambda)},\\-\lambda,v,n,x>0 f(x)=vλΓ(n)Γ(−λ)(v+nx2)(n−λ)2nnΓ(n−λ)x2n−1​,−λ,v,n,x>0 n n n Is the number of image views , λ \lambda λ For shape parameters , v v v It is a scale parameter , K n K_n Kn​ by n n n The second kind of modified Bessel function of order F ( x ) = ∫ 0 x f ( t ) d t F(x)=\int_{0}^{x}f(t)dt F(x)=∫0x​f(t)dt
In a broad sense gamma Distribution (Li Improved version ) f ( x ) = ∣ v ∣ κ κ σ Γ ( κ ) ( x σ ) κ v − 1 e x p { − κ ( x σ ) v } , ∣ v ∣ , σ , κ , x > 0 f(x)=\frac{\mid v\mid \kappa^{\kappa}}{\sigma\Gamma(\kappa)}(\frac{x}{\sigma})^{\kappa v-1}exp\{-\kappa(\frac{x}{\sigma})^v\},\\ \mid v\mid,\sigma,\kappa, x>0 f(x)=σΓ(κ)∣v∣κκ​(σx​)κv−1exp{ −κ(σx​)v},∣v∣,σ,κ,x>0 κ \kappa κ For shape parameters , σ \sigma σ It is a scale parameter , v v v Is the power parameter , Also known as the second shape parameter F ( x ) = { Γ ( κ ( x σ ) v , κ ) , v > 0 1 − Γ ( κ ( x σ ) v , κ ) , v < 0 F(x)=\left\{\begin{aligned}\Gamma(\kappa(\frac{x}{\sigma})^v,\kappa),v>0\\ 1-\Gamma(\kappa(\frac{x}{\sigma})^v,\kappa),v<0\end{aligned}\right. F(x)=⎩⎪⎨⎪⎧​Γ(κ(σx​)v,κ),v>01−Γ(κ(σx​)v,κ),v<0​
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本文为[Xuan yanru Liu]所创，转载请带上原文链接，感谢
https://yzsam.com/2022/199/202207151739037600.html

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