G0 polarimetric model for PolSAR data (R6) — G0Polarimetric • SITSAR

R6 class for the $\mathcal{G}^0_m(\alpha, \Sigma, L)$ law (see dg0p()). Following Nascimento, Ferreira and Frery (2023), $\Sigma$ is estimated by the sample mean (since $E(Z) = \Sigma$) and $(\alpha, L)$ by maximising the likelihood (analytic score). The variance of the entropy estimator combines the inverse observed information of $(\alpha, L)$ with a moment estimate of the variance of $m\log|\hat\Sigma|$.

Super class

SARModel -> G0Polarimetric

Methods

Inherited methods

`G0Polarimetric$new()`

Create a G0 polarimetric model.

Usage

G0Polarimetric$new(alpha = -3, Sigma = diag(3) + (0+0i), L = 4)

Arguments

alpha: Roughness (< -1).
Sigma: Hermitian positive definite matrix.
L: Number of looks.

`G0Polarimetric$density()`

(Log-)density.

Usage

G0Polarimetric$density(x, log = FALSE)

Arguments

x: PolSAR observations.
log: Return log-densities?

`G0Polarimetric$random()`

Simulate PolSAR observations.

Usage

G0Polarimetric$random(n, output = "array")

Arguments

n: Number of observations.
output: "array" or "vec".

`G0Polarimetric$fit()`

Fit by maximum likelihood.

Usage

G0Polarimetric$fit(x, L = NULL)

Arguments

x: PolSAR observations.
L: Known number of looks. If NULL (default) it is estimated.

`G0Polarimetric$entropy()`

Shannon entropy.

Usage

G0Polarimetric$entropy()

`G0Polarimetric$clone()`

The objects of this class are cloneable with this method.

Usage

G0Polarimetric$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

set.seed(1)
Z <- rg0p(400, alpha = -4, Sigma = polsar_example_sigma("urban"), L = 4)
m <- G0Polarimetric$new()$fit(Z, L = 4)
m
#> <G0 polarimetric> fitted to n = 400 observations
#>   alpha = -4.56299
#>   Sigma:
#>                   [,1]              [,2]             [,3]
#> [1,]  0.88150+0.00000i  0.02508+0.00207i -0.15380+0.1836i
#> [2,]  0.02508-0.00207i  0.05535+0.00000i -0.00867+0.0141i
#> [3,] -0.15380-0.18360i -0.00867-0.01410i  0.47100+0.0000i
#>   L = 4 (fixed)
#>   logLik = 3778.55
#>   Shannon entropy = -9.51015
m$entropy_variance()
#> [1] 0.0976793