Scaled complex Wishart model for PolSAR data (R6)

R6 class for the scaled complex Wishart law $\mathcal{W}_m(\Sigma, L)$ (see dwishart_sar()). The maximum likelihood estimator of $\Sigma$ is the sample mean and $L$ solves $m\log L - \psi^{(0)}_m(L) = \log|\bar Z| - \overline{\log|Z|}$ (Anfinsen et al., 2009). The entropy variance is available in closed form (Nascimento, Ferreira and Frery, 2023).

References

Anfinsen, S. N., Doulgeris, A. P. and Eltoft, T. (2009). Estimation of the equivalent number of looks in polarimetric synthetic aperture radar imagery. IEEE Transactions on Geoscience and Remote Sensing, 47(11), 3795–3809.

Super class

SARModel -> WishartSAR

Methods

Inherited methods

`WishartSAR$new()`

Create a Wishart model.

Usage

WishartSAR$new(Sigma = diag(3) + (0+0i), L = 4)

Arguments

Sigma: Hermitian positive definite matrix (default identity 3x3).
L: Number of looks.

`WishartSAR$density()`

(Log-)density.

Usage

WishartSAR$density(x, log = FALSE)

Arguments

x: PolSAR observations (array m x m x n or vec matrix).
log: Return log-densities?

`WishartSAR$random()`

Simulate PolSAR observations.

Usage

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

Arguments

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

`WishartSAR$fit()`

Fit by maximum likelihood.

Usage

WishartSAR$fit(x, L = NULL)

Arguments

x: PolSAR observations (array m x m x n or vec matrix).
L: Known number of looks. If NULL (default) it is estimated.

`WishartSAR$entropy()`

Shannon entropy.

Usage

WishartSAR$entropy()

`WishartSAR$entropy_variance()`

Asymptotic variance of the entropy estimator (closed form).

Usage

WishartSAR$entropy_variance(n = self$n)

Arguments

n: Sample size.

`WishartSAR$clone()`

The objects of this class are cloneable with this method.

Usage

WishartSAR$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

set.seed(1)
Z <- rwishart_sar(300, polsar_example_sigma("forest"), L = 4)
m <- WishartSAR$new()$fit(Z)
m
#> <Scaled complex Wishart> fitted to n = 300 observations
#>   Sigma:
#>                  [,1]              [,2]              [,3]
#> [1,] 0.34230+0.00000i 0.013160+0.00643i 0.059910-0.00602i
#> [2,] 0.01316-0.00643i 0.101100+0.00000i 0.001538+0.00261i
#> [3,] 0.05991+0.00602i 0.001538-0.00261i 0.212300+0.00000i
#>   L = 3.97893
#>   logLik = 3618.44
#>   Shannon entropy = -12.0615
m$entropy_variance()
#> [1] 0.02448245