Compound complex Wishart models (R6)

R6 class for the compound truncated Poisson (CTPCW) and compound geometric (CGCW) complex Wishart laws of Ferreira, Nascimento and Frery (2022); see dctpcw(). Parameters are estimated by the expectation-maximisation (EM) algorithm, treating the number of scatterers \(N\) as missing data:

• E-step: \(\hat N_i = E(N \mid S_i)\);

• M-step: \(\hat\Sigma = \bar S / (L \bar N)\) and \(\hat\lambda/(1 - e^{-\hat\lambda}) = \bar N\) (CTPCW) or \(\hat p = 1/\bar N\) (CGCW).

The Shannon entropy has no closed form and is approximated by Monte Carlo.

References

Ferreira, J. A., Nascimento, A. D. C. and Frery, A. C. (2022). PolSAR models with multimodal intensities. Remote Sensing, 14(20), 5083. doi:10.3390/rs14205083

Super class

SARModel -> CompoundWishart

Public fields

counting

Counting law: "poisson" (zero-truncated) or "geometric".

iterations

Number of EM iterations of the last fit.

Methods

Public methods

• CompoundWishart$new()

• CompoundWishart$density()

• CompoundWishart$random()

• CompoundWishart$fit()

• CompoundWishart$entropy()

• CompoundWishart$entropy_variance()

• CompoundWishart$clone()

Inherited methods

• SARModel$glance()
• SARModel$log_likelihood()
• SARModel$n_parameters()
• SARModel$print()
• SARModel$tidy()

---

CompoundWishart$new()

Create a compound Wishart model.

Usage

CompoundWishart$new(
  counting = c("poisson", "geometric"),
  Sigma = diag(3) + (0+0i),
  L = 4,
  lambda = 1,
  p = 0.5
)

Arguments

counting

"poisson" (CTPCW) or "geometric" (CGCW).

Sigma

Hermitian positive definite matrix.

L

Number of looks of each component.

lambda, p

Parameter of the counting law.

---

CompoundWishart$density()

(Log-)density.

Usage

CompoundWishart$density(x, log = FALSE)

Arguments

x

PolSAR observations.

log

Return log-densities?

---

CompoundWishart$random()

Simulate PolSAR observations.

Usage

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

Arguments

n

Number of observations.

output

"array" or "vec".

---

CompoundWishart$fit()

Fit by the EM algorithm.

Usage

CompoundWishart$fit(x, L, tol = 1e-06, max_iter = 500L)

Arguments

x

PolSAR observations.

L

Known number of looks of each component.

tol

Convergence tolerance (relative change of the parameters).

max_iter

Maximum number of iterations.

---

CompoundWishart$entropy()

Monte Carlo approximation of the Shannon entropy.

Usage

CompoundWishart$entropy(nsim = 2000L)

Arguments

nsim

Number of simulated observations.

---

CompoundWishart$entropy_variance()

Not available for compound models.

Usage

CompoundWishart$entropy_variance(n = self$n)

Arguments

n

Ignored.

---

CompoundWishart$clone()

The objects of this class are cloneable with this method.

Usage

CompoundWishart$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

set.seed(1)
S <- rctpcw(200, lambda = 1.5, Sigma = polsar_example_sigma("forest"), L = 4)
m <- CompoundWishart$new(counting = "poisson")$fit(S, L = 4)
m$params$lambda
#> [1] 1.462612
m$iterations
#> [1] 33