sim_2Dimage {BSPBSS}

Simulate image data using ICA

Description

The function simulates image data using a probabilistic ICA model whose latent components have specific spatial patterns.

Usage

sim_2Dimage(length = 20, n = 50, sigma = 0.002, smooth = 6)

Arguments

length

The length of the image.

n

sample size.

sigma

variance of the noise.

smooth

smoothness of the latent components.

Details

The observations are generated using probabilistic ICA:

X_i(v) = \sum_{j=1}^q A_{i,j} S_j(v) + \epsilon_i(v) ,

where S_j, j=1,...,q are the latent components, A_{i,j} is the mixing coeffecient and \epsilon_i is the noise term. Specifically, the number of components in this function is q = 3, with each of them being a specific geometric shape. The mixing coefficient matrix is generated with a von Mises-Fisher distribution with the concentration parameter being zero, which means it is uniformly distributed on the sphere. \epsilon_i is a i.i.d. Gaussian noise term with 0 mean and user-specified variance.

Value

List that contains the following terms:

X

Data matrix with n rows (sample) and p columns (pixel).

coords

Cordinate matrix with p rows (pixel) and d columns (dimension)

S

Latent components.

A

Mixing coefficent matrix.

snr

Signal-to-noise ratio.

Examples

sim = sim_2Dimage(length = 30, sigma = 5e-4, n = 30, smooth = 6)