LS2W (version 1.3.6)

Haar2MA.vert: Generate 2-D Haar MA process (vertical direction).

Description

These functions generate an arbitrary number of observations from a Haar MA process of any order with a particular variance. We will focus here on Haar2MA.vert --- the routine which generates processes having spectral structure solely in the vertical decomposition direction.

Usage

Haar2MA.vert(n, sd = 1, order = 5)

Value

A matrix containing a realisation of the specified dimension, order and standard deviation.

Arguments

n

The dimension of the realisation that you want to create. Note that n does NOT have to be a power of two, though it is square (nxn).

sd

The standard deviation of the innovations.

order

The order of the MA process.

Author

Idris Eckley

Details

A two-dimensional Haar MA process is a special kind of moving-average (MA) field. A vertical Haar MA process of order $k$ is a MA field of order $2^k-1$, the coefficients of the process being given by the filter coefficients of the two-dimensional, discrete Haar wavelet at various scales within the vertical direction. For example: the vertical Haar MA field of order 1 is an MA process of order 1. It is possible to define such processes for other wavelets as well.

References

Eckley, I.A., Nason, G.P. and Treloar, R.L. (2010) Locally stationary wavelet fields with application to the modelling and analysis of image texture. Journal of the Royal Statistical Society (Series C), 59, 595 - 616.

Eckley, I.A. and Nason, G.P. (2011). LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R, Journal of Statistical Software, 43(3), 1-23. URL http://www.jstatsoft.org/v43/i03/.

See Also

Haar2MA.diag, HaarMontage

Examples

#
# Generate a realisation of a diagonal component 2-D MA field
# of order 4.
#
image1 <- Haar2MA.vert(n=128, sd=3, order=4)
#
#
#