HaarMontage {LS2W}

Generate a 2-D Haar MA process.

Description

This function generates a particular set of four 2-D Haar MA processes. These are subsequently collated to form a montage.

Usage

HaarMontage(n=128, direction = "diagonal", sd = 1)

Arguments

n

The dimension of the realisations that you want to create. Note that n does NOT have to be a power of two, though the output will always be square (n x n).

direction

Three directions can be specified: horizontal, vertical and diagonal. The direction chosen dictates the decomposition direction in which the wavelet spectral structure exists.

sd

The standard deviation of the innovations.

Details

This function generates a realisation of a particular kind of non-stationary lattice model, an example of which is displayed in figure 3 of Eckley, Nason and Treloar (2009). The returned lattice is the result of combining four HaarMA processes. One process is of order 1, whilst another is of order 2. The two remaining processes are of order 3 and 4 respectively. Each individual lattice has dimension n/2*n/2. The standard deviation of the innovations is sd.

Value

A vector containing n*n observations from four collated 2-D Haar MA processes.

Author(s)

Idris Eckley and Sarah Taylor

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,Haar2MA.horiz,Haar2MA.vert

Examples

# Generate a realisation of the non-stationary combined Haar MA
# process with structure in the vertical direction. 
MyHaar2 <- HaarMontage(128,direction="diagonal",sd=1) 
# Plot it.
#
 image(MyHaar2)