multirestransforms.q

This library contains several multiresolution transforms, and allows image processing algorithms to use the same interface to each of these transforms. This has the benefit that transforms can easily be changed/combined. The technique is always the same: first “build” your transform, as follows

[W, W_T] = build_XXXX(parameters)

where W - the forward transformation function W_T - the backward transformation function For orthogonal transforms, we have that W * W_T = I or, equivalently that W = transpose(W_T).

Summary

multirestransforms.q	This library contains several multiresolution transforms, and allows image processing algorithms to use the same interface to each of these transforms.
Functions
lincell	Linearize a cell array, i.e.
build_dwt	Constructs a 2D wavelet transform
build_dtcwt	Construct a 2D DT-CWT transform
build_stp	Builds a steerable pyramid transform
build_dst2d	Build a 2D shearlet transform
build_energyweighted_dst2d	Builds an energy-weighted (non-Parseval) 2D shearlet transform (in which the variance of white noise is preserved in the subbands)

Functions

lincell

Linearize a cell array, i.e. convert nested cell arrays to one 1D cell array.

function y = lincell(x)

Notes

this function only involves pointer copies, which are very fast

build_dwt

Constructs a 2D wavelet transform

function [W, W_T] = build_dwt(w, J)

Parameters

w	the wavelet filters to be used for the construction (e.g. db2,sym8,...)
J	the number of scales
W	the forward wavelet transform
W_T	the inverse wavelet transform

build_dtcwt

Construct a 2D DT-CWT transform

function [W, W_T] = build_dtcwt(w1, w2, J)

Parameters

w1	the wavelet filters to be used for the first scale of the DT-CWT
w2	the wavelet filters to be used for the other scales
J	the number of scales
W	the forward complex wavelet transform
W_T	the inverse complex wavelet transform

build_stp

Builds a steerable pyramid transform

function [S, S_H] = build_stp(sz, K, J)

Parameters

sz	size of the images that have to be processed
K	the number of orientations of the transform
J	the number of scales of the transform

build_dst2d

Build a 2D shearlet transform

function [S, S_H] = build_dst2d(sz, K, J)

Parameters

sz	size of the images that have to be processed
K	the number of orientations of the transform
J	the number of scales of the transform
S	the forward shearlet transform
S_H	the adjoint shearlet transform

Notes

In this implementation, the number of orientations is the same for all scales - so a scalar number needs to be specified for K.

build_energyweighted_dst2d

Builds an energy-weighted (non-Parseval) 2D shearlet transform (in which the variance of white noise is preserved in the subbands)

function [S, S_H] = build_energyweighted_dst2d(sz, K, J)

Parameters

sz	size of the images that have to be processed
K	the number of orientations of the transform
J	the number of scales of the transform
S	the forward shearlet transform
S_H	the backward shearlet transform

Notes

S_back is actually not the adjoint of S; this is due to the normalization is being done.