readme

This package is a free collection of Matlab routines for computing wave atom transforms in one, two

README

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1. Introduction

This package is a free collection of Matlab routines for computing
wave atom transforms in one, two and three dimensions. The
implementation is described in detail in the following two papers:

(a) L. Demanet, L. Ying, Wave atoms and sparsity of oscillatory
patterns, to appear in Appl. Comput. Harmon. Anal. 2007.

(b) L. Demanet, L. Ying, Curvelets and wave atoms for mirror-extended
images, technical report. 2007.

Both of them can be downloaded from www.waveatom.org.

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2. List of files

Most of the transform functions have two versions: standard and
symmetric. In the standard version, the coefficients are organized in
a cell array as described in the papers. In the symmetric version, the
coefficients are stored in an array. The symmetric version is
particularly useful for applications like thresholding.

1D wave atom transform
	fwa1.m - forward transform
	iwa1.m - inverse transform
	fwa1sym.m - forward transform, symmetric version
	iwa1sym.m - inverse transform, symmetric version

2D wave atom transform
	fwa2.m - forward transform
	iwa2.m - inverse transform
	fwa2sym.m - forward transform, symmetric version
	iwa2sym.m - inverse transform, symmetric version

3D wave atom transform
	fwa3.m - forward transform
	iwa3.m - inverse transform
	fwa3sym.m - forward transform, symmetric version
	iwa3sym.m - inverse transform, symmetric version

2D mirror-extended wave atom transform
	mefwa2.m - forward transform
	meiwa2.m - inverse transform
	mefwa2sym.m - forward transform, symmetric version
	meiwa2sym.m - inverse transform, symmetric version

2d mirror-extended curvelet transform
	mefcv2.m - forward transform
	meicv2.m - inverse transform

test functions
	test_wa1.m - display several members of 1D wave atom orthobasis
	test_wa2.m - display several members of 2D wave atom orthobasis
	test_wa3.m - display one member of 3D wave atom orthobasis
	test_wa2_reconstruction.m - partial image reconstruction using wave atoms
	test_wa2_denoising.m - image denoising  using 2D wave atom frame with hard thresholding and cycle spinning
	test_mewa2.m - display several 2D mirror-extended wave atoms
	test_mecv2.m - display several 2D mirror-extended curvelets
	test_mewa2_reconstruction.m - partial image reconstruction using mirror-extended wave atoms
	test_mecv2_reconstruction.m - partial image reconstruction using mirror-extended curvelets

internal functions
	freq_pat.m
	g.m
	kf_lf.m
	kf_rt.m
	cvwindow.m
	mescatter.m
	mecombine.m
	dct2.m
	idct2.m
	
data files
	data_fingerprint.jpg - fingerprint image from Chris Brislawn
	data_seismic.jpg - seismic data from Eric Verschuur and Felix Herrman

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3. Copyright

Copyright (c) 2007 Lexing Ying and Laurent Demanet

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
 
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
USA.

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4. Contacts

For further information, please contact [e-mail] or
[e-mail].