Publisher review:2-D lifting wavelet transform - Self-contained 2-D image decomposition and reconstruction based on lifting wavelet algorithm WAVELIFT: Multi-level discrete two-dimension wavelet transform based on lifting method.c = wavelift(x, nlevel, wname) performs the follows according to the value of nlevel:nlevel > 0: decomposes 2-dimension matrix x up to nlevel level;nlevel < 0: does the inverse transform to nlevel level;nlevel = 0: sets c equal to x;wname is name of wavelet used for DWT or IDWT. It can be omitted. If so, WAVELIFT use the default Cohen-Daubechies-Feauveau (CDF) 9/7 wavelet, which is the name 'cdf97'.Currently, WAVELIFT only support two kind of wavelets, i.e. cdf97 and spline 5/3 with the name 'spl53'.However, aided with the organized lifting structure illustrated below, it is adaptive to other specific lifting realizations. The only thing needed in most cases is only to modify the structure L and the mode to indicate lossy or lossless compression.WAVELIFT call another function COLWAVELIFT to perform 1-D FWT based on lifting method. Deliberately organized lifting structure is provided to COLWAVELIFT as a major parameter.The lifting structure is organized as follows:L: 1-by-1 structure with two fields lamdaz and K.K is two-element vector [K0, K1], which is the lifting gains.lamdaz is 1-by-M structure if M lifting units are used.lamdaz's two fields coeff and zorder denote the transfer functionof every lifting units lamda(Z)e.g. for a wavelet transform with 3 lifting units aslamda1 = a1 a2*z, lamda2 = b1 b2*z^-1, lamda3 = c1*z^(-1) c2*zand the lifting gains K0 and K1L is to be organized aslamdaz = struct('coeff', {[a1, a2], [b1, b2], [c1, c2], ...'zorder', {[ 0, 1], [ 0, -1], [-1, 1 ]} );L = struct('lamdaz', lamdaz, 'K', [K0, K1]);You can test WAVELIFT with following lines:x=imread('E:studyjpeg2000imageslena.tif');% see the decomposition coefficients y=wavelift(x, 1, 'spl53'); using lossless spline 5/3 waveletfigure; subplot(1,2,1); imshow(x); subplot(1,2,2); imshow(mat2gray(y))% see the reconstruction precisionyy=wavelift(x, 5); using lossy cdf 9/7 waveletix=wavelift(yy, -5); inversesum(sum((double(x)-ix).^2)) Requirements: ยท MATLAB Release: R2006a
2-D lifting wavelet transform is a Matlab script for Signal Processing scripts design by Wang Tianhui.
It runs on following operating system: Windows / Linux / Mac OS / BSD / Solaris.
Operating system:Windows / Linux / Mac OS / BSD / Solaris
2-D lifting wavelet transform script details 
