# 2-D lifting wavelet transform 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Sep 12, 2007

Downloads : 9

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## WAVELIFT: Multi-level discrete two-dimension wavelet ...

wavelift: Multi-level discrete two-dimension wavelet transform based on lifting method.

c = wavelift(x, nlevel, wname) performs the follows according to the

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.

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 function

of every lifting units lamda(Z)

e. g. for a wavelet_transform with 3 lifting units as

lamda1 = a1 a2*z, lamda2 = b1 b2*z^-1, lamda3 = c1*z^(-1) c2*z

and the lifting gains K0 and K1

L is to be organized as

lamdaz = struct('coeff', {[a1, a2], [b1, b2], [c1, c2], . . .

'zorder', {[ 0, 1], [ 0, -1], [-1, 1 ]} );

L = struct('lamdaz', lamdaz, 'K', [K0, K1]);

% see the decomposition coefficients

y=wavelift(x, 1, 'spl53'); using lossless spline 5/3 wavelet

figure; subplot(1, 2, 1); imshow(x); subplot(1, 2, 2); imshow(mat2gray(y))

% see the reconstruction precision

yy=wavelift(x, 5); using lossy cdf 9/7 wavelet

ix=wavelift(yy, -5); inverse

sum(sum((double(x)-ix). ^2))

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 function

of every lifting units lamda(Z)

e. g. for a wavelet_transform with 3 lifting units as

lamda1 = a1 a2*z, lamda2 = b1 b2*z^-1, lamda3 = c1*z^(-1) c2*z

and the lifting gains K0 and K1

L is to be organized as

lamdaz = 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 wavelet

figure; subplot(1, 2, 1); imshow(x); subplot(1, 2, 2); imshow(mat2gray(y))

% see the reconstruction precision

yy=wavelift(x, 5); using lossy cdf 9/7 wavelet

ix=wavelift(yy, -5); inverse

sum(sum((double(x)-ix). ^2))

**• MATLAB Release: R2006a**

**Demands:****2-D lifting wavelet transform 1.0 scripting tags:**wavelet transform, wavelift, organized, lifting, structure, signal processing, 2-d lifting wavelet transform.

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