dwtper2 (Wavelet Toolbox)

Single-level discrete 2-D wavelet transform (periodized).

[cA,cH,cV,cD] = dwtper2(X,'wname')
[cA,cH,cV,cD] = dwtper2(X,Lo_D,Hi_D)

Description

dwtper2 is a two-dimensional wavelet analysis function.

[cA,cH,cV,cD] = dwtper2(X,'wname') computes the approximation coefficients matrix cA and details coefficients matrices cH, cV, and cD, obtained by periodized wavelet decomposition of the input matrix X.

'wname' is a string containing the wavelet name (see wfilters).

Instead of giving the wavelet name, you can give the filters. When used with three arguments: [cA,cH,cV,cD] = dwtper2(X,Lo_D,Hi_D), Lo_D is the decomposition low-pass filter and Hi_D is the decomposition high-pass filter.

If sx = size(X) then size(cA) = size(cH) = size(cV) = size(cD) = ceil(sx/2).

Examples

% Set initial signal and get filters. 
    load tire 
    % X contains the loaded image. 
    sx = size(X)

sx =
    205 232

w = 'db9'; 
[Lo_D,Hi_D,Lo_R,Hi_R] = wfilters(w);

% DWT with zero-padding image extension. 
[ca0,ch0,cv0,cd0] = dwt2(X,w);

% The transform uses some extra coefficients. 
sxtzp = 2*size(ca0)
sxtzp =
    222 248

% Reconstruction 
x0 = idwt2(ca0,ch0,cv0,cd0,w,sx); 

% Error with zero-padding. 
err0 = max(max(abs(X-x0)))
err0 =
    6.3292e-09

% Periodized DWT 
[cap,chp,cvp,cdp] = dwtper2(X,w);

% The transform uses a minimum of extra coefficients. 
lxtp = 2*size(cap)
lxtp =
    206 232

% Reconstruction. 
xp = idwtper2(cap,chp,cvp,cdp,w,sx);

% Error with periodized DWT. 
errp = max(max(abs(X-xp)))
errp =
    6.7353e-09

Algorithm

See the dwtper algorithm section.