idwtper2 (Wavelet Toolbox)

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

X = idwtper2(cA,cH,cV,cD,'wname')
X = idwtper2(cA,cH,cV,cD,Lo_R,Hi_R)
X = idwtper2(cA,cH,cV,cD,'wname',S)
X = idwtper2(cA,cH,cV,cD,Lo_R,Hi_R,S)

Description

idwtper2 is a two-dimensional wavelet analysis function.

X = idwtper2(cA,cH,cV,cD,'wname') returns the single-level reconstructed approximation coefficients vector X based on approximation and details vectors cA, cH, cV, and cD at a given level, using the periodized inverse wavelet transform. 'wname' is a string containing the wavelet name (see wfilters).

Instead of giving the wavelet name, you can give the filters.

For X = idwtper2(cA,cH,cV,cD,Lo_R,Hi_R), Lo_R is the reconstruction low-pass filter and Hi_R is the reconstruction high-pass filter.

If sa = size(cA) = size(cH) = size(cV) = size(cD), then size(X) = 2*sa.

For X = idwtper2(cA,cH,cV,cD,'wname',S) or
X = idwtper2(cA,cH,cV,cD,Lo_R,Hi_R,S), S is the size of the result.

idwtper2 is the inverse function of dwtper2 in the sense the abstract statement idwtper2(dwtper2(X,'wname'),'wname') gets back to X.

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

Note: In general, the following abstract statement is not true: idwtper2(dwt2(X,'wname'),'wname') = X.