idwt2 (Wavelet Toolbox)

Single-level inverse discrete 2-D wavelet transform.

X = idwt2(cA,cH,cV,cD,'wname')
X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R)
X = idwt2(cA,cH,cV,cD,'wname',S)

X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R,S)

Description

The idwt2 command performs a single-level two-dimensional wavelet reconstruction with respect to either a particular wavelet ('wname', see wfilters) or particular wavelet reconstruction filters (Lo_R and Hi_R) you specify.

X = idwt2(cA,cH,cV,cD,'wname') uses the wavelet 'wname' to compute the single-level reconstructed approximation coefficients vector X based on approximation vector cA and (horizontal, vertical, and diagonal) detail vectors cH,cV and cD.

X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R) reconstructs as above, using filters you specify:

Lo_R is the reconstruction low-pass filter
Hi_R is the reconstruction high-pass filter

Lo_R and Hi_R must be the same length.

If sa = size(cA) = size(cH) = size(cV) = size(cD) and lf is the length of the filters, then size(X) = 2*size(cA)-lf+2.

X = idwt2(cA,cH,cV,cD,'wname',S) and X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R,S) return the size S central portion of the result obtained using the syntax idwt2(cA,cH,cV,cD,'wname'). S must be less than 2*size(cA)-lf+2.

Examples

idwt2 is the inverse function of dwt2 in the sense that the abstract statement
idwt2(dwt2(X,'wname'),'wname') gives back X. Consider this example.

% Load original image. 
    load woman; 
    % X contains the loaded image. 
    sX = size(X);

% Perform single-level decomposition 
% of X using db4. 
    [cA1,cH1,cV1,cD1] = dwt2(X,'db4');

% Invert directly decomposition of X 
% using coefficients at level 1. 
    A0 = idwt2(cA1,cH1,cV1,cD1,'db4',sX);

% Check for perfect reconstruction. 
    max(max(X-A0))
ans =
    3.3032e-10

Algorithm