idwt2 (Wavelet Toolbox)

Single-level inverse discrete 2-D wavelet transform

Syntax

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)
X = idwt2(...,'mode',MODE)

Description

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

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

X = idwt2(cA,cH,cV,cD,Lo_R,Hi_R) reconstructs as above, using filters that 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.

Let sa = size(cA) = size(cH) = size(cV) = size(cD) and lf the length of the filters; then size(X) = SX, where SX = 2* SA, if the DWT extension mode is set to periodization. For the other extension modes, SX = 2*size(cA)-lf+2.

For more information about the different Discrete Wavelet Transform extension modes, see dwtmode.

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 SX.

X = idwt2(...,'mode',MODE) computes the wavelet reconstruction using the extension mode MODE that you specify.

X = idwt2(cA,[],[],[],...) returns the single-level reconstructed approximation coefficients matrix X based on approximation coefficients matrix cA.

X = idwt2([],cH,[],[],...) returns the single-level reconstructed detail coefficients matrix X based on horizontal detail coefficients matrix cH.

The same result holds for X = idwt2([],[],cV,[],...) and
X = idwt2([],[],[],cD,...), based on vertical and diagonal details.

More generally, X = idwt2(AA,HH,VV,DD,...) returns the single-level reconstructed matrix X where AA can be cA or [], and so on.

idwt2 is the inverse function of dwt2 in the sense that the abstract statement
idwt2(dwt2(X,'wname'),'wname') would give back X.

Examples

% The current extension mode is zero-padding (see dwtmode).

% 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(abs(X-A0)))
ans =
    3.4176e-10

Algorithm

See Also
dwt2, dwtmode, upwlev2

idwt ilwt