# Documentation

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# upcoef2

Direct reconstruction from 2-D wavelet coefficients

## Syntax

Y = upcoef2(O,X,'wname',N,S)
Y = upcoef2(O,X,Lo_R,Hi_R,N,S)
Y = upcoef2(O,X,'wname',N)
Y = upcoef2(O,X,Lo_R,Hi_R,N)
Y = upcoef2(O,X,'wname')
Y = upcoef2(O,X,'wname',1)
Y = upcoef2(O,X,Lo_R,Hi_R)
Y = upcoef2(O,X,Lo_R,Hi_R,1)

## Description

upcoef2 is a two-dimensional wavelet analysis function.

Y = upcoef2(O,X,'wname',N,S) computes the N-step reconstructed coefficients of matrix X and takes the central part of size S. 'wname' is a character vector containing the name of the wavelet. See wfilters for more information.

If O = 'a', approximation coefficients are reconstructed; otherwise if O = 'h' ('v' or 'd', respectively), horizontal (vertical or diagonal, respectively) detail coefficients are reconstructed. N must be a strictly positive integer.

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

For Y = upcoef2(O,X,Lo_R,Hi_R,N,S) is the reconstruction low-pass filter and Hi_R is the reconstruction high-pass filter.

Y = upcoef2(O,X,'wname',N) or Y = upcoef2(O,X,Lo_R,Hi_R,N) returns the computed result without any truncation.

Y = upcoef2(O,X,'wname') is equivalent to Y = upcoef2(O,X,'wname',1).

Y = upcoef2(O,X,Lo_R,Hi_R) is equivalent to
Y = upcoef2(O,X,Lo_R,Hi_R,1).

## Examples

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

% Load original image.
% X contains the loaded image.

% Perform decomposition at level 2
% of X using db4.
[c,s] = wavedec2(X,2,'db4');

% Reconstruct approximation and details
% at level 1, from coefficients.
% This can be done using wrcoef2, or
% equivalently using:
%
% Step 1: Extract coefficients from the
% decomposition structure [c,s].
%
% Step 2: Reconstruct using upcoef2.

siz = s(size(s,1),:);

ca1 = appcoef2(c,s,'db4',1);
a1 = upcoef2('a',ca1,'db4',1,siz);

chd1 = detcoef2('h',c,s,1);
hd1 = upcoef2('h',chd1,'db4',1,siz);

cvd1 = detcoef2('v',c,s,1);
vd1 = upcoef2('v',cvd1,'db4',1,siz);

cdd1 = detcoef2('d',c,s,1);
dd1 = upcoef2('d',cdd1,'db4',1,siz);

See upcoef.