# waverec2

Multilevel 2-D discrete wavelet transform reconstruction

## Description

example

imrec = waverec2(c,s,wname) reconstructs the image, imrec, based on the multilevel discrete wavelet transform (DWT), c, and the bookkeeping matrix, s. The waverec2 function uses the wavelet specified by wname.

imrec = waverec2(c,s,wname) is equivalent to imrec = appcoef2(c,s,wname,0).

imrec = waverec2(c,s,LoR,HiR) reconstructs imrec using the specified lowpass (scaling) and highpass (wavelet) reconstruction filters LoR and HiR, respectively.

example

imrec = waverec2(___,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in previous syntaxes. For example, to specify a gain of 0.25 for the lowpass (scaling) coefficients, set LowpassGain to 0.25.

## Examples

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Perform a level 2 wavelet decomposition of the image using the sym4 wavelet.

wv = 'sym4';
[c,s] = wavedec2(X,2,wv);

Reconstruct the image from the wavelet decomposition structure.

xrec = waverec2(c,s,wv);

Check for perfect reconstruction.

max(abs(X(:)-xrec(:)))
ans = 2.0989e-10

Import an image of a hexagon.

imagesc(im)
title("Original Image")

Obtain a one-level discrete wavelet decomposition of the image using the bior4.4 wavelet.

wv = "bior4.4";
lev = 1;
[c,s] = wavedec2(im,lev,wv);

Reconstruct the image without the finest-scale HH subband. Recall the HH subband corresponds to the diagonal details in the image.

dgain = ones(lev,3);
dgain(lev,3) = 0;
imrec = waverec2(c,s,wv,DetailGain=dgain);
imagesc(imrec)
title("Reconstruction")

## Input Arguments

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Wavelet decomposition vector, specified as a real-valued vector. The vector c contains the approximation and detail coefficients organized by level. The bookkeeping matrix s is used to parse c. c and s are outputs of wavedec2.

Data Types: double

Bookkeeping matrix, specified as an integer-valued matrix. The matrix s contains the dimensions of the wavelet coefficients by level and is used to parse the wavelet decomposition vector c. c and s are outputs of wavedec2.

Data Types: double

Analyzing wavelet, specified as a character vector or string scalar.

Note

waverec2 supports only Type 1 (orthogonal) or Type 2 (biorthogonal) wavelets. See wfilters for a list of orthogonal and biorthogonal wavelets.

Wavelet reconstruction filters, specified as a pair of even-length real-valued vectors. LoR is the lowpass (scaling) reconstruction filter, and HiR is the highpass (wavelet) reconstruction filter. The lengths of LoR and HiR must be equal. See wfilters for additional information.

Data Types: double

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: imrec = waverec2(c,s,Lo,Hi,LowpassGain=0.5) sets the lowpass gain to 0.5.

Since R2023a

Wavelet subband gains, specified as a real-valued lev-by-3 matrix, where lev is the level of the DWT. lev is equal to size(s,1)-2. DetailGain must have three columns, one for each of the wavelet subbands in the order LH (horizontal details), HL (vertical details), and HH (diagonal details). The elements of DetailGain are real numbers in the interval [0, 1] and represent the gain the waverec2 function applies to the coefficients in each subband.

Example: imrec = waverec2(c,s,Lo,Hi,DetailGain=[0 1 1; 0 1 1]) sets gain of the LH subband at all levels to 0.

Data Types: double

Since R2023a

Lowpass gain, specified as a real number in the interval [0, 1]. The waverec2 function applies the gain to the scaling coefficients for use in the reconstruction.

Example: imrec = waverec2(c,s,"db2",Lowpassgain=0) sets the gain for the lowpass (scaling) coefficients to 0.

Data Types: double

## Tips

• If c and s are obtained from an indexed image analysis or a truecolor image analysis, imrec is an m-by-n matrix or an m-by-n-by-3 array, respectively.

For more information on image formats, see the image and imfinfo reference pages.

## Version History

Introduced before R2006a

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