waverec2

Multilevel 2-D discrete wavelet transform reconstruction

Syntax

imrec = waverec2(c,s,wname)

imrec = waverec2(c,s,LoR,HiR)

imrec = waverec2(___,Name=Value)

Description

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.

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

2-D Wavelet Reconstruction

Load an image.

load woman

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

Apply Gains to Wavelet Subbands and Reconstruct Image

Import an image of a hexagon.

im = imread("hexagon.jpg");
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

c — Wavelet decomposition vector

real-valued vector

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

s — Bookkeeping matrix

integer-valued matrix

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

wname — Analyzing wavelet

character vector | string scalar

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.

LoR,HiR — Wavelet reconstruction filters

even-length real-valued vectors

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.

DetailGain — Wavelet subband gains

lev-by-3 matrix of ones, where lev is the level of the DWT (default) | lev-by-3 matrix

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

LowpassGain — Lowpass gain

1 (default) | real number

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The input wname must be constant.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The input wname must be constant.

• For optimized GPU code generation, specify the bookkeeping matrix s as a compile-time constant.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• waverec2 supports only the 'sym' and 'per' extension modes. See dwtmode.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023a: Specify gains for lowpass coefficients and wavelet coefficient subbands

To specify gains for the lowpass (scaling) coefficients and wavelet subbands, use the name-value arguments LowpassGain and DetailGain, respectively.