wrcoef2

Reconstruct single branch from 2-D wavelet coefficients

Syntax

x = wrcoef2(type,c,s,wname)

x = wrcoef2(type,c,s,LoR,HiR)

x = wrcoef2(___,n)

Description

wrcoef2 is a two-dimensional wavelet analysis function. wrcoef2 reconstructs the coefficients of an image.

x = wrcoef2(type,c,s,wname) returns the matrix of reconstructed coefficients of type type based on the wavelet decomposition structure [c,s] of an image (see wavedec2 for more information) using the wavelet specified by wname. The coefficients at the maximum decomposition level are reconstructed. The size of x is equal to the size of the original image.

x = wrcoef2(type,c,s,LoR,HiR) uses the lowpass and highpass reconstruction filters LoR and HiR, respectively.

x = wrcoef2(___,n) reconstructs the coefficients at level n using any of the previous syntaxes.

Examples

Reconstruct 2-D Wavelet Coefficients

Save the current extension mode. Load an image.

origMode = dwtmode("status","nodisp");
load woman
imagesc(X)
title("Original")
colormap gray

Use dwtmode to change the extension mode to zero-padding. Obtain the 2-level wavelet decomposition of the image using the sym5 wavelet.

dwtmode("zpd","nodisp")
[c,s] = wavedec2(X,2,"sym5");

Reconstruct the approximation coefficients at levels 1 and 2. Display the results.

a1 = wrcoef2("a",c,s,"sym5",1);
a2 = wrcoef2("a",c,s,"sym5",2);
subplot(1,2,1)
imagesc(a1)
title("Level 1")
subplot(1,2,2)
imagesc(a2)
title("Level 2")
colormap gray

Reconstruct the horizontal, vertical, and diagonal detail coefficients at level 2.

h2 = wrcoef2("h",c,s,"sym5",2);
v2 = wrcoef2("v",c,s,"sym5",2);
d2 = wrcoef2("d",c,s,"sym5",2);

Confirm all the reconstructions are the same size as the original image.

sX = size(X);
sa1 = size(a1);
sa2 = size(a2);
sh2 = size(h2);
sv2 = size(v2);
sd2 = size(d2);
[sX;sa1;sa2;sh2;sv2;sd2]

ans = 6×2

   256   256
   256   256
   256   256
   256   256
   256   256
   256   256

Restore the extension mode to the original setting.

dwtmode(origMode,"nodisp")

Input Arguments

type — Coefficients to reconstruct

"a" | "h" | "v" | "d"

Coefficients to reconstruct, specified as follows:

• "a" — Approximation coefficients

• "h" — Horizontal detail coefficients

• "v" — Vertical detail coefficients

• "d" — Diagonal detail coefficients

Data Types: string | char

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. See 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. See wavedec2.

Data Types: double

wname — Wavelet

character vector | string scalar

Wavelet, specified as a character vector or string scalar. wrcoef2 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 reconstruction filter, and HiR is the highpass reconstruction filter. The lengths of LoR and HiR must be equal. See wfilters for additional information.

Data Types: double

n — Coefficients level

size(s,1)-2 (default) | integer

Coefficients level, specified as an integer.

• When type is "a", n must be an integer such that 0 ≤ n ≤ size(s,1)-2.

• When type is "h", "v", or "d", n must be an integer such that 1 ≤ n ≤ size(s,1)-2.

Data Types: double

Output Arguments

x — Reconstructed coefficients

matrix

Reconstructed coefficients, returned as a matrix. The size of x is equal to the size of the original image

Data Types: double

Version History

Introduced before R2006a