appcoef2

2-D approximation coefficients

Syntax

A = appcoef2(C,S,wname)

A = appcoef2(C,S,LoR,HiR)

A = appcoef2(___,N)

Description

A = appcoef2(C,S,wname) returns the approximation coefficients at the coarsest scale using the wavelet decomposition structure [C,S] of a 2-D signal and the wavelet specified by wname. (See wavedec2 for more information.)

A = appcoef2(C,S,LoR,HiR) uses the lowpass reconstruction filter LoR and highpass reconstruction filter HiR. (See wfilters for more information.)

A = appcoef2(___,N) returns the approximation coefficients at level N. If [C,S] is the M-level wavelet decomposition structure of a 2-D signal, then 0 ≤ N ≤ M.

Examples

Reconstruct Approximation Coefficients of an Image

This example shows how to reconstruct approximation coefficients from a multilevel wavelet decomposition of an image.

Set the DWT extension mode to zero-padding. Load and display an image.

origmode = dwtmode('status','nodisplay');
dwtmode('zpd','nodisp')
load woman
image(X)
colormap(map)
title('Original')

size(X)

ans = 1×2

   256   256

Perform a three-level wavelet decomposition of the image using the db1 wavelet. Display the number of elements in the coefficients array cfs, and the contents of the bookkeeping matrix inds. Note that cfs has the same number of elements as X.

wv = 'db1';
[cfs,inds] = wavedec2(X,3,wv);
numel(X)

ans = 
65536

numel(cfs)

ans = 
65536

inds

inds = 5×2

    32    32
    32    32
    64    64
   128   128
   256   256

Extract and display the approximation coefficients at level 2.

cfs2 = appcoef2(cfs,inds,wv,2);
figure
imagesc(cfs2)
colormap('gray')
title('Level 2 Approximation Coefficients')

size(cfs2)

ans = 1×2

    64    64

Extract and display the approximation coefficients at level 3.

cfs3 = appcoef2(cfs,inds,wv,3);
figure
imagesc(cfs3)
colormap('gray')
title('Level 3 Approximation Coefficients')

size(cfs3)

ans = 1×2

    32    32

Restore the original extension mode.

dwtmode(origmode,'nodisplay')

Input Arguments

C — Wavelet decomposition vector

real-valued vector

Wavelet decomposition vector of a 2-D signal, specified as a real-valued vector. C is the output of wavedec2. The bookkeeping matrix S contains the dimensions of the coefficients by level.

Example: [C,S] = wavedec2(randn(256,256),4,'db4') returns the 4-level wavelet decomposition of a matrix.

Data Types: double

S — Bookkeeping matrix

matrix of positive integers

Bookkeeping matrix of the wavelet decomposition of a 2-D signal, specified as a matrix of positive integers. The bookkeeping matrix is used to parse the coefficients in the wavelet decomposition vector C by level.

Example: [C,S] = wavedec2(randn(256,256),4,'db4') returns the 4-level wavelet decomposition of a matrix.

Data Types: double

wname — Wavelet

character vector | string scalar

Wavelet used to generate the wavelet decomposition of a 2-D signal, specified as a character vector or string scalar. The wavelet is from one of the following wavelet families: Best-localized Daubechies, Beylkin, Coiflets, Daubechies, Fejér-Korovkin, Haar, Han linear-phase moments, Morris minimum-bandwidth, Symlets, Vaidyanathan, Discrete Meyer, Biorthogonal, and Reverse Biorthogonal. See wavemngr for the wavelets available in each family.

Example: 'db4'

LoR — Wavelet lowpass reconstruction filter

even-length real-valued vector

Wavelet lowpass reconstruction filter, specified as an even-length real-valued vector. LoR must be the same length as HiR. LoR must be the lowpass reconstruction filter associated with the wavelet used to create the wavelet decomposition structure [C,S]. (See wfilters for more information.)

Data Types: double

HiR — Wavelet highpass reconstruction filter

even-length real-valued vector

Wavelet highpass reconstruction filter, specified as an even-length real-valued vector. HiR must be the same length as LoR. HiR must be the highpass reconstruction filter associated with the wavelet used to create the wavelet decomposition structure [C,S]. (See wfilters for more information.)

Data Types: double

N — Approximation coefficients level

positive integer

Approximation coefficients level, specified as a positive integer. If [C,S] is the M-level wavelet decomposition structure of a 2-D signal, then 0 ≤ N ≤ M.

Data Types: double

Output Arguments

A — Approximation coefficients

real-valued matrix | real-valued 3-D array

Approximation coefficients at level N, returned as a real-valued matrix or 3-D real-valued array. If C and S are obtained from an indexed image analysis or a truecolor image analysis, A is an m-by-n matrix or an m-by-n-by-3 array, respectively.

For more information on image formats, see image and imfinfo.

Data Types: double

Algorithms

The input vector C and bookkeeping matrix S contain all the information about the 2-D signal decomposition.

Let NMAX = size(S,1)-2; then C = [A(NMAX) H(NMAX) V(NMAX) D(NMAX) … H(1) V(1) D(1)] where A, H, V, and D are vectors. If N = NMAX, then a simple extraction is done; otherwise, appcoef2 computes iteratively the approximation coefficients using the inverse wavelet transform.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• Variable-size data support must be enabled.

• The input wname must be constant.

GPU Arrays

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

The appcoef2 function supports GPU array input with these usage notes and limitations:

• appcoef2 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