Talk about the WAVEDEC2 function.

Http://maiqiuzhizhu.blog.sohu.com/110325150.html

WAVEDEC2 function:

1. Function: realize multi-layer decomposition of image (i.e., two-dimensional signal).

Multilayer, that is, multi-scale.

2. Format: [C,s]=wavedec2 (X,n, ' wname ')

[C,s]=wavedec2 (X,n,lo_d,hi_d) (I don't discuss it)

3. Parameter description: N-layer decomposition using wname wavelet function for image x

Here the wavelet function should be selected according to the actual situation, the specific choice method can be searched. The output is c,s.

c is the decomposition coefficient of each layer, s is the decomposition coefficient length of each layer, that is, size.

Structure of 4.c: C=[a (N) | H (N) | V (N) | D (N) | H (N-1) | V (N-1) | D (N-1) | H (N-2) | V (N-2) | D (N-2) |...| H (1) | V (1) | D (1)]

Visible, C is a line vector, that is: 1* (Size (X)), (e.g,x=256*256,then C size: 1* (256*256) =1*65536)

A (n) represents the nth-layer low-frequency coefficient, H (n) | V (N) | D (n) represents the nth layer high frequency coefficients, respectively horizontal, vertical, diagonal high frequency, and so on, to H (1) | V (1) | D (1).

S structure: is the storage of the decomposition coefficient length of each layer, that is, the first line is a (n) length, the second line is H (n) | V (N) | D (N) | The length of the third line is

H (N-1) | V (N-1) | D (N-1) length, the penultimate line is H (1) | V (1) | D (1) length, the last line is the length of x (size)

So what's the use of s?

s structure: is the storage of the decomposition coefficient length of each layer, that is, the first line is a (n) length (in fact, a (n) of the original matrix of the number of rows and columns),

the second line is H (N) | V (N) | The length of D (N) |,

the third line is

H (N-1) | V (N-1) | The length of D (N-1),

the penultimate line is H (1) | V (1) | D (1) Length,

the last line is the length of x (size)

from the above figure can know: the length of Can is 32*32,ch1, cV1, cD1 length is 256*256.

so far, you might want to ask why the output of C is a line vector?

1, not that a language can dynamically output the number of parameters, not to mention the C language written matlab

2. The size of the detailed coefficient matrix at all levels (size) is not the same, so it cannot be combined into a large matrix output.

Therefore, it is the best and the only choice to output the result as a row vector.

Another: MATLAB help inside said very clearly, hehe.

Wavedec2

Multilevel 2-d wavelet decomposition Syntax [c,s] = WAVEDEC2 (x,n, ' wname ')

[C,s] = WAVEDEC2 (x,n,lo_d,hi_d)

Description WAVEDEC2 is a two-dimensional wavelet analysis function.

[C,s] = WAVEDEC2 (x,n, ' wname ') returns the wavelet decomposition of the matrix X at level N, using the wavelet named in Str ing ' wname ' (see wfilters for more information).

Outputs is the decomposition vector C and the corresponding bookkeeping matrix S. N must be a strictly positive integer ( See Wmaxlev for more information).

Instead of giving the wavelet name, you can give the filters. for [c,s] = WAVEDEC2 (x,n,lo_d,hi_d), Lo_d is the decomposition Low-pass filter and hi_d are the Decomposition High-pass fil ter.

Vector C is organized as C = [A (N) | H (N) | V (N) | D (N) | ... H (N-1) | V (N-1) | D (N-1) | ... | H (1) | V (1) | D (1)]. Where a, H, V, D, is row vectors such that a = approximation coefficients H = horizontal detail coefficients V = Vertical Detail coefficients D = diagonal detail coefficients each vector is the vector column-wise storage of a matrix.

Matrix S is such this s (1,:) = size of approximation coefficients (N) S (i,:) = size of detail coefficients (n-i+2) for i = 2 , ... N+1 and S (n+2,:) = Size (X)

examples% the current extension mode was zero-padding (see Dwtmode).

% Load Original image.
Load woman;
% X contains the loaded image.

% Perform decomposition at level 2
% of X using DB1.
[C,s] = WAVEDEC2 (x,2, ' db1 ');

% decomposition structure organization.
Sizex = Size (X)

Sizex =
256 256
Sizec = Size (c)

Sizec =
1 65536
val_s = S

val_s =
64 64
64 64
128 128
256 256

Algorithm for images, a algorithm similar to the one-dimensional case was possible for two-dimensional wavelets and Scali ng functions obtained from one-dimensional ones by tensor product. This kind of two-dimensional DWT leads-a decomposition of approximation coefficients at level J-four Components:the Approximation at level j+1, and the details in three orientations (horizontal, vertical, and diagonal). The following chart describes the basic decomposition step for images:  so, for j=2, the two-dimensional wavelet tree Have the form  see ALSODWT, Waveinfo, WAVEREC2, Wfilters, Wmaxlev Referencesdaubechies, I. (1992), Ten Lectures on WA Velets, CBMS-NSF conference series in Applied Mathematics. SIAM Ed Mallat, S. (1989), "A Theory for multiresolution signal decomposition:the wavelet representation," IEEE Pattern Anal. and Machine Intell., vol. one, No. 7, pp. 674-693. Meyer, Y. (1990), ondelettes et opérateurs, Tome 1, Hermann Ed. (中文版 translation:wavelets and OperAtors, Cambridge Univ Press. 1993.