Wavedec2 in MATLAB, talk about the wavedec2 function [easy to understand]

Hello everyone , I meet you again , I'm your friend, Quan Jun .

wavedec2 function :

1. function : Implementation image ( That is, two-dimensional signal ) Multilayer decomposition of .

Multi-storey , That is, multi-scale .

2. Format :[c,s]=wavedec2(X,N,’wname’)

[c,s]=wavedec2(X,N,Lo_D,Hi_D)( I won't discuss it )

3. Parameter description : To image X use wname Wavelet basis function implementation N Layer decomposition ,

The wavelet basis function here should be selected according to the actual situation , Specific options can be found . Output is c,s.

c Is the decomposition coefficient of each layer ,s Is the decomposition coefficient length of each layer , That's the size .

4.c Structure :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)]

so ,c It's a row vector , namely :1*(size(X)),(e.g,X=256*256,then c The size is :1*(256*256)=1*65536)

A(N) On behalf of the N Layer low frequency coefficient ,H(N)|V(N)|D(N) On behalf of the N Layer high frequency coefficient , They are horizontal , vertical , Diagonal high frequency , And so on , To H(1)|V(1)|D(1).

s Structure : Is the length of the decomposition coefficient of each layer , The first line is A(N) The length of , 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) The length of , The penultimate line is H(1)|V(1)|D(1) length , The last line is X The length of ( size )

another :MATLAB HELP It's very clear , ha-ha .

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 string ‘wname’ (see wfilters for more information).

Outputs are 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 is the decomposition high-pass filter.

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, are 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 that 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 is 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, an algorithm similar to the one-dimensional case is possible for two-dimensional wavelets and scaling functions obtained from one-dimensional ones by tensor product. This kind of two-dimensional DWT leads to a decomposition of approximation coefficients at level j in 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 has the form See Alsodwt, waveinfo, waverec2, wfilters, wmaxlev ReferencesDaubechies, I. (1992), Ten lectures on wavelets, 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. 11, no. 7, pp. 674-693. Meyer, Y. (1990), Ondelettes et opérateurs, Tome 1, Hermann Ed. (English translation: Wavelets and operators, Cambridge Univ. Press. 1993.

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