SPIHT_Matlab_Demo.rar_ SPIHT_Matlab_Demo_JPEG2000_image splittin

function varargout = wavelet(WaveletName,Level,X,Ext,Dim) %WAVELET Discrete wavelet transform. % Y = WAVELET(W,L,X) computes the L-stage discrete wavelet transform % (DWT) of signal X using wavelet W. The length of X must be % divisible by 2^L. For the inverse transform, WAVELET(W,-L,X) % inverts L stages. Choices for W are % 'Haar' Haar % 'D1','D2','D3','D4','D5','D6' Daubechies' % 'Sym1','Sym2','Sym3','Sym4','Sym5','Sym6' Symlets % 'Coif1','Coif2' Coiflets % 'BCoif1' Coiflet-like [2] % 'Spline Nr.Nd' (or 'bior Nr.Nd') for Splines % Nr = 0, Nd = 0,1,2,3,4,5,6,7, or 8 % Nr = 1, Nd = 0,1,3,5, or 7 % Nr = 2, Nd = 0,1,2,4,6, or 8 % Nr = 3, Nd = 0,1,3,5, or 7 % Nr = 4, Nd = 0,1,2,4,6, or 8 % Nr = 5, Nd = 0,1,3, or 5 % 'RSpline Nr.Nd' for the same Nr.Nd pairs Reverse splines % 'S+P (2,2)','S+P (4,2)','S+P (6,2)', S+P wavelets [3] % 'S+P (4,4)','S+P (2+2,2)' % 'TT' "Two-Ten" [5] % 'LC 5/3','LC 2/6','LC 9/7-M','LC 2/10', Low Complexity [1] % 'LC 5/11-C','LC 5/11-A','LC 6/14', % 'LC 13/7-T','LC 13/7-C' % 'Le Gall 5/3','CDF 9/7' JPEG2000 [7] % 'V9/3' Visual [8] % 'Lazy' Lazy wavelet % Case and spaces are ignored in wavelet names, for example, 'Sym4' % may also be written as 'sym 4'. Some wavelets have multiple names, % 'D1', 'Sym1', and 'Spline 1.1' are aliases of the Haar wavelet. % % WAVELET(W) displays information about wavelet W and plots the % primal and dual scaling and wavelet functions. % % For 2D transforms, prefix W with '2D'. For example, '2D S+P (2,2)' % specifies a 2D (tensor) transform with the S+P (2,2) wavelet. % 2D transforms require that X is either MxN or MxNxP where M and N % are divisible by 2^L. % % WAVELET(W,L,X,EXT) specifies boundary handling EXT. Choices are % 各种支持的延拓类型： % 'sym' Symmetric extension (same as 'wsws') 同wsws % 'asym' Antisymmetric extension, whole-point antisymmetry 反对称延拓 % 'zpd' 补零延拓 % 'per' 周期延拓 % 'sp0' 边界固定值重复 % % 'wsws' 两边的对称点都在边界 % 'hshs' 两边的对称点都在边界点 % 'wshs' 左边对称点：边界，右边对称点：边界点 % 'hsws' 左边对称点：边界点，右边对称点：边界 % 'spws' 左边边界重复，右边对称点：边界；即：111 1234 4321， % 'wssp' 左边对称点：边界，右边边界重复；即：4321 1234 4444， % 'wsymA' 对称点在边界，即……32 1234 34…… % 'wsymB' 对称点在边界点，即……21 1234 45…… % 'wsymC' 对称点在边界，负值，即……-3 -2 1234 -3 -2 % % % Antisymmetric boundary handling is used by default, EXT = 'asym'. % % WAVELET(...,DIM) operates along dimension DIM. % % [H1,G1,H2,G2] = WAVELET(W,'filters') returns the filters % associated with wavelet transform W. Each filter is represented % by a cell array where the first cell contains an array of % coefficients and the second cell contains a scalar of the leading % Z-power. % % [X,PHI1] = WAVELET(W,'phi1') returns an approximation of the % scaling function associated with wavelet transform W. % [X,PHI1] = WAVELET(W,'phi1',N) approximates the scaling function % with resolution 2^-N. Similarly, % [X,PSI1] = WAVELET(W,'psi1',...), % [X,PHI2] = WAVELET(W,'phi2',...), % and [X,PSI2] = WAVELET(W,'psi2',...) return approximations of the % wavelet function, dual scaling function, and dual wavelet function. % % Wavelet transforms are implemented using the lifting scheme [4]. % For general background on wavelets, see for example [6]. % % % Examples: % % Display information about the S+P (4,4) wavelet % wavelet('S+P (4,4)'); % % % Plot a wavelet decomposition % t = linspace(0,1,256); % X = exp(-t) + sqrt(t - 0.3).*(t > 0.3) - 0.2*(t > 0.6); % wavelet('RSpline 3.1',3,X); % Plot the decomposition of X % % % Sym4 with periodic boundaries % Y = wavelet('Sym4',5,X,'per'); % Forward transform with 5 stages % R = wavelet('Sym4',-5,Y,'per'); % Invert 5 stages % % ################ % 2D transform on an image % t = linspace(-1,1,128); [x,y] = meshgrid(t,t); % X = ((x+1).*(x-1) - (y+1).*(y-1)) + real(sqrt(0.4 - x.^2 - y.^2)); % Y = wavelet('2D CDF 9/7',2,X); % 2D wavelet transform % R = wavelet('2D CDF 9/7',-2,Y); % Recover X from Y % imagesc(abs(Y).^0.2); colormap(gray); axis image; % % % Plot the Daubechies 2 scaling function % [x,phi] = wavelet('D2','phi'); % plot(x,phi); % % References: % [1] M. Adams and F. Kossentini. "Reversible Integer-to-Integer % Wavelet Transforms for Image Compression." IEEE Trans. on % Image Proc., vol. 9, no. 6, Jun. 2000. % % [2] M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies. "Image % Coding using Wavelet Transforms." IEEE Trans. Image Processing, % vol. 1, pp. 205-220, 1992. % % [3] R. Calderbank, I. Daubechies, W. Sweldens, and Boon-Lock Yeo. % "Lossless Image Compression using Integer to Integer Wavelet % Transforms." ICIP IEEE Press, vol. 1, pp. 596-599. 1997. % % [4] I. Daubechies and W. Sweldens. "Factoring Wavelet Transforms % into Lifting Steps." 1996. % % [5] D. Le Gall and A. Tabatabai. "Subband Coding of Digital Images % Using Symmetric Short Kernel Filters and Arithmetic Coding % Techniques." ICASSP'88, pp.761-765, 1988. % % [6] S. Mallat. "A Wavelet Tour of Signal Processing." Academic % Press, 1999. % % [7] M. Unser and T. Blu. "Mathematical Properties of the JPEG2000 % Wavelet Filters." IEEE Trans. on Image Proc., vol. 12, no. 9, % Sep. 2003. % % [8] Qinghai Wang and Yulong Mo. "Choice of Wavelet Base in % JPEG2000." Computer Engineering, vol. 30, no. 23, Dec. 2004. if nargin < 1, error('Not enough input arguments.'); end if ~ischar(WaveletName), error('Invalid wavelet name.'); end % Get a lifting scheme sequence for the specified wavelet Flag1D = isempty(findstr(lower(WaveletName),'2d')); [Seq,ScaleS,ScaleD,Family] = getwavelet(WaveletName); if isempty(Seq) error(['Unknown wavelet, ''',WaveletName,'''.']); end if nargin < 2, Level = ''; end if ischar(Level) [h1,g1] = seq2hg(Seq,ScaleS,ScaleD,0); [h2,g2] = seq2hg(Seq,ScaleS,ScaleD,1); if strcmpi(Level,'filters') varargout = {h1,g1,h2,g2}; else if nargin < 3, X = 6; end switch lower(Level) case {'phi1','phi'} [x1,phi] = cascade(h1,g1,pow2(-X)); varargout = {x1,phi}; case {'psi1','psi'} [x1,phi,x2,psi] = cascade(h1,g1,pow2(-X)); varargout = {x2,psi}; case 'phi2' [x1,phi] = cascade(h2,g2,pow2(-X)); varargout = {x1,phi}; case 'psi2' [x1,phi,x2,psi] = cascade(h2,g2,pow2(-X)); varargout = {x2,psi}; case '' fprintf('\n%s wavelet ''%s'' ',Family,WaveletName); if all(abs([norm(h1{1}),norm(h2{1})] - 1) < 1e-11) fprintf('(orthogonal)\n'); else fprintf('(biorthogonal)\n'); end fprintf('Vanishing moments: %d analysis, %d reconstruction\n',... numvanish(g1{1}),numvanish(g2{1})); fprintf('Filter lengths: %d/%d-tap\n',... length(h1{1}),length(g1{1})); fprintf('Implementation lifting steps: %d\n\n',... size(Seq,1)-all([Seq{1,:}] == 0)); fprintf('h1(z) = %s\n',filterstr(h1,ScaleS)); fprintf('g1(z) = %s\n',filterstr(g1,ScaleD)); fprintf('h2(z) = %s\n',filterstr(h2,1/ScaleS