mhaar.m

matlab程序

function X = mhaar(X, Level, Dim)
%MHAAR  Morphological Haar wavelet transform.
%   Y = MHAAR(X,L) computes the L level decomposition of a signal X
%   using the morphological Haar wavelet [1].  If the input is
%   integer-valued, the transform coefficients are also integer-
%   valued.  The signal length must be divisible by 2^L.  If X is a
%   matrix, the transform is applied to each column.
%
%   MHAAR(X,-L) is the inverse transform, reversing L levels.
%
%   MHAAR(X,L,DIM) applies the transform across the dimension DIM.
%
%   Example:
%   Y = mhaar(X,3);   % Perform 3 levels of decomposition on X
%   R = mhaar(Y,-3);  % Recover X from Y
%
%   Reference:
%   [1] Heijmans and Goutsias.  ``Nonlinear Multiresolution Signal
%       Decomposition Schemes--Part II: Morphological Wavelets.''  IEEE
%       Transactions on Image Processing, Vol. 9, No. 11, Nov. 2000.
%
%   See also SEQHAAR.

% Pascal Getreuer 2005

if nargin < 2, error('Not enough input arguments.'); end
if nargin < 3, Dim = min(find(size(X) ~= 1)); end

XSize = size(X);
N = XSize(Dim);
Perm = [Dim:max(length(XSize),Dim) 1:Dim-1];
X = reshape(permute(X,Perm),N,prod(XSize)/N);

if rem(N,pow2(abs(Level))), error('Invalid input size.'); end

if Level > 0
   for k = 1:Level
      N = size(X,1)*pow2(1-k);
      X(1:N,:) = [min(X(1:2:N,:),X(2:2:N,:));X(1:2:N,:) - X(2:2:N,:)];
   end
elseif Level < 0
   for k = Level:-1
      N = size(X,1)*pow2(k+1);
      X([1:2:N,2:2:N],:) = [X(1:N/2,:) + max(X(N/2+1:N,:),0);
         X(1:N/2,:) - min(X(N/2+1:N,:),0)];
   end
end

X = ipermute(reshape(X,XSize(Perm)),Perm);