perform_lifting_transform_slow.m

小波提升算法的实现

function y = perform_lifting_transform_slow(x, step_type, step_param, Jmin, dir, options)

% perform_lifting_transform_slow - perform a lifting transform without relying on Mex file
%
%   This is the Matlab non-optimized version of the function.
%   See 'perform_lifting_transform' for the Mex version.
%
%   y = perform_lifting_transform_slow(x, step_type, step_param, Jmin, dir, options);
%
%   x: the 1D signal to transform in place.
%   step_type: an integer array telling the succession of steps.
%       0 is for 'predict' step : detail channel is computed using
%           predicted value from coarse scale.
%       1 is for 'update' step : coarse channel is computed using
%           value from detail channel to enforce moment conservation.
%       2 is for 'scaling' step : coarse channel is multiplied by some
%           'zeta' factor, while coarse channel is divided by 'zeta'.
%       3 is for 'scaling' on details only.
%       4 is for 'scaling' on coarse only.
%       5 is for 'predict' without feedback
%       6 is for 'update' without feedback
%   step_param : same length as step_types, 1 parameter for each step.
%   Jmin: the coarsest scale. If Jmin=0, then it
%       will perform a full transform (i.e. last coarse value is the mean).
%   dir: +1 for forward transform (default), -1 for backward transform.
%
%   'options' is an (optional) structure that can contain:
%       - 'verb' : control verbosity.
%       - 'disc' : position of a discontinuity.
%
%   Example of use : 
%       % the parameters of a 7/9 biorthgonal Wavelet
%       alpha = -1.586134342;
%       beta = -0.05298011854;
%       gamma = 0.8829110762;
%       delta = 0.4435068522;
%       zeta = 1.149604398;
%       step_types = [0,1,0,1,2];   
%       step_param = [alpha,beta,gamma,delta,zeta];
%       x = sqrt(1:100);
%       y = perform_lifting_transform_slow(x, step_type, step_param, 3);
%
%   NB: if you don't understand lifting, don't use
%       this function directly, but rather its
%       wrappers like 'perform_lifting_transform_byname'.
%
%   NB: After spliting coarse/detail the signal, i.e. x = [s,d]^T, the types of
%   steps correspond to the matrix multiplications :
%
%   Type 0 :    |1 alpha*(1+z^-1)|
%               |0      1        |
%
%   Type 1 :    |1            0|
%               |beta*(1+z)   1|
%
%   Type 2 :    |zeta   0   |
%               |  0  1/zeta|
%
%   Type 3 :    |1   0  |
%               |0  zeta|
%
%   Type 4 :    |zeta 0|
%               |0    1|
%
%   Type 5 :    |1 alpha+alpha'z^-1)|
%               |0         1        |
%
%   Type 6 :    |1               0|
%               |beta+beta'*z)   1|
%  
%   Copyright (c) 2005 Gabriel Peyr