匹配追踪算法matching pursuit

function [S,R,e,indx] = matchPurs(x,W)
% This function computes the projection of a given input vector or matrix
% onto a "dictionary" of other vectors or matrices using a matching pursuit
% algorithm.
%
% USAGES
% [S,R,e,indx] = matchPurs(x,W)  
% 
% INPUT
% x: An Mx1 or MxN array. This array synthesized using dictionary 
%       elements from matrix W.
% W: An MxN or MxNxP array of dictionary elements used to synthesize
%       input x. If x is an Mx1 vector, W must be an MxN matrix. If x is
%       an MxN array, W must be an MxNxP matrix containing the dictionary
%       elements.
%
% OUTPUT
% S:    The projection of each residual onto each dictionary element.
% R:    The residual x - sum(W,dim), where dim is 2 if x is a vector and
%       is 3 if x is a matrix.
% e:    The projection coefficients.
% indx  The index vector for the dictionary elements used in projections
%
% -------------------------------------------------------------------------
% TEST
% To ensure that the signal energy is preserved, the following relations
% should hold:
%
% Matrix Case:
%