user_alg5.m

The ICA/BSS algorithms are pure mathematical formulas, powerful, but rather mechanical procedures: T

function [H,S,D]=acsobiro(X,n,p),
% Program implemented and improved by A. Cichocki
% on basis of the classical SOBI algorithm of Belouchrani.
% Attention for noisy data you should take at least 
% 100 the time-delayed covariance matrices.
% Robust Second Order Blind Identification SOBI-RO
% (c) 
% This function was created on the basis of publications 
% of Belouchrani et al., F. Cardoso et al.,
% A. Belouchrani - A. Cichocki, S. Choi - A. Cichocki, 
% S. Cruces, A. Cichocki- S. Amari and P. Georgiev-A. Cichocki.
%
%**************************************************
% Blind identification by joint diagonalization   *
% of the time-delayed covariance matrices.        *
%                       			              *
% ------------------------------------------------*
% THIS CODE ASSUMES TEMPORALLY CORRELATED SIGNALS *
%                                                 * 
%**************************************************
%
% [H,S]=acsobiro(X,n,p) produces a mixing matrix H of dimension [n by m] 
% and a source signals matrix S of dimension [n by  N] or [m by N]. 
% Note: 
% > X: Data matrix X of dimension m by N representing sensor (observed) signals,
% > m: sensor number,
% > n: source number by default m=n,
% > N: sample number,
% > p: number of the time delay covriance matrices to be diagonalized by default p=100.
%
% REFERENCES:
%  A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines, ``Second-order
%  blind separation of temporally correlated sources,'' in Proc. Int. Conf. on
%  Digital Sig. Proc., (Cyprus), pp. 346--351, 1993.
%
%  A. Belouchrani, and A. Cichocki, 
%  Robust whitening procedure in blind source separation context, 
%  Electronics Letters, Vol. 36, No. 24, 2000, pp. 2050-2053.
%  
%  A. Cichocki and S. Amari, 
%  Adaptive Blind Signal and Image Processing, Wiley,  2002.
%
 [m,N]=size(X);
if nargin==1,
   n=m; 
   p=100; % The number of the time delayed covariance matrices to be diagonalized 
end;
if nargin==2,
   p=100 ; 
end; 
X=X-(mean(X')'*ones(1,N)); %Removing  mean value
Rxx=(X(:,1:N-1)*X(:,2:N)')/(N-1); %Estimation of sample covariance matrix 
%for the time delay p=1 in order to reduce influence of a white noise.
%
 [Ux,Dx,Vx]=svd(Rxx);
 Dx=diag(Dx);
% n=11;
 if n<m, % under assumption of additive white noise and
        %when the number of sources are known or can a priori estimated
  Dx=Dx-real((mean(Dx(n+1:m))));
  Q= diag(real(sqrt(1./Dx(1:n))))*Ux(:,1:n)';
else    % under assumption of no additive noise and when the 
        % number of sources is unknown
   n=max(find(Dx>1e-14)); %Detection the number of sources
   Q= diag(real(sqrt(1./Dx(1:n))))*Ux(:,1:n)';
end;
Xb=Q*X; % prewhitened data
% Estimation of the time delayed covariance matrices:
k=1;
pn=p*n; 
for u=1:n:pn, k=k+1; Rxp=Xb(:,k:N)*Xb(:,1:N-k+1)'/(N-k+1);
    M(:,u:u+n-1)=norm(Rxp,'fro')*Rxp; 
end;
% Approximate joint diagonalization:
eps=1/sqrt(N)/100; encore=1; U=eye(n);
while encore, encore=0;
 for p=1:n-1,
  for q=p+1:n,
    % Givens rotations:
    g=[ M(p,p:n:pn)-M(q,q:n:pn)  ;
        M(p,q:n:pn)+M(q,p:n:pn)  ;
        i*(M(q,p:n:pn)-M(p,q:n:pn))];
   [Ucp,D] = eig(real(g*g')); [la,K]=sort(diag(D));
   angles=Ucp(:,K(3));angles=sign(angles(1))*angles;
   c=sqrt(0.5+angles(1)/2);
   sr=0.5*(angles(2)-j*angles(3))/c; sc=conj(sr);
   asr = abs(sr)>eps ;
   encore=encore | asr ;
   if asr , %U pdate of the M and U matrices: 
     colp=M(:,p:n:pn);colq=M(:,q:n:pn);
     M(:,p:n:pn)=c*colp+sr*colq;M(:,q:n:pn)=c*colq-sc*colp;
     rowp=M(p,:);rowq=M(q,:);
     M(p,:)=c*rowp+sc*rowq;M(q,:)=c*rowq-sr*rowp;
     temp=U(:,p);
     U(:,p)=c*U(:,p)+sr*U(:,q);U(:,q)=c*U(:,q)-sc*temp;
   end  %% if
  end  %% q loop
 end  %% p loop
end  %% while
% Estimation of the mixing matrix H and the sources S:
H= pinv(Q)*U(1:n,1:n); S=[];
%
%W=U(1:n,1:n)'*Q; S= W*X;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [m,N]=size(X);
% if nargin==1,
%  n=m; % source detection 
% %
%  p=100; % number of correlation matrices to be diagonalized 
%  end;
% if nargin==2,
%  p=100 ; % number of correlation matrices to be diagonalized
% end; 
% pm=p*m; % for convenience
% 
% X=X-(mean(X')'*ones(1,N)); %removing  mean value
%  Rx=(X(:,1:N-1)*X(:,2:N)')/(N-1);
%   %Rx=X*X'/N;
%   %[U,D,V]=svd(Rx+eye(m));
%   %D=diag(D)-1; 
%   %n=max(find(D>1e-99));
%   %sigma=(1e-99)*min(D);
%   %BL=(U(:,1:n)*diag(real(sqrt(1./(D(1:n)+sigma./D(1:n))))))'; 
%   %IBL=pinv(BL);
% %%%% whitening
% % Rx=(X*X')/N;
% if m<n, %assumes white noise
%   [U,D]=eig(Rx); [puiss,k]=sort(diag(D));
%   ibl= sqrt(puiss(n-m+1:n)-mean(puiss(1:n-m)));
%  bl = ones(m,1) ./ ibl ;
%   Q=diag(bl)*U(1:n,k(n-m+1:n))';
%   IQ=U(1:n,k(n-m+1:n))*diag(ibl);
% else    %assumes no noise
%    IQ=sqrtm(Rx);
%    Q=inv(IQ);
% end;
% X=Q*X;
% 
% %%%correlation matrices estimation
% k=1;
% for u=1:m:pm, k=k+1; Rxp=X(:,k:N)*X(:,1:N-k+1)'/(N-k+1);
%     M(:,u:u+m-1)=norm(Rxp,'fro')*Rxp; 
% end;
% %%%joint diagonalization
% seuil=1/sqrt(N)/100; encore=1; V=eye(m);
% while encore, encore=0;
%  for p=1:m-1,
%   for q=p+1:m,
%    %%% Givens rotations
%    g=[   M(p,p:m:pm)-M(q,q:m:pm)  ;
%          M(p,q:m:pm)+M(q,p:m:pm)  ;
%       i*(M(q,p:m:pm)-M(p,q:m:pm)) ];
% 	  [vcp,D] = eig(real(g*g')); [la,K]=sort(diag(D));
%    angles=vcp(:,K(3));angles=sign(angles(1))*angles;
%    c=sqrt(0.5+angles(1)/2);
%    sr=0.5*(angles(2)-j*angles(3))/c; sc=conj(sr);
%    oui = abs(sr)>seuil ;
%    encore=encore | oui ;
%    if oui , %%%updMte of the M and V matrices 
%     colp=M(:,p:m:pm);colq=M(:,q:m:pm);
%     M(:,p:m:pm)=c*colp+sr*colq;M(:,q:m:pm)=c*colq-sc*colp;
%     rowp=M(p,:);rowq=M(q,:);
%     M(p,:)=c*rowp+sc*rowq;M(q,:)=c*rowq-sr*rowp;
%     temp=V(:,p);
%     V(:,p)=c*V(:,p)+sr*V(:,q);V(:,q)=c*V(:,q)-sc*temp;
%    end%% if
%   end%% q loop
%  end%% p loop
% end%% while
% %%%estimation of the mixing matrix H and separating matrix W
% H=IQ*V; %H= pinv(Q)*V; W=V'*Q
% %W=V'*Q; % estimating separating matrix
% 
% S=[];