123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288 |
- % C-FICA algorithm - time-domain Convolutive extension of FastICA - v1.2
- %
- % J. Thomas, Y. Deville and S. Hosseini
- % "Time-domain fast fixed-point algorithms for convolutive ICA",
- % IEEE Signal Processing Letters, vol. 13, no. 4, pp. 228-231, April 2006.
- %
- %
- % [Sc,sc,Isc,y,fe,fc,te,tc]=cfica(x,non-lin,epsi,Re,[we1 we2],Rc,[wc1 wc2],itermax,initializ,verbose)
- %
- % Inputs (place the deconvolution parameters before the recoloration ones
- % themselves before iter_max)
- %
- % x : observation vector
- % non-lin : 'k'->kurtosis, 'g'->Gaussian, 't'->tanh default 'g'
- % initializ : 'i' for initialization with unit filters optional
- % epsi : stopping criterion (between 0 and 1) default 10^-12
- % Re : order of the extraction filters default 80
- % [we1 we2] : extraction time window optional
- % Rc : order of the recoloration filters default 3R1
- % [wc1 wc2] : recoloration time window optional
- % itermax : maximum number of iteration default 10000
- % verbose : 'v' for verbose optional
- %
- % Outputs
- %
- % Sc : most powerful contributions for each estimated source
- % sc : estimated source contributions (tensor N*N*nb_samples)
- % Isc : indices of the most powerful contributions
- % y : N-1 estimated innovation processes (matrix (N-1)*nb_samples)
- % fe : extraction filters
- % fc : recoloration filters
- % te : times of extraction
- % tc : times of recoloration
- % -------------------------------------------------------------------------
- % History of the software:
- % V1.1: original software written by J. Thomas
- %
- % V1.2: Error messages appeared with recent releases of Matlab in the function
- % conv_mix_nc. This version corrects them.
- % Author: Matthieu PUIGT Contact: matthieu.puigt@univ-littoral.fr
- %
- % -------------------------------------------------------------------------
- function [Sc,sc,Isc,y,fe,fc,te,tc]=cfica(x,varargin)
- % N: number of observations, n: number of samples
- [N,n]=size(x);
- % centering of the observations
- x=x-mean(x,2)*ones(1,n);
- % ordering of the input arguments
- [criterion,initializ,epsi,Re,we1,we2,Rc,wc1,wc2,iter_max,verbose]=args(varargin,n);
- % R1 non-causal filter coefficients
- % R2 strictly causal filter coefficients
- R1=floor(Re/2);Rc1=floor(Rc/2);
- clear Re Rc
- R2=R1;Rc2=Rc1;
- % unit filter
- id=[zeros(1,R1),1,zeros(1,R2)];
- % deflated observation vector
- x_def=x;
- for r=1:N-1
-
- if verbose,fprintf('convolutive sphering %d .. \n',r),end
- tic
- % creation of a multi-delayed observation vector
- for k=1:N-r+1
- for i=-R1:R2
- x_tilde((R1+R2+1)*(k-1)+i+1+R1,:)=x_def(k,we1-i:we2-i);
- end
- end
- % whitening process
- [x_prime,B]=white(x_tilde,we2-we1+1);
- clear x_tilde;
- % initialization of the extraction process
- if initializ
- id1=id(ones(1,N-r+1),:);
- id1=reshape(id1',1,(N-r+1)*(R1+R2+1));
- fe0=id1*B^-1;
- else
- fe0=ones(1,(N-r+1)*(R1+R2+1))*B^-1;
- end
- if verbose,fprintf('fixed-point extraction %d .. \n',r),end
- % extraction of a non-Gaussian innovation process
- [fe{r},iter]=extract(x_prime,fe0,criterion,epsi,iter_max);
- te(r)=toc;
- clear x_prime;
- fe{r}=fe{r}*B;
- % reshaping of the extraction vector
- fe{r}=reshape1(fe{r},[1,N-r+1,R1+R2+1],[3 2 1]);
- % application of the extraction filters
- y(r,:)=conv_mix_nc(fe{r},x_def(1:N-r+1,:),R1);
- for k=1:N
- % coloration of the r^th source for the r^th sensor
- if verbose,fprintf('recoloration process %d-%d .. \n',k,r),end
- tic
- [sc(k,r,:),fc{k,r}]=color(y(r,:),x(k,:),wc1,wc2,Rc1,Rc2);
- tc(k,r)=toc;
- end
- % removing of the last estimated contributions from the sensors
- for t=1:N
- s0(1,:)=sc(t,r,:);
- x_def(t,:)=x_def(t,:)-s0;
- end
- clear s0;
- end
- % the last contributions corresponding to the N^th source
- sc(:,N,:)=x_def;
- % identification of the most powerful contribution
- [M,Isc]=max(mean(sc.^2,3));
- % output signals
- for k=1:N
- Sc(k,:)=sc(Isc(k),k,:);
- end
- %-----------------------------------------
- function [x_prime,B]=white(x_tilde,n)
- % eigendecomposition of xxt
- [E,D]=eig(x_tilde*x_tilde');
- % computation of whitening matrix
- sqD=sqrt(n)*D^(-1/2);
- B=sqD*E';
- % whitening process
- x_prime=B*x_tilde;
- %------------------------------------------------------------
- function [w,iter]=extract(x_prime,w,criterion,epsi,iter_max)
- [N,n]=size(x_prime);
- % extraction vector normalization
- w=w./norm(w);
- test=1;iter=0;
- while test>epsi & iter<iter_max
-
- y=w*x_prime;
-
- switch criterion
- case 'k'
- % kurtosis fixed-point iteration
- w1=1/n*(y.^3)*x_prime'-3*w;
- case 'g'
- % Gaussian negentropic fixed-point iteration
- gauss_y=exp(-y.^2/2);
- w1=1/n*(y.*gauss_y)*x_prime' - 1/n*sum(((1-y.^2).*gauss_y))*w;
- case 't'
- % hyperbolic-tangent negentropic fixed-point iteration
- tanh_y=tanh(y);
- w1=1/n*tanh_y*x_prime' - 1/n*sum(1-tanh_y.^2)*w;
- end
-
- % vector normalization
- w1=w1./norm(w1);
-
- % computation of the stopping criterion
- test=min([abs(w1-w) abs(w1+w)]);
- w=w1;
-
- iter=iter+1;
- end
- %-------------------------------------------------------
- function [sc,c]=color(y,x,w1,w2,R1,R2)
- n=w2-w1+1;
- % computation of the autocorrelation matrix of y
- y2=y(w1+R1:w2+R1);
- for r=-R1:R2
- y1=y(w1-r:w2-r);
- Ry1(r+R1+1)=1/n*y1*y2';
- end
- for r1=-R1:R2
- for r2=-R1:R2
- Ry(r1+R1+1,r2+R1+1)=Ry1(abs(r2-r1)+1);
- end
- % computation of the intercorrelation vector of y and x
- y1=y(w1-r1:w2-r1);
- ryx(r1+R1+1)=1/n*y1*(x(w1:w2))';
- end
- % computation of the wiener filter
- c=Ry^(-1)*ryx';
- % non-causal filtering process
- sc=filter_nc(c,y,R1);
- %-------------------------------------------------
- function x=conv_mix_nc(A,s,R1);
- % R1 non-causal coefficients
- % R2 strictly causal coefficients
- R2=size(A,3)-R1-1;
- for i=1:size(A,1)
- x(i,:)=zeros(1,size(s,2)+R1+R2);
- for j=1:size(s,1)
- x(i,:)=x(i,:)+conv(reshape(A(i,j,:),size(A,3),1,1),s(j,:));
- end
- end
- % removing of the out samples
- x=x(:,1+R1:end-R2);
- %-------------------------------------------------
- function s=filter_nc(h,e,R1);
- R2=length(h)-R1-1;
- % convolution process
- s=conv(h,e);
- % removing of the out samples
- s=s(1+R1:end-R2);
- %---------------------------------------------------
- function w1=reshape1(w,dims,order)
- % ordering of the tensor dimensions
- dims1=dims(order);
- % reshaping of the vector w
- w1=reshape(w,dims1);
- % re-ordering of the tensor
- w1=ipermute(w1,order);
- %-----------------------------------------------------
- function [criterion,initializ,epsi,Re,we1,we2,Rc,wc1,wc2,iter_max,verbose]=args(varargin,n)
- % ordering of the input arguments
- for i=1:length(varargin)
- if length(varargin{i})==1
- switch varargin{i}
- case {'k','g','t'},criterion=varargin{i};
- case 'i',initializ=1;
- case 'v',verbose=1;
- otherwise
- if varargin{i}<1 & varargin{i}>0,epsi=varargin{i};
- else,if ~exist('Re'),Re=varargin{i};
- else,if ~exist('Rc'),Rc=varargin{i};
- else iter_max=varargin{i};end,end,end
- end
- else,if ~exist('we1'),we1=varargin{i}(1);we2=varargin{i}(2);
- else,wc1=varargin{i}(1);wc2=varargin{i}(2);end
- end
- end
- if ~exist('criterion'), criterion='g';end
- if ~exist('initializ'), initializ=0;end
- if ~exist('epsi'), epsi=1e-12;end
- if ~exist('Re'), Re=80;end
- if ~exist('we1'), we1=Re+1;we2=n-Re-1;end
- if ~exist('Rc'), Rc=2*Re;end
- if ~exist('wc1'), wc1=Rc+1;wc2=n-Rc-1;end
- if ~exist('iter_max'), iter_max=1e4;end
- if ~exist('verbose'), verbose=0; end
- if verbose,criterion,initializ,epsi,Re,extr_window=[we1,we2],Rc,col_window=[wc1,wc2],iter_max,verbose,end
|