comparison util/classes/dictionaryMatrices/iterativeprojections.m @ 169:290cca7d3469 danieleb

Added dictionary decorrelation functions and test script for ICASSP paper.

+function [A G res muMin] = grassmannian(n,m,nIter,dd1,dd2,initA,verb)
+% grassmanian attempts to create an n by m matrix with minimal mutual
+% coherence using an iterative projection method.
+%
+% [A G res] = grassmanian(n,m,nIter,dd1,dd2,initA)
+%
+% REFERENCE
+% M. Elad, Sparse and Redundant Representations, Springer 2010.
+
+%% Parameters and Defaults
+error(nargchk(2,7,nargin));
+
+if ~exist('verb','var')  || isempty(verb),  verb = false; end %verbose output
+if ~exist('initA','var') || isempty(initA), initA = randn(n,m); end %initial matrix
+if ~exist('dd2','var')   || isempty(dd2),   dd2 = 0.99; end %shrinking factor
+if ~exist('dd1','var')   || isempty(dd1),   dd1 = 0.9; end %percentage of coherences to be shrinked
+if ~exist('nIter','var') || isempty(nIter), nIter = 10; end %number of iterations
+
+%% Main algo
+A = normc(initA); %normalise columns
+[Uinit Sigma] = svd(A);
+G = A'*A; %gram matrix
+
+muMin = sqrt((m-n)/(n*(m-1)));              %Lower bound on mutual coherence (equiangular tight frame)
+res = zeros(nIter,1);
+if verb
+	fprintf(1,'Iter		mu_min		mu \n');
+end
+
+% optimise gram matrix
+for iIter = 1:nIter
+	gg  = sort(abs(G(:))); %sort inner products from less to most correlated
+	pos = find(abs(G(:))>=gg(round(dd1*(m^2-m))) & abs(G(:)-1)>1e-6); %find large elements of gram matrix
+	G(pos) = G(pos)*dd2;	%shrink large elements of gram matrix
+	[U S V] = svd(G);	%compute new SVD of gram matrix
+	S(n+1:end,1+n:end) = 0; %set small eigenvalues to zero (this ensures rank(G)<=d)
+	G = U*S*V';			%update gram matrix
+	G = diag(1./abs(sqrt(diag(G))))*G*diag(1./abs(sqrt(diag(G)))); %normalise gram matrix diagonal
+	if verb
+		Geye = G - eye(size(G));
+		fprintf(1,'%6i    %12.8f  %12.8f  \n',iIter,muMin,max(abs(Geye(:))));
+	end
+end
+
+% [~, Sigma_gram V_gram] = svd(G); %calculate svd decomposition of gramian
+
+% A = normc(A);					%normalise dictionary
+
+[V_gram Sigma_gram] = svd(G);				%calculate svd decomposition of gramian
+Sigma_new = sqrt(Sigma_gram(1:n,:)).*sign(Sigma); %calculate singular values of dictionary
+A = Uinit*Sigma_new*V_gram';				%update dictionary
+
+% param.step  = 0.01;
+% param.reg   = 0.01;
+% param.nIter = 20;
+% A = rotatematrix(initA,A,'linesearchlie',param);
+
+% %% Debug visualization function
+% function plotcart2d(A)
+% compass(A(1,:),A(2,:));