ivan@152: function dico = dico_decorr(dico, mu, amp)
ivan@152:     %DICO_DECORR decorrelate a dictionary
ivan@152:     %   Parameters:
ivan@152:     %   dico: the dictionary
ivan@152:     %   mu: the coherence threshold
ivan@152:     %   amp: the amplitude coefficients, only used to decide which atom to
ivan@152:     %   project
ivan@152:     %
ivan@152:     %   Result:
ivan@152:     %   dico: a dictionary close to the input one with coherence mu.
ivan@152:     
ivan@152:     % compute atom weights
ivan@152:     if nargin > 2
ivan@152:         rank = sum(amp.*amp, 2);
ivan@152:     else
ivan@152:         rank = randperm(length(dico));
ivan@152:     end
ivan@152:     
ivan@152:     % several decorrelation iterations might be needed to reach global
ivan@152:     % coherence mu. niter can be adjusted to needs.
ivan@152:     niter = 1;
ivan@152:     while niter < 5 && ...
ivan@152:             max(max(abs(dico'*dico -eye(length(dico))))) > mu + 10^-6
ivan@152:         % find pairs of high correlation atoms
ivan@152:         colors = dico_color(dico, mu);
ivan@152:         
ivan@152:         % iterate on all pairs
ivan@152:         nbColors = max(colors);
ivan@152:         for c = 1:nbColors
ivan@152:             index = find(colors==c);
ivan@152:             if numel(index) == 2
ivan@152:                 % decide which atom to change (the one with lowest weight)
ivan@152:                 if rank(index(1)) < rank(index(2))
ivan@152:                     index = fliplr(index);
ivan@152:                 end
ivan@152:                 
ivan@152:                 % update the atom
ivan@152:                 corr = dico(:,index(1))'*dico(:,index(2));
ivan@152:                 alpha = sqrt((1-mu*mu)/(1-corr*corr));
ivan@152:                 beta = corr*alpha-mu*sign(corr);
ivan@152:                 dico(:,index(2)) = alpha*dico(:,index(2))...
ivan@152:                     -beta*dico(:,index(1));
ivan@152:             end
ivan@152:         end
ivan@152:         niter = niter+1;
ivan@152:     end
ivan@152: end
ivan@152: