Mercurial > hg > smallbox
view util/classes/dictionaryMatrices/iterativeprojections.m @ 171:e8428989412f danieleb
Added dictionary decorrelation functions and test script for Letters paper.
author | Daniele Barchiesi <daniele.barchiesi@eecs.qmul.ac.uk> |
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date | Thu, 06 Oct 2011 14:33:52 +0100 |
parents | 68fb71aa5339 |
children | 8fc38e8df8c6 |
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function [dic mus srs] = iterativeprojections(dic,mu,Y,X,params) % grassmanian attempts to create an n by m matrix with minimal mutual % coherence using an iterative projection method. % % REFERENCE % %% Parameters and Defaults if ~nargin, testiterativeprojections; return; end if ~exist('params','var') || isempty(param), params = struct; end if ~isfield(params,'nIter'), params.nIter = 10; end %number of iterations if ~isfield(params,'eps'), params.eps = 1e-9; end %tolerance level [n m] = size(dic); SNR = @(dic) snr(Y,dic*X); %SNR function MU = @(dic) max(max(abs((dic'*dic)-diag(diag(dic'*dic))))); %coherence function %% Main algorithm dic = normc(dic); %normalise columns alpha = m/n; %ratio between number of atoms and ambient dimension mus = zeros(params.nIter,1); %coherence at each iteration srs = zeros(params.nIter,1); %signal to noise ratio at each iteration iIter = 1; while iIter<=params.nIter && MU(dic)>mu fprintf(1,'Iteration number %u\n', iIter); % calculate snr and coherence mus(iIter) = MU(dic); srs(iIter) = SNR(dic); % calculate gram matrix G = dic'*dic; % project into the structural constraint set H = zeros(size(G)); %initialise matrix ind1 = find(abs(G(:))<=mu); %find elements smaller than mu ind2 = find(abs(G(:))>mu); %find elements bigger than mu H(ind1) = G(ind1); %copy elements belonging to ind1 H(ind2) = mu*sign(G(ind2)); %threshold elements belonging to ind2 H(1:m+1:end) = 1; %set diagonal to one % project into spectral constraint set [~ , S, V] = svd(H); %G = alpha*(V(:,1:n)*V(:,1:n)'); G = V(:,1:n)*S(1:n,1:n)*V(:,1:n)'; % calculate dictionary [~, S V] = svd(G); dic = sqrt(S(1:n,:))*V'; % rotate dictionary options = struct('nIter',100,'step',0.001); [~, ~, W] = rotatematrix(Y,dic*X,'conjgradlie',options); dic = W*dic; iIter = iIter+1; end if iIter<params.nIter mus(iIter:end) = mus(iIter); srs(iIter:end) = srs(iIter); end % Test function function testiterativeprojections clc %define parameters n = 256; %ambient dimension m = 512; %number of atoms N = 1024; %number of signals mu_min = sqrt((m-n)/(n*(m-1))); %minimum coherence %initialise data X = sprandn(m,N,1); %matrix of coefficients phi = normc(randn(n,m)); %dictionary temp = randn(n); W = expm(0.5*(temp-temp')); %rotation matrix Y = W*phi*X; %observed signals %optimise dictionary [~, mus srs] = iterativeprojections(phi,0.2,Y,X); %plot results nIter = length(mus); figure, subplot(2,1,1) plot(1:nIter,srs,'kd-'); xlabel('nIter'); ylabel('snr (dB)'); grid on subplot(2,1,2), hold on plot(1:nIter,mus,'ko-'); plot([1 nIter],[mu_min mu_min],'k') grid on legend('\mu','\mu_{min}');