changeset 167:8324c7ea6602 danieleb

Added symmetric de-correlation function, modified target de-correlation in test function.

--- a/DL/two-step DL/SMALL_two_step_DL.m	Mon Sep 19 14:53:23 2011 +0100
+++ b/DL/two-step DL/SMALL_two_step_DL.m	Tue Sep 20 14:27:14 2011 +0100
@@ -116,7 +116,7 @@
     dico = normcols(dico);
         switch DL.param.decFcn
             case 'mailhe'
-                dico = dico_decorr(dico, mu, solver.solution);
+                dico = dico_decorr_symetric(dico, mu, solver.solution);
             case 'tropp'
                 [n m] = size(dico);
                 dico = grassmannian(n,m,[],[],[],dico,true);

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/DL/two-step DL/dico_decorr_symetric.m	Tue Sep 20 14:27:14 2011 +0100
@@ -0,0 +1,62 @@
+function dico = dico_decorr_symetric(dico, mu, amp)
+    %DICO_DECORR decorrelate a dictionary
+    %   Parameters:
+    %   dico: the dictionary
+    %   mu: the coherence threshold
+    %   amp: the amplitude coefficients, only used to decide which atom to
+    %   project
+    %
+    %   Result:
+    %   dico: a dictionary close to the input one with coherence mu.
+    
+    eps = 1e-6; % define tolerance for normalisation term alpha
+    
+    % convert mu to the to the mean direction
+    theta = acos(mu)/2;
+    ctheta = cos(theta);
+    stheta = sin(theta);
+    
+    % compute atom weights
+    %     if nargin > 2
+    %         rank = sum(amp.*amp, 2);
+    %     else
+    %         rank = randperm(length(dico));
+    %     end
+    
+    % several decorrelation iterations might be needed to reach global
+    % coherence mu. niter can be adjusted to needs.
+    niter = 1;
+    while niter < 5 && ...
+            max(max(abs(dico'*dico -eye(length(dico))))) > mu + eps
+        % find pairs of high correlation atoms
+        colors = dico_color(dico, mu);
+        
+        % iterate on all pairs
+        nbColors = max(colors);
+        for c = 1:nbColors
+            index = find(colors==c);
+            if numel(index) == 2
+                if dico(:,index(1))'*dico(:,index(2)) > 0               
+                    %build the basis vectors
+                    v1 = dico(:,index(1))+dico(:,index(2));
+                    v1 = v1/norm(v1);
+                    v2 = dico(:,index(1))-dico(:,index(2));
+                    v2 = v2/norm(v2);
+                    
+                    dico(:,index(1)) = ctheta*v1+stheta*v2;
+                    dico(:,index(2)) = ctheta*v1-stheta*v2;
+                else
+                    v1 = dico(:,index(1))-dico(:,index(2));
+                    v1 = v1/norm(v1);
+                    v2 = dico(:,index(1))+dico(:,index(2));
+                    v2 = v2/norm(v2);
+                    
+                    dico(:,index(1)) = ctheta*v1+stheta*v2;
+                    dico(:,index(2)) = -ctheta*v1+stheta*v2;
+                end
+            end
+        end
+        niter = niter+1;
+    end
+end
+

--- a/examples/SMALL_test_coherence.m	Mon Sep 19 14:53:23 2011 +0100
+++ b/examples/SMALL_test_coherence.m	Tue Sep 20 14:27:14 2011 +0100
@@ -18,7 +18,8 @@
 % Dependent parameters
 nActiveAtoms = fix(blockSize/100*percActiveAtoms); %number of active atoms
 epsilon      = 1/sigma; %error constraint for sparse representation step (corresponds to noise applied to signals)
-minCoherence = sqrt((dictSize-blockSize)/(blockSize*(dictSize-1))); %target coherence (based on coherence lower bound)
+%minCoherence = sqrt((dictSize-blockSize)/(blockSize*(dictSize-1))); %target coherence (based on coherence lower bound)
+minCoherence = 0.4;		%target coherence
 
 % Initial dictionaries
 dctDict = dictionary('dct',blockSize,dictSize);
@@ -167,28 +168,28 @@
 minMu = sqrt((dictSize-blockSize)/(blockSize*(dictSize-1)));
 maxSNR = max(sigNoiseRatio);
 
-figure, subplot(2,2,1)
+figure, subplot(1,2,1)
 snrMat = buffer(sigNoiseRatio(1:9),3);
 bar(snrMat');
-title('SNR - KSVD Update')
+title('Signal to noise ratio')
 xlabel('Initial dictionary')
 ylabel('SNR (dB)')
-set(gca,'XTickLabel',{'data','dct','gabor'},'YLim',[0 maxSNR+1]);
+set(gca,'XTickLabel',{'data','dct','gabor'});
 legend('none','Mailhe','Tropp')
 grid on
 
-subplot(2,2,2), grid on
-snrMat = buffer(sigNoiseRatio(10:18),3);
-bar(snrMat');
-title('SNR - Mailhe Update')
-xlabel('Initial dictionary')
-ylabel('SNR (dB)')
-set(gca,'XTickLabel',{'data','dct','gabor'},'YLim',[0 maxSNR+1]);
-legend('none','Mailhe','Tropp')
-grid on
+% subplot(2,2,2), grid on
+% snrMat = buffer(sigNoiseRatio(10:18),3);
+% bar(snrMat');
+% title('SNR - Mailhe Update')
+% xlabel('Initial dictionary')
+% ylabel('SNR (dB)')
+% set(gca,'XTickLabel',{'data','dct','gabor'},'YLim',[0 maxSNR+1]);
+% legend('none','Mailhe','Tropp')
+% grid on
 
-subplot(2,2,3), hold on, grid on
-title('Coherence - KSVD Update')
+subplot(1,2,2), hold on, grid on
+title('Coherence')
 muMat = buffer(mu(1:9),3);
 line([0.5 3.5],[1 1],'Color','r');
 bar(muMat');
@@ -198,13 +199,13 @@
 ylabel('\mu')
 xlabel('Initial dictionary')
 
-subplot(2,2,4), hold on, grid on
-title('Coherence - Mailhe Update')
-muMat = buffer(mu(10:18),3);
-line([0.5 3.5],[1 1],'Color','r');
-bar(muMat');
-line([0.5 3.5],[minMu minMu],'Color','k');
-set(gca,'XTick',1:3,'XTickLabel',{'data','dct','gabor'},'YLim',[0 1.05])
-legend('\mu_{max}','none','Mailhe','Tropp','\mu_{min}')
-ylabel('\mu')
-xlabel('Initial dictionary')
+% subplot(2,2,4), hold on, grid on
+% title('Coherence - Mailhe Update')
+% muMat = buffer(mu(10:18),3);
+% line([0.5 3.5],[1 1],'Color','r');
+% bar(muMat');
+% line([0.5 3.5],[minMu minMu],'Color','k');
+% set(gca,'XTick',1:3,'XTickLabel',{'data','dct','gabor'},'YLim',[0 1.05])
+% legend('\mu_{max}','none','Mailhe','Tropp','\mu_{min}')
+% ylabel('\mu')
+% xlabel('Initial dictionary')