comparison DL/two-step DL/dico_decorr_symetric.m @ 195:d50f5bdbe14c luisf_dev

- Added SMALL_DL_test: simple DL showcase
- Added dico_decorr_symmetric: improved version of INK-SVD decorrelation step
- Debugged SMALL_learn, SMALLBoxInit and SMALL_two_step_DL

+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 max(max(abs(dico'*dico -eye(length(dico))))) > mu + 0.01
+        % 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
+