comparison DL/Majorization Minimization DL/mm1.m @ 155:b14209313ba4 ivand_dev

Integration of Majorization Minimisation Dictionary Learning

+function [unhat,er] = mm1(Phi,x,u0,to,lambda,maxIT,eps,map)
+%% Iterative Soft Thresholding (with optional debiasing)
+%
+% Phi = Normalized Dictionary
+% x = Signal(x). This can be a vector or a matrix
+% u0 = Initial guess for the coefficients
+% to = 1/(step size) . It is larger than spectral norm of dictionary Phi
+% lambda = Lagrangian multiplier. (regulates shrinkage)
+% eps = Stopping criterion for iterative softthresholding and MM dictionary update
+% map = Debiasing. 0 = No, 1 = Yes
+% unhat = Updated coefficients
+% er = Objective cost
+%%
+cont = 1;
+in = 1;
+% un = zeros(size(u0,1),size(u0,2));    
+un = u0;
+c1 = (1/to^2)*Phi'*x;
+c2 = (1/to^2)*(Phi'*Phi);
+%%%%
+while (cont && (in<=maxIT))
+    unold = un;
+    %%%%%% Soft Thresholding %%%%%%%
+    alphap = (un + c1 - c2*un);
+    un = (alphap-(lambda/(2*to^2))*sign(alphap)).*(abs(alphap)>=(lambda/(2*to^2)));
+    in = in+1;
+    cont = sum(sum((unold-un).^2))>eps;
+end
+%%%%%%%%%%
+if map == 1,
+    %% Mapping on the selected space %%%%
+    [uN,uM] = size(un);
+    unhat = zeros(uN,uM);
+    for l = 1:uM,
+        unz = (abs(un(:,l))>0);
+        M = diag(unz);
+        PhiNew = Phi*M;
+        PhiS = PhiNew(:,unz);
+        unt = inv(PhiS'*PhiS+.0001*eye(sum(unz)))*PhiS'*x(:,l);
+        unhat(unz,l) = unt;
+    end    
+else
+    unhat = un;
+end
+%%% Cost function calculation
+if map == 1,
+    er = sum(sum((Phi*unhat-x).^2))+lambda*(sum(sum(abs(unhat)>0))); %% l_0 Cost function     
+else   
+    er = sum(sum((Phi*unhat-x).^2))+lambda*(sum(sum(abs(unhat))));
+end