ivan@155: function [Phiout,unhatnz] = dict_update_REG_fn(Phi,x,unhat,maxIT,eps,cvset)
ivan@155: %% Regularized Dictionary Learning with the constraint on the matrix frobenius norms %%%%%
ivan@155: % Phi = Normalized Initial Dictionary
ivan@155: % x = Signal(x). This can be a vector or a matrix
ivan@155: % unhat = Initial guess for the coefficients
ivan@155: % to = 1/(step size) . It is larger than spectral norm of coefficient matrix x
ivan@155: % eps = Stopping criterion for iterative softthresholding and MM dictionary update
ivan@155: % cvset = Dictionary constraint. 0 = Non convex ||D|| = N, 1 = Convex ||D||<=N
ivan@155: % Phiout = Updated Dictionary
ivan@155: % unhatnz Updated Coefficients (the same as input in this version)
ivan@155: 
ivan@155: %%
ivan@155: B = Phi;
ivan@155: phim = norm(Phi, 'fro');
ivan@155: K = zeros(size(Phi,1),size(Phi,2));
ivan@155: c = .1 + svds(unhat,1)^2; 
ivan@155: 
ivan@155: %%
ivan@155: i = 1;       
ivan@155: while (sum(sum((B-K).^2)) > eps)&&(i<=maxIT)
ivan@155:     if i>1
ivan@155:         B = K;
ivan@155:     end
ivan@155:     K = 1/c *(x*unhat' + B*(c*eye(size(B,2))-unhat*unhat'));
ivan@155:     Kfn = sum(sum(K.^2));
ivan@155:     if cvset == 1,
ivan@155:         K = min(1,phim/Kfn)*K; % with convex constraint set
ivan@155:     else
ivan@155:         K = (phim/Kfn)*K; % with fixed-norm constraint set
ivan@155:     end
ivan@155:     i = i+1;
ivan@155: end
ivan@155: 
ivan@155: %% depleted atoms cancellation %%%
ivan@155: [Y,I] = sort(sum(K.^2),'descend');
ivan@155: RR = sum(Y>=0.0001);
ivan@155: Phiout = K(:,I(1:RR));
ivan@155: unhatnz = unhat(I(1:RR),:);
ivan@155: end