annotate DL/Majorization Minimization DL/mm1.m @ 243:1fbd28dfb99e unlocbox

setup file

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