低秩矩阵恢复代码参考.pdf

function x_out= MSB(Aop,y_vec,s_x,lambda1,rnk,iter) % function [x_out obj_func]= MSB(Aop,y_vec,[m n],lambda1,rnk) % This code solves the problem of recovering a low rank matrix from its % lower dimensional projections % Minimize ||X||* (nuclear norm of Z) % Subject to A(X) = Y %formulated as an unconstarined nuclear norm minmization problem using Split bregman algorithm % Minmimize (lambda1)||W||* + 1/2 || A(X) - y ||_2^2 + eta/2 || W-X-B1 ||_2^2 %W is auxillary variable and B1 is the bregman variable %INPUTS %Aop : Linear operator %y_vec : Vector of observed values %s_x : size of the data matrix to be recovered (in form of [m n]) %lambda1:regularization parameter %rnk : rank estimation for X %iter : maximum number of iterations to be carried out %OUTPUTS %x_out : recovered matrix if nargin 6 error( Insufficient Number of arguments ); end %Variable and parameter initialization eta1=.001; % Regularization parameter s_new=s_x(1)*s_x(2); W=zeros(s_new,1); % proxy variable B1=ones(s_new,1); % bregman variable % create operator for least square mimimization I=opDiag(s_new,1); Aop_concat = opStack([1 eta1],Aop,I); %run iterative algorithm for iteration=1:iter %measurement vector for L2 minimization b_vec=[y_vec;eta1*(W-B1)]; %L2 minimization step (subproblem 1) X=lsqr(@lsqrAop,b_vec); %Nuclear norm minization Step (subproblem 2) W=X+B1; [W, s_thld]=nuc_norm(W,s_x,s_new,lambda1,eta1,rnk); %bregman variable update B1 = B1+X-W; %Objective function value obj_func(iteration)=0.5*norm(y_vec-Aop(X,1))+ lambda1*sum(s_thld) ; if iteration10 abs(obj_func(iteration)-obj_func(iteration-10))1e-7 break end end %reshaping recovered vector to matrix form x_out = reshape(X,s_x(1),s_x(2)); %Plot objective function plo