function [ G , F , R ] = SpAIN_Cal( W , X , G , F , Omega_G , Omega_F , Phi_G , Phi_F , D , k , lambda , Mean_F , mu , F_theo , N_iter ) % Author: Clément DORFFER % Date: 26/11/2018 % @: clement.dorffer@ensta-bretagne.fr % Goal: perform mobile sensor calibration using the Sparsity- and Average-Constrained Informed NMF calibraton technique. % If you use this code for research or educational purpose, please cite: % % C. Dorffer, M. Puigt, G. Delmaire, G. Roussel, Informed Nonnegative Matrix Factorization Methods for % Mobile Sensor Network Calibration, IEEE Transactions on Signal and Information Processing over Networks, % Volume 4, Issue 4, pp. 667-682, December 2018. % W2 = W.^2; tilde_W2 = [W2,lambda*ones(size(W,1),1)]; Omega_Bar_G = ones(size(G))-Omega_G; Omega_Bar_F = ones(size(F))-Omega_F; Delta_G = G.*Omega_Bar_G; Delta_F = F.*Omega_Bar_F; m = size(F,2)-1; R = zeros(N_iter+1,1); R(1) = norm(F(2,1:end-1)-F_theo(2,1:end-1),2)/sqrt(size(F_theo,2)-1); for i = 1 : N_iter x = OMP(G(:,2),D,k); tilde_X = [X,D*x]; tilde_F = [F,[0;1]]; % updating G Delta_G = Updt_Delta_G( tilde_W2 , tilde_X , Delta_G , Phi_G , tilde_F , Omega_Bar_G ); G = Phi_G + Delta_G; % updating F Delta_F = Updt_Delta_F( W2 , X , G , Delta_F , Phi_F , Omega_Bar_F , Mean_F , mu , m ); F = Phi_F + Delta_F; R(i+1) = norm(F(2,1:end-1)-F_theo(2,1:end-1),2)/sqrt(size(F_theo,2)-1); end end function [ Delta_F ] = Updt_Delta_F( W , X , G , Delta_F , Phi_F , Omega_B_F , Mean_F , mu , m ) %%%%%%%%%%%%%%%%%%%%%%%%%%% % Update rule for Delta_F % %%%%%%%%%%%%%%%%%%%%%%%%%%% Delta_F = Delta_F.*(Omega_B_F.*(G'*(W.*secu_plus(X-G*Phi_F)))+mu/m*diag(Mean_F)*Omega_B_F)./(Omega_B_F.*(G'*(W.*(G*Delta_F)))+mu/m^2*diag(Delta_F*ones(m+1,1))*Omega_B_F); Delta_F(isnan(Delta_F))=0; end function [ Delta_G ] = Updt_Delta_G( W , X , Delta_G , Phi_G , F , Omega_B_G ) %%%%%%%%%%%%%%%%%%%%%%%%%%% % Update rule for Delta_G % %%%%%%%%%%%%%%%%%%%%%%%%%%% Delta_G = Delta_G.*(Omega_B_G).*((W.*secu_plus(X-Phi_G*F))*F')./((W.*(Delta_G*F)*F')); % mise à jour Delta_G(isnan(Delta_G))=0; end function [toto] = secu_plus(tutu,s) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Goal: Security in the NMF procedure which project the negative data to % epsilon (small user-defined threshold) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if(nargin<2) s=1.e-12; end toto=max(tutu,s); toto(isnan(tutu)) = 0; end