How to implement these multiplicative updates in MATLAB? - matlab

Question

I am doing two updates for h and x given in this [paper] http://paris.cs.illinois.edu/pubs/nasser-icassp2015.pdf (You don't have to read the paper, just look for the equations 4,10 and 14 for updating h and x given on page 2 and 3).
This is the code snippet that I have tried so far. Can you tell me if its correct? Also, is there any way to optimize these for loops?
In some cases (t-tau) term was negative and MATLAB was giving an error. So, I put a condition that only implement if (t-tau)>0. Doing this is correct or is there any other way to take care of the negative indices?
%updates
Lh=10;
lambda = 0.1*(sum(reverberatedspeechspec(:))/(size(Y,1)*size(Y,2)));
S=reverberatedspeechspec;
W=basis_mel_act; W=gather(W); W = double(W); %W is the dictionary
%---initialization for H(RIR)----
H=rand(size(Y,1),Lh);
nmfIter = 50;
%---initialization for X(Activations)-----
W_trans=W';
X=W_trans*S; X=double(X);
Y = zeros(size(S,1));
for idx = 1 : size(Y,1)
Y(idx,:) = filter(S(idx,:),1,H(idx,:));
end
Stilde = zeros(size(S));
Ytilde = zeros(size(S));
for iter=1:nmfIter
% update for H
Stilde = W*X;
Ytilde = zeros(size(S));
for j=1:size(Stilde,1)
Ytilde (j,:) = filter(Stilde(j,:),1,H(j,:));
end
ratio = Y./Ytilde;
numerator = zeros(size(H));
denominator = numerator;
for k = 1 :size(Y,1)
for tau = 1:Lh
for t= 1:size(Y,2)
if gt (t-tau , 0)
numerator (k,tau) = numerator(k,tau) + ratio(k,t) * Stilde(k,t-tau);
denominator(k,tau) = denominator (k,tau) + Stilde (k,t-tau);
end
end
end
end
H = H .* numerator ./denominator ;
%updating Ytilde after getting a new value for H
for j=1:size(Stilde,1)
Ytilde (j,:) = filter(Stilde(j,:),1,H(j,:));
end
%update for X
ratio = Y./Ytilde;
ratio = [ratio zeros(size(Y,1),Lh)]; %zero padding Y and Ytilde for (t+tau) term in update of X.
Product = H.' * W; % Product of H_transpose and W in th update which is equivalent to the term ∑H(k,tau)W(k,r)
numerator = zeros(size(H));
denominator = numerator;
for r = 1:size(W,2)
for t = 1:size(Y,2)
for k = 1:size(Y,1)
for tau = 1:Lh
numerator(r,t) = numerator(r,t) + ratio(k,t+tau) * Product(tau,r);
denominator(r,t) = denominator(r,t) + Product(tau,r) + lambda;
end
end
end
end
X = X .* numerator ./denominator;
end