Hi all matlab GURUs (Tim Davis, John D’Errico, Bruno Luong and others) ,
1) I am working on L1-norm solver. However, in the split Bregman method, L1-problem is approximated as small L2-subproblems; so, I am talking about L2-norm minimization . The subproblem that I am solving is:
J(u) := |A*u - yo|^2 + tol^2 |D*u-y1|^2
Where yo and y1 keeps changing between various iterations.
2) Before solving this, I am converting it into single term L2-norm:
J(u) := |[A; D]*u – [yo; tol*y1]|^2 = |AF*u – b|^2
3) My matrices A, AF are sparse.
4) Quite frequently (20-30% of time, my solver which uses backslash operator runs into usual problem of “Rank deficiency”).
a. I tried “PSEUDOINVERSE” by Bruno. I believe that his code uses QR method. I calculate solution as
xF = pseudoinverse(AF)*b;
But, even there I am running into the same trouble of rank deficiency. Some guidance regarding appropriate solver would be highly appreciated.