Fast log-decon with a quasi-Newton solver |

Contrary to steepest descent where the step length is estimated with a Newton-search technique, the step length in L-BFGS is computed such that sufficient decrease of the error and of the local curvature is attained (so called ``Wolfe conditions''). The appendix shows the L-BFGS solver in more details. The L-BFGS code can be downloaded at http://users.eecs.northwestern.edu/~nocedal/lbfgs.html The pseudo-code below shows both the steepest-descent and L-BFGS algorithms.

U = 0. # or other initializations Remove the mean from U(omega). Iteration { dU = 0 Compute dU Remove mean from dU du = FT(dU) if (steepest descent) { Compute alfa with Newton iterations u = u + alfa*du } else if (L-BFGS) { Compute alfa with More and Thuente method u = u + alfa*Qdu # Q = inverse approximate Hessian } }

2012-10-29