Deconvolution of Levy Processes Using Message Passing Technique
Pedram PAD, EPFL STI LIB

Seminar • 05 September 2011 • BM 4.233

Abstract
Using message passing techniques, we perform the MMSE estimation of a Levy process from its noisy convolved version. First we define the underlying graph model and define the exact messages that have to be passed along the edges (which are some functions). Then we try to simplify the messages to be some “numbers” that parameterize the “functions”. Up to this point we obtain a very efficient algorithm for MMSE denoising of Levy processes. To generalize the method for the deconvolution problem, we need to further simplify the method by decreasing the number of passed messages; the latter is achieved by restricting the number of messages to the number of vertices rather than the edges. This simplification usually decreases the computational complexity from O(n^2) to O(n).