ABCS: Approximate Bayesian Compressed Sensing

In this work we present a new approximate Bayesian compressed sensing scheme. The new method is based on a unique type of sparseness-promoting prior, termed here semi-Gaussian owing to its Gaussian-like formulation. The semi-Gaussian prior facilitates the derivation of a closed-formrecursion for solving the noisy compressed sensing problem. As part of this, the discrepancy between the exact and the approximate posterior pdf is shown to be of the order of a quantity that is computed online by the new scheme. In the second part of this work, a random field-based classifier utilizing the approximate Bayesian CS scheme is shown to attain a zero error rate when applied to fMRI classification.

By: Avishy Carmy; Pini Gurfil; Dimitri Kanevsky; Bhuvana Ramabhadran

Published in: RC24816 in 2009

LIMITED DISTRIBUTION NOTICE:

This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.

rc24816.pdf

Questions about this service can be mailed to reports@us.ibm.com .