Bayesian compressive sensing and projection optimization

Abstract

This paper introduces a new problem for which machine-learning tools may make an impact. The problem considered is termed "compressive sensing", in which a real signal of dimension N is measured accurately based on K << N real measurements. This is achieved under the assumption that the underlying signal has a sparse representation in some basis (e.g., wavelets). In this paper we demonstrate how techniques developed in machine learning, specifically sparse Bayesian regression and active learning, may be leveraged to this new problem. We also point out future research directions in compressive sensing of interest to the machine-learning community.