Signal Recovery in Compressed Sensing via Universal Priors

Details Signal Recovery in Compressed Sensing via Universal Priors Signal Recovery in Compressed Sensing via Universal Priors

2012-04-12

arxiv.org/abs/1204.2611v1

Computer Science

Information Theory

24 pages, 5 figures

Scientific paper

We study the compressed sensing (CS) signal estimation problem where an input is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the observed signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. We focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors such as Kolmogorov complexity and minimum description length. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation through a Markov Chain Monte Carlo implementation. We also include simulation results that showcase the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.

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