Sparse Signal Recovery Using Markov Random Fields

Part of Advances in Neural Information Processing Systems 21 (NIPS 2008)

Bibtex Metadata Paper

Authors

Volkan Cevher, Marco Duarte, Chinmay Hegde, Richard Baraniuk

Abstract

Compressive Sensing (CS) combines sampling and compression into a single sub-Nyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we use Markov Random Fields (MRFs) to represent sparse signals whose nonzero coefficients are clustered. Our new model-based reconstruction algorithm, dubbed Lattice Matching Pursuit (LaMP), stably recovers MRF-modeled signals using many fewer measurements and computations than the current state-of-the-art algorithms.