Model-Based Compressive Sensing

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquisition of sparse or compressible signals that can be well approximated by just K N elements from an N-dimensional basis. Instead of taking periodic samples, we measure inner products with M < N random vectors and then recover the signal via a sparsity-seeking optimization or greedy algorithm. The standard CS theory dictates that robust signal recovery is possible from M = O (K log(N/K)) measurements. The goal of this paper is to demonstrate that it is possible to substantially decrease M without sacrificing robustness by leveraging more realistic signal models that go beyond simple sparsity and compressibility by including dependencies between values and locations of the signal coefficients. We introduce a modelbased CS theory that parallels the conventional theory and provides concrete guidelines on how to create

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, Chinmay Hegde
• Keywords: CORR 2008, CS Theory, Education, Robust Signal Recovery, Standard Cs Theory