Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898192 | Applied and Computational Harmonic Analysis | 2018 | 41 Pages |
Abstract
Applications such as wireless communications require efficient sensing techniques of signals with the a priori knowledge of those being lattice-valued. In this paper, we study the impact of this prior information on compressed sensing methodologies, and introduce and analyze PROMP (“PReprojected Orthogonal Matching Pursuit”) as a novel algorithmic approach for sparse recovery of lattice-valued signals. More precisely, we first show that the straightforward approach to project the solution of Basis Pursuit onto a prespecified lattice does not improve the performance of Basis Pursuit in this situation. We then introduce PROMP as a novel sparse recovery algorithm for lattice-valued signals which has very low computational complexity, alongside a detailed mathematical analysis of its performance and stability under noise. Finally, we present numerical experiments which show that PROMP outperforms standard sparse recovery approaches in the lattice-valued signal regime.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Axel Flinth, Gitta Kutyniok,