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Flinth, Axel ORCID logoORCID: https://orcid.org/0000-0003-3370-5528 und Kutyniok, Gitta ORCID logoORCID: https://orcid.org/0000-0001-9738-2487 (2018): PROMP: A sparse recovery approach to lattice-valued signals. In: Applied and Computational Harmonic Analysis, Bd. 45, Nr. 3: S. 668-708

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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.

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