PROMP: A sparse recovery approach to lattice-valued signals

Flinth, Axel und Kutyniok, Gitta (2018): PROMP: A sparse recovery approach to lattice-valued signals. In: Applied and Computational Harmonic Analysis, Vol. 45, No. 3: pp. 668-708

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1063-5203
• Language: English