On the Identifiability of Sparse Vectors from Modulo Compressed Sensing Measurements

Prasanna, D and Sriram, C and Murthy, CR (2021) On the Identifiability of Sparse Vectors from Modulo Compressed Sensing Measurements. In: IEEE Signal Processing Letters, 28 . pp. 131-134.

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Abstract

Compressed sensing deals with recovery of sparse signals from low dimensional projections, but under the assumption that the measurement setup has infinite dynamic range. In this letter, we consider a system with finite dynamic range, and to counter the clipping effect, the measurements crossing the range are folded back into the dynamic range of the system through modulo arithmetic. For this setup, we derive theoretical results on the minimum number of measurements required for unique recovery of sparse vectors. We also show that recovery using the minimum number of measurements is achievable by using a measurement matrix whose entries are independently drawn from a continuous distribution. Finally, we present an algorithm based on convex relaxation and develop a mixed integer linear program (MILP) for recovering sparse signals from the modulo measurements. Our empirical results demonstrate that the minimum number of measurements required for recovery using the MILP algorithm is close to the theoretical result for signals with low variance.

Item Type:	Journal Article
Publication:	IEEE Signal Processing Letters
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Compressed sensing; Integer programming; Recovery; Relaxation processes, Continuous distribution; Convex relaxation; Identifiability; Low dimensional; Measurement matrix; Measurement setup; Mixed integer linear program; Modulo arithmetic, Signal reconstruction
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	24 Feb 2023 05:02
Last Modified:	24 Feb 2023 05:02
URI:	https://eprints.iisc.ac.in/id/eprint/80456

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