Modulo Compressed Sensing

Talk Timings: April 30, 2021 (Friday) 2.50 PM – 3.50 PM IST

Abstract:

Compressed sensing deals with recovery of sparse signals from low dimensional projections, but under the assumption that the measurement setup has infinite precision. In practice, analog-to-digital converters are a key component in signal acquisition systems, which are inherently finite precision systems. To counter the clipping effect in these systems, a recent approach called self-reset ADCs or modulo ADCs can be used, which fold the measurements crossing the range back to the dynamic range of the ADCs using modulo arithmetic. For this setup combined with compressed measurements, called modulo-CS, we present theoretical results on the minimum number of measurements required for unique recovery of sparse vectors. We also show that recovery using the minimal number of measurements is achievable by using a measurement matrix whose entries are independently drawn from a continuous distribution. We also present an algorithm based on convex relaxation and provide guarantees for recovering sparse signal from the modulo measurements, and a mixed integer linear program (MILP) for the convex relaxation algorithm. 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. Finally, we consider the effect of quantization, and present the advantage of modulo-ADCs for compressed sensing when compared to the traditional sparse recovery methods and a methodology to recovery sparse vectors from clipped measurements. This is joint work with Dheeraj Prasannaand Chandrasekhar Sriram.

Bio:

Chandra R. Murthy is a professor in the ECE department, Indian Institute of Science. His research interests include sparse signal recovery, its applications, and wireless communications in 5G/Beyond 5G systems.