On the Identifiability of Sparse Vectors From Modulo Compressed Sensing Measurements
Dheeraj Prasanna, Chandrasekhar Sriram, Chandra R. Murthy
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.