Signal Reconstruction from Modulo Observations

Abstract--We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less wellknown imagingmechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction under this model is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to (rigorously) solving the inverse problem, inspired by recent advances in algorithms for phase retrieval under sparsity constraints. We prove that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide extensive experiments on both synthetic and real data to support our claims. A. Motivation I.INTRODUCTION The problem of reconstructing a signal (or image) from (possibly) nonlinear observations is widely encountered in standard signal acquisition and imaging systems.