Signal Reconstruction from Modulo Observations
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We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism 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.
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