Sparse signal recovery from modulo observations

• Main Authors: Viraj Shah, Chinmay Hegde
• Format: Article
• Language: English
• Published: SpringerOpen 2021-04-01
• Series: EURASIP Journal on Advances in Signal Processing
• Subjects: Sparse recovery; High dynamic range imaging; Modulo sensing
• Online Access: https://doi.org/10.1186/s13634-021-00722-w

Abstract We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a relatively new 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 in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the signal recovery problem under sparsity constraints for the special case to modulo folding limited to two periods. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide experiments validating our approach on toy signal and image data and demonstrate its promising performance.