Sparse signal recovery from modulo observations

Viraj Shah, Chinmay Hegde

    Research output: Contribution to journalArticlepeer-review

    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.

    Original languageEnglish (US)
    Article number15
    JournalEurasip Journal on Advances in Signal Processing
    Volume2021
    Issue number1
    DOIs
    StatePublished - Dec 2021

    Keywords

    • High dynamic range imaging
    • Modulo sensing
    • Sparse recovery

    ASJC Scopus subject areas

    • Signal Processing
    • Information Systems
    • Hardware and Architecture
    • Electrical and Electronic Engineering

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