Phase retrieval for signals in union of subspaces

M. Salman Asif, Chinmay Hegde

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length n are observed after passing it through a random m × n supports M matrix1 We also assume that the signal belongs to the span of a single d-dimensional subspace out of R subspaces, where d ≤ n. We assume the knowledge of all possible subspace, but the true subspace of the signal is unknown. We present an algorithm that jointly estimates the phase of the measurements and the subspace support of the signal. We discuss theoretical guarantees on the recovery of signals and present simulation results to demonstrate the empirical performance of our proposed algorithm. Our main result suggests that if properly initialized, then O(d + log R) random measurements are sufficient for phase retrieval if the unknown signal belongs to the union of R low-dimensional subspaces.

    Original languageEnglish (US)
    Title of host publication2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Proceedings
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages356-359
    Number of pages4
    ISBN (Electronic)9781728112954
    DOIs
    StatePublished - Feb 20 2019
    Event2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Anaheim, United States
    Duration: Nov 26 2018Nov 29 2018

    Publication series

    Name2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Proceedings

    Conference

    Conference2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018
    CountryUnited States
    CityAnaheim
    Period11/26/1811/29/18

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    Keywords

    • Alternating minimization
    • Block sparsity
    • Subspace identification

    ASJC Scopus subject areas

    • Information Systems
    • Signal Processing

    Cite this

    Asif, M. S., & Hegde, C. (2019). Phase retrieval for signals in union of subspaces. In 2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Proceedings (pp. 356-359). [8646334] (2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/GlobalSIP.2018.8646334