Convex optimization-based windowed Fourier filtering with multiple windows for wrapped-phase denoising

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    The windowed Fourier filtering (WFF), defined as a thresholding operation in the windowed Fourier transform (WFT) domain, is a successful method for denoising a phase map and analyzing a fringe pattern. However, it has some shortcomings, such as extremely high redundancy, which results in high computational cost, and difficulty in selecting an appropriate window size. In this paper, an extension of WFF for denoising a wrapped-phase map is proposed. It is formulated as a convex optimization problem using Gabor frames instead of WFT. Two Gabor frames with differently sized windows are used simultaneously so that the above-mentioned issues are resolved. In addition, a differential operator is combined with a Gabor frame in order to preserve discontinuity of the underlying phase map better. Some numerical experiments demonstrate that the proposed method is able to reconstruct a wrapped-phase map, even for a severely contaminated situation.

    Original languageEnglish
    Pages (from-to)4632-4641
    Number of pages10
    JournalApplied Optics
    Issue number17
    Publication statusPublished - 2016 Jun 10


    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics

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