Sparsity regularized optical interferometric imaging

Jasleen Birdi, Audrey Repetti, Yves Wiaux

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Abstract

Optical interferometry involves acquisition of under-sampleddata related to the Fourier coefficients of the intensity image of interest,with missing phase information. It poses an ill-posed non-linear inverseproblem for image recovery. In this context, for monochromatic imaging,a tri-linear data model was proposed in [1], leading to a non-negative nonlinear least squares minimization problem, solved using a Gauss-Seidel method. In the recently submitted paper [2], we have developed a new robust method to improve upon the previous approach, by introducing as parsity prior, imposed either by an ℓ1 or a reweighted ℓ1 regularization term. The resulting problem is solved using an alternating forward backward algorithm, which is applicable to both smooth and non-smooth functions, and provides convergence guarantees in the non-convex context of interest. Moreover, our method presenting a general framework, we have extended it to hyperspectral imaging, where we have promoted a joint sparsity prior by an ℓ2,1 norm. Here we describe the proposed method and present simulation results to show its performance.
Original languageEnglish
Title of host publicationProceedings of SPARS 2017
Pages1-2
Number of pages2
Publication statusPublished - 2017

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    Birdi, J., Repetti, A., & Wiaux, Y. (2017). Sparsity regularized optical interferometric imaging. In Proceedings of SPARS 2017 (pp. 1-2)