A regularized tri-linear approach for optical interferometric imaging

Abstract

In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging, leading to an alternated minimization problem. In that work, only a positivity constraint was considered, and the problem was solved by an approximated Gauss-Seidel method. In this paper, we propose to improve the approach on three fundamental aspects. Firstly, we define the estimated image as a solution of a regularized minimization problem, promoting sparsity in a fixed dictionary using either an ${\ell }_1$ or a weighted-${\ell }_1$ regularization term. Secondly, we solve the resultant non-convex minimization problem using a block-coordinate forward-backward algorithm. This algorithm is able to deal both with smooth and non-smooth functions, and benefits from convergence guarantees even in a non-convex context. Finally, we generalize our model and algorithm to the hyperspectral case, promoting a joint sparsity prior through an ${\ell }_{2,1}$ regularization term. We present simulation results, both for monochromatic and hyperspectral cases, to validate the proposed approach.

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Cited by in corpus (1)

• Sparse interferometric Stokes imaging under polarization constraint (Polarized SARA)