# A regularized tri-linear approach for optical interferometric imaging

Jasleen Birdi, Audrey Repetti, Yves Wiaux

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
24 Downloads (Pure)

## Abstract

In the context of optical interferometry, only under-sampled 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.
Original language English 1142–1155 14 Monthly Notices of the Royal Astronomical Society 468 1 17 Feb 2017 https://doi.org/10.1093/mnras/stx415 Published - 11 Jun 2017

## Keywords

• techniques: interferometric
• Techniques: image processing