# A regularized tri-linear approach for optical interferometric imaging

## Introduction

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. We propose to improve the approach on three fundamental aspects. First, we define the estimated image as a solution of a regularized minimization problem, promoting sparsity in a fixed dictionary using either an l1 or a (re)weighted-l1 regularization term. Second, 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 l2,1 regularization term.

The code made available here represents MATLAB implementation of the proposed algorithm.

### Authors

- Ms. Jasleen Birdi
- Dr. Audrey Repetti
- Prof. Yves Wiaux

#### Article

J. Birdi, A. Repetti, and Y. Wiaux - A regularized tri-linear approach for optical interferometric imaging, * Monthly Notices of the Royal Astronomical Society*, vol. 468, no. 1, pp. 1142-1155, 2017.