A regularized tri-linear approach for optical interferometric imaging

TL;DR

This paper introduces a regularized tri-linear model for optical interferometric imaging that enhances image reconstruction by promoting sparsity, employing a block-coordinate forward-backward algorithm, and extending to hyperspectral data with joint sparsity.

Contribution

It proposes a novel regularized tri-linear approach with a convergence-guaranteed algorithm, extending the model to hyperspectral imaging with joint sparsity promotion.

Findings

Effective in monochromatic imaging with improved reconstruction quality.

Successfully extended to hyperspectral imaging with joint sparsity.

Simulation results validate the approach's effectiveness.

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.