In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible, creating 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.
The Optical-Interferometry-Trilinear code improves the approach on three fundamental aspects. First, the estimated image is defined 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, the resultant non-convex minimization problem is solved 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, the model and algorithm are generalized to the hyperspectral case, promoting a joint sparsity prior through an l2,1 regularization term.