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. 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. 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 ℓ2,1 regularization term. We present simulation results, both for monochromatic and hyperspectral cases, to validate the proposed approach.
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- June 2017
- techniques: image processing;
- techniques: interferometric;
- Astrophysics - Instrumentation and Methods for Astrophysics
- Mon Not R Astron Soc 2017, 468 (1): 1142-1155