A regularized tri-linear approach for optical interferometric imaging

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 trilinear 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 ℓ 1 or a (re)weighted-ℓ 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 ℓ 2,1 regularization term. We present simulation results, both for monochromatic and hyperspectral cases, to validate the proposed approach.

Sparse interferometric Stokes imaging under the polarization constraint (Polarized SARA)

“…In this case, we can either apply our technique on the self-calibrated Stokes I data or work with phase-insensitive observables, as in the case of optical interferometry (OI) (Thiébaut & Giovannelli 2010). With this in mind, we can combine the current proposed method with other sparse modelling techniques in OI (Birdi et al 2017;Akiyama et al 2017b). This will be advantageous for polarimetric imaging from VLBI observations.…”

Scalable Bayesian Uncertainty Quantification in Imaging Inverse Problems via Convex Optimization

“…We also plan to generalize the proposed approach to solve more sophisticated inverse problems. For instance, often when the inverse problem is non-linear, the MAP approach leads to a non-convex minimization problem [54,10,55,12]. In this case, the theoretical results of [49] do not hold, and our approach cannot be directly applied.…”

Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging

“…This framework has shown to give good reconstruction results in several application fields such as astronomical remote sensing (Bobin et al 2008), optical interferometric imaging (Auria et al 2014;Birdi et al 2017), and RI imaging (Wiaux et al 2009a;Li et al 2011;Garsden et al 2015;Dabbech et al 2015). In this context, the regularization function r in eq.…”

“…Compressive sensing theory makes use of the assumption that the image x has a sparse representation Ψ † x ∈ C D in a given dictionary Ψ ∈ C N ×D (Fornasier & Rauhut 2011), where † is the transpose conjugate operator. This framework has shown to give good reconstruction results in several application fields such as astronomical remote sensing (Bobin et al 2008), optical interferometric imaging (Auria et al 2014Birdi et al 2017), andRI imaging (Wiaux et al 2009a;Li et al 2011;Garsden et al 2015;Dabbech et al 2015). In this context, the regularization function r in eq.…”

“…Nevertheless, it is worth emphasizing that the forward-backward algorithm, and in general optimization algorithms (Combettes & Pesquet 2010;Komodakis & Pesquet 2015), can be used to introduce more sophisticated regularization terms. Moreover, it has been shown in the last years that using optimization and compressive sensing theories leads to very competitive results with respect to traditional radio interferometric methods such as CLEAN (Onose et al 2016, 2017), yet comparisons have mostly been performed on smaller images, and the computational costs so far have not been competitive.…”