PAINTER: a spatiospectral image reconstruction algorithm for optical interferometry

Abstract

Astronomical optical interferometers sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid perturbations caused by atmospheric turbulence, the phases of the complex Fourier samples (visibilities) cannot be directly exploited. Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic optical interferometric instruments are now paving the way to multiwavelength imaging. This paper is devoted to the derivation of a spatio-spectral ("3D") image reconstruction algorithm, coined PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also differential phases, which helps to better constrain the polychromatic reconstruction. Simulations on synthetic data illustrate the efficiency of the algorithm and in particular the relevance of injecting a differential phases model in the reconstruction.

Proximity operators for phase retrieval

“…In this paper, we derive a likelihood function adapted to the statistics of the noise via a simple modification of the intensity-projection operator. We had previously established the formulation of this proximity operator in the Gaussian case with a specific ADMM algorithm for image reconstruction in optical long-baseline interferometry [24] ; a similar result was also published recently [25]. But neither further characterization nor comparison with standard projection methods were done.…”

Principles of image reconstruction in optical interferometry: tutorial

“…When f (x) is convex but not smooth, the optimization can be carried out by an augmented Lagrangian method like the Alternating Direction Method of Multipliers (ADMM) [65] which exploits a variable splitting strategy to separate the complex optimization problem into sub-problems which are easier to solve, sometimes even exactly. ADMM also provides a flexible way to impose the strict constraints implemented by Ω. ADMM has been successfully used in a number of algorithms for interferometric imaging [36,49,66,67] but it requires as many control parameters as there are splittings and constraints. These must be treated as additional hyper-parameters needed to tune the algorithm.…”

A regularized tri-linear approach for optical interferometric imaging

“…In particular, the method proposed by Kluska et al (2014), namely SPARCO, is a semi-parametric approach for image reconstruction of chromatic objects, whereas the method proposed by Thiébaut et al (2013) deals with a sparsity regularized approach considering the observed scene to be a collection of point-like sources. Recently the use of differential phases for hyperspectral imaging has been proposed in PAINTER (Schutz et al 2014). The methods proposed by Thiébaut et al (2013) and Schutz et al (2014) use the alternating direction method of multipliers (ADMM) algorithm (Boyd et al 2010) to solve the considered minimization problem.…”

“…Recently the use of differential phases for hyperspectral imaging has been proposed in PAINTER (Schutz et al 2014). The methods proposed by Thiébaut et al (2013) and Schutz et al (2014) use the alternating direction method of multipliers (ADMM) algorithm (Boyd et al 2010) to solve the considered minimization problem.…”