Radio-interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio-interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a blockcoordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both point sources images and complex extended sources.
The code made available here represents a proof of concept MATLAB implementation of the proposed algorithm.
A. Repetti, J. Birdi, A. Dabbech, and Y. Wiaux - Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging, Monthly Notices of the Royal Astronomical Society, vol. 470, no. 4, pp. 3981-4006, Oct. 2017. Arxiv preprint
A. Repetti and Y. Wiaux - A non-convex perspective on calibration and imaging in radio interferometry, In Proceedings of the conference on Wavelets and Sparsity XVII, part of the SPIE Optical Engineering + Applications, San Diego, California, United States, 6-9 August 2017.