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 Square Kilometre Array, aim at improving imaging resolution and sensitivity by orders ofmagnitude. 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 block-coordinate 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 modeled 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 source images and complex extended sources. MATLAB code is available on GitHub.
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- School of Engineering & Physical Sciences - Assistant Professor
- School of Mathematical & Computer Sciences - Assistant Professor
- School of Engineering & Physical Sciences, Institute of Sensors, Signals & Systems - Assistant Professor
- School of Mathematical & Computer Sciences, Actuarial Mathematics & Statistics - Assistant Professor
Person: Academic (Research & Teaching)