Advanced sparse optimization algorithms for interferometric imaging inverse problems in astronomy
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In the quest to produce images of the sky at unprecedented resolution with high sensitivity, new generation of astronomical interferometers have been designed. To meet the sensing capabilities of these instruments, techniques aiming to recover the sought images from the incompletely sampled Fourier domain measurements need to be reinvented. This goes hand-in-hand with the necessity to calibrate the measurement modulating unknown effects, which adversely affect the image quality, limiting its dynamic range. The contribution of this thesis consists in the development of advanced optimization techniques tailored to address these issues, ranging from radio interferometry (RI) to optical interferometry (OI). In the context of RI, we propose a novel convex optimization approach for full polarization imaging relying on sparsity-promoting regularizations. Unlike standard RI imaging algorithms, our method jointly solves for the Stokes images by enforcing the polarization constraint, which imposes a physical dependency between the images. These priors are shown to enhance the imaging quality via various performed numerical studies. The proposed imaging approach also benefits from its scalability to handle the huge amounts of data expected from the new instruments. When it comes to deal with the critical and challenging issues of the direction-dependent effects calibration, we further propose a non-convex optimization technique that unifies calibration and imaging steps in a global framework, in which we adapt the earlier developed imaging method for the imaging step. In contrast to existing RI calibration modalities, our method benefits from well-established convergence guarantees even in the non-convex setting considered in this work and its efficiency is demonstrated through several numerical experiments. Last but not least, inspired by the performance of these methodologies and drawing ideas from them, we aim to solve image recovery problem in OI that poses its own set of challenges primarily due to the partial loss of phase information. To this end, we propose a sparsity regularized non-convex optimization algorithm that is equipped with convergence guarantees and is adaptable to both monochromatic and hyperspectral OI imaging. We validate it by presenting the simulation results.