Advanced image analysis techniques for extragalactic surveys

Image analysis applied to astronomy is a vast field. It contains several solutions to handle the many issues inherent to the peculiar nature of astronomical images. The entire area is cross-disciplinary, and it is based on a variety of mathematical and computer science approaches, which are also at the foundation of two techniques that are essential for the analysis of astronomical extragalactic images: ``denoising'' and ``deblending''. On the one hand, the goal of denoising algorithms is to reduce the observational noise intrinsic to the images without losing details (in our case, for example, faint distant galaxies). On the other hand, the purpose of deblending algorithms is to efficiently separate objects that appear overlapped in the image. State-of-the-art mathematical algorithms for denoising are commonly used in several fields, but there is almost no trace of application to astronomical observations in the scientific literature, in particular concerning optical and near-IR extragalactic observations. These algorithms have the potential to enhance objects detection, granting improved statistics without requiring additional telescope time. Deblending parametric algorithms have been tested, with good, albeit not optimal, results. Many new methods, based on machine learning techniques, have been developed and are now being proposed. Improved deblending algorithms have the potential to enhance high-precision measurements at the basis of cosmological and galaxy evolution investigations. Therefore, an in-depth study of these techniques is mandatory to assess all their possible advantages and risks quantitatively, and plan their application to forthcoming surveys where unsupervised image analysis will be unavoidable due to the massive amount of data that will be acquired. The goal of this thesis is to test new approaches to the denoising and deblending of astronomical images. In particular, we found that a small group of denoising algorithms (ATVD, Perona-Malik, Bilateral, and TV Chambolle) enhance objects detection without altering fluxes and shapes. Whereas, tested machine learning techniques (ASTErIsM-DENCLUE, blend2flux, and blend2mask2flux) accurately separate and recover fluxes of two blended objects, more reliably than the standard approaches.