Reconstructing Background Galaxies via Sparse Horseshoe Prior and Starlet Basis

Hasti Nafisi ( Université de Montréal )

Gravitational lensing is a phenomenon in which the path of light from a distant galaxy is bent by the gravitational field of a foreground galaxy or cluster of galaxies. This could cause the appearance of background galaxies to be distorted and look like an arc. Reconstructing the original appearance of these background galaxies is an important problem in astrophysics, as it can provide insights into the distribution of dark matter and the structure of the Universe. we propose a sparse Bayesian approach to reconstruct the background galaxies that have been distorted by gravitational lensing. We use a horseshoe prior and a starlet basis to promote sparsity in the reconstructed images. The horseshoe prior is a type of Bayesian prior that allows for the selection of relevant features for sparsity, while the starlet basis is a set of wavelet functions that decompose an image into some scales and encourage sparsity in different scales. We introduce the basics of gravitational lensing and its effects on the observed images of galaxies. We then describe the theoretical background and methodology of sparse Bayesian inference using horseshoe priors and starlet bases. We will present a detailed algorithm for the reconstruction of the background galaxies using these techniques.