In this project, we focus on the deconvolution problem, where the measurements of the object of interest come from the convolution of the ground truth with a known blur kernel. On top of that, those measurements are corrupted by Poisson noise. The goal of this project is to mathematically derive a variational formulation of the problem and to solve it. To make the reconstruction better, we will use a convex data-driven regularization scheme which has state-of-the-art performance for image recovery among convex regularizers. The student will need to find the suitable optimization approach to find the solution and benchmark the performance of the regularizer. Good Pytorch and optimization knowledge is required.