l1-minimization has proved a powerful tool for image restoration. In this framework, the degraded image is iteratively deblurred in the space-domain and denoised with a soft thresholding in some transform-domain in which the original image is supposed to be sparse. In this project, we will adopt a learning approach to optimize the denoising step. Instead of using a soft thresholding, we learn a nonlinear shrinkage function from a collection of images and their synthetically degraded versions. The sparsifying transform can also be learned to improve the performance of the restoration. You are supposed to implement a learning algorithm for some reconstruction method such as total variation. Prerequisites: a good knowledge of image processing, linear algebra, a little vector calculus, and a little nonlinear optimization.