From Midjourney to Dall-E, learning and understanding the geometry of images is now, more than ever, a crucial challenge. At its core is a conflict between expressive and fast methods -neural networks vs classical signal processing- where a balance has to be found. Indeed, at the heart of each method, the scientist has to enforce how the geometry will be learned, keeping both expressiveness and speed at their highest. The task is then to understand which are the ways to promote geometries in high dimensions and what are the advantages and disadvantages. In this project, the student will have to understand, implement, and compare several algorithms for the learning and the super-resolution of 2D height maps (images). These algorithms will be based on HTV regularized inverse problems, separable spline-based techniques, and ReLU neural networks. Proficiency in Python is requiered. The student is also welcome to use his favorite (own ?) algorithm for the learning of images, whether it is deep learning-based or not.