Sparse coding for machine learning, image processing and computer vision.

Summary We study in this thesis a particular representation of signals based on a statistical learning method, which consists in modeling data as linear combinations of some elements of a learned dictionary. This can be seen as an extension of the classical wavelet framework, whose goal is to build such dictionaries (often orthonormal bases) that are adapted to natural signals. An important success of this approach has been its ability to model imagelets, and the performance of image denoising methods based on it. We address several open questions, which are related to this framework: How to efficiently learn a dictionary? How can we enrich this model by adding underlying structure to the dictionary? Is it possible to improve current image processing methods based on this approach? How should the dictionary be learned when it is used for a task other than signal reconstruction? Are there interesting applications of this method in computer vision? We answer these questions, with a multidisciplinary point of view, by borrowing tools from statistical learning, convex and stochastic optimization, signal and image processing, computer vision, but also optimization on graphs.