Efficient signal representation is critical in virtually all disciplines of science. Sparse representations have recently drawn much attention from the signal processing community. The basic model consists of considering that natural signals admit a sparse decomposition as a combination of very few atoms in some redundant dictionary. Recent results have shown that learning overcomplete non-parametric dictionaries for image representation, instead of using classical off-the-shelf ones, significantly improves numerous image and video processing tasks. This research aims at developing a comprehensive theoretical, computational, and practical framework for learning sparse representations for numerous signal analysis tasks.
First, the research concentrates on learning sparse representations for global and local robust image classification tasks, proposing formulations with both sparse reconstruction and class discrimination components, jointly optimized during dictionary learning. Multiscale dictionary learning and investigating a number of critical optimization challenges are integral components of this project as well. The framework of learning multiscale sparse representations is then extended to multimodal data. As in the work with images and video, the energies proposed for multimodality consider both reconstructive and discriminative terms, learning the optimal representations both for the given data and the given tasks. In addition to image, video, and audio, other signal modalities studied include tensors, which are critical in diffusion MRI, and bring the additional challenge of developing sparse representations for non-flat data. The proposed work is also extended to learning to sense, where combined with the learning of the optimal dictionaries, the learning of the best linear sensing procedures is studied.
