Learning sparse representations for restoration and classification: Theory, Computations, and Applications in Image, Video, and Multimodal Analysis

有效的信号表示在几乎所有的科学学科中都是至关重要的。稀疏表示最近引起了信号处理界的广泛关注。的基本模型包括考虑自然信号承认稀疏分解为一些冗余字典中的很少的原子的组合。最近的研究结果表明，学习过完备的非参数字典的图像表示，而不是使用经典的现成的，显着改善了许多图像和视频处理任务。本研究的目的是发展一个全面的理论，计算和实践框架学习稀疏表示众多的信号分析tasks.First，研究集中在学习稀疏表示的全局和局部鲁棒的图像分类任务，提出配方稀疏重建和类歧视的组成部分，联合优化字典学习。多尺度字典学习和调查一些关键的优化挑战也是该项目的组成部分。学习多尺度稀疏表示的框架，然后扩展到多模态数据。与图像和视频的工作一样，为多模态提出的能量考虑了重建和判别项，学习给定数据和给定任务的最佳表示。除了图像、视频和音频之外，研究的其他信号形式包括张量，张量在扩散MRI中至关重要，并带来了为非平面数据开发稀疏表示的额外挑战。所提出的工作也扩展到学习感，其中结合学习的最佳字典，学习的最佳线性感测程序进行了研究。

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.