Sparse Modeling of High - Dimensional Data for Learning and Vision

Sparse representations account for most or all of the information of a signal by a linear combination of a few elementary signals called atoms, and have increasingly become recognized as providing high performance for applications as diverse as noise reduction, compression, inpainting, compressive sensing, pattern classification, and blind source separation. In this dissertation, we learn the sparse representations of high-dimensional signals for various learning and vision tasks, including image classification, single image super-resolution, compressive sensing, and graph learning. Based on the bag-of-features (BoF) image representation in a spatial pyramid, we first transform each local image descriptor into a sparse representation, and then these sparse representations are summarized into a fixed-length feature vector over different spatial locations across different spatial scales by max pooling. The proposed generic image feature representation properly handles the large in-class variance problem in image classification, and experiments on object recognition, scene classification, face recognition, gender recognition, and handwritten digit recognition all lead to state-of-the-art performances on the benchmark datasets. We cast the image super-resolution problem as one of recovering a highresolution image patch for each low-resolution image patch based on recent sparse signal recovery theories, which state that, under mild conditions, a high-resolution signal can be recovered from its low-resolution version if the signal has a sparse representation in terms of some dictionary. We jointly learn the dictionaries for highand low-resolution image patches and enforce them to have common sparse representations for better recovery. Furthermore, we employ image features and enforce patch overlapping constraints to improve prediction accuracy. Experiments show that the algorithm leads to surprisingly good results. Graph construction is critical for those graph-orientated algorithms designed for the purposes of data clustering, subspace learning, and semi-supervised learning. We model the graph construction problem, including neighbor selection and