Nonlocal and Randomized Methods in Sparse Signal and Image Processing

Abstract

This thesis focuses on the topics of sparse and non-local signal and image processing. In particular, I present novel algorithms that exploit a combination of sparse and non-local data models to perform tasks such as compressed-sensing reconstruction, image compression, and image denoising. The contributions in this thesis are: (1) a fast, approximate minimum mean-squared error (MMSE) estimation algorithm for sparse signal reconstruction, called Randomized Iterative Hard Thresholding (RIHT). This algorithm has applications in compressed sensing, image denoising, and other sparse inverse problems. (2) An extension to the Block-Matching 3D (BM3D) denoising algorithm that matches blocks at different rotation angles. This algorithm improves on the performance of BM3D in terms of both visual quality and quantitative denoising accuracy. (3) A novel non-local, causal image prediction algorithm, and a corresponding codec implementation that achieves state of the art lossless compression performance on 8-bit grayscale images. (4) A deep convolutional neural network (CNN) architecture that achieves state-of-the-art results in bilnd image denoising, and a novel non-local deep network architecture that further improves performance.