Signal Classification Under Structured Sparsity Constraints

• Main Author: Vu, Tiep Huu
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2019
• Subjects: Electrical engineering
• ISBN: 1392318998; 9781392318997

Object Classification is a key direction of research in signal and image processing, computer vision and artificial intelligence. The goal is to come up with algorithms that automatically analyze images and put them in predefined categories. This dissertation focuses on the theory and application of sparse signal processing and learning algorithms for image processing and computer vision, especially object classification problems. A key emphasis of this work is to formulate novel optimization problems for learning dictionary and structured sparse representations. Tractable solutions are proposed subsequently for the corresponding optimization problems.Sparse signal processing has had remarkable recent success in problems such as classification, object detection, image and audio recognition, image super-resolution, etc. It essentially attempts to represent any signal (e.g. image, video, audio, etc.) using only a few number of observations or features from the same physical phenomenon. Based on this theory, a sparse representation-based classifier (SRC) [1] was initially developed for robust face recognition, and thereafter was extended to several other signal classification problems. It has been shown that SRC can be further improved by learning a dictionary from the training samples instead of using all of them as a dictionary. In the first part of the dissertation, we develop a discriminative dictionary learning framework for histopathological image analysis. Particularly, we propose an automatic feature discovery framework via learning class-specific dictionaries and present a low-complexity method for classification and disease grading in histopathology. Essentially, our Discriminative Feature-oriented Dictionary Learning (DFDL) [2] method learns class-specific dictionaries such that under a sparsity constraint, the learned dictionaries allow representing a new image sample parsimoniously via the dictionary corresponding to the class identity of the sample. At the same time, the dictionary is designed to be poorly capable of representing samples from other classes.The next part of this dissertation exploits the observation that although different objects possess distinct characteristics, they also usually share common patterns. A recently proposed dictionary learning framework has shown the benefit of separating the particularity and the commonality (COPAR) [3]. Inspired by this, we propose a novel method to explicitly and simultaneously learn a set of common patterns as well as class-specific features for classification with more intuitive constraints. Our dictionary learning framework is hence characterized by both a shared dictionary and particular (class-specific) dictionaries. The shared dictionary is constrained to have low-rank, i.e. its spanning subspace should have low dimension and the coefficients corresponding to this dictionary should be similar. For the particular dictionaries, we impose on them the well-known constraints stated in the Fisher discrimination dictionary learning (FDDL) [4]. Further, new fast and accurate algorithms are developed to solve the subproblems in the learning step, accelerating its convergence. The said algorithms could also be applied to FDDL and its extensions. The efficiency of these algorithms is theoretically and experimentally verified by quantifying their complexity and running time with other well-known dictionary learning methods. The work has culminated into a dictionary learning toolbox called DICTOL [5] (https://github.com/tiepvupsu/DICTOL). The toolbox (in Matlab and Python) implements numerous sparse coding algorithms as well as widely used generative and discriminative dictionary learning methods. Many classical methods are sped up via new numerical optimization innovations.We also extend sparsity models to tensor sparsity models which significantly enhance classification accuracy for signals with multi-channels and multi-views. In this part, we present three novel sparsity-driven techniques, which not only exploit the subtle features of raw captured data but also take advantage of the polarization diversity and the aspect angle dependence information from multi-channel signals. First, the traditional SRC is generalized to exploit shared information of classes and various sparsity structures of tensor coefficients for multi-channel data. Corresponding tensor dictionary learning models are consequently proposed to enhance classification accuracy. Lastly, a new tensor sparsity model is proposed to model responses from multiple consecutive looks of objects, which is a unique characteristic of the dataset.An important goal of this dissertation is to demonstrate the wide applications of these algorithmic tools for real-world applications. To that end, we explored important problems in the areas of:(1) Medical imaging: histopathological images acquired from mammalian tissues, human breast tissues, and human brain tissues. (2) Low-frequency (UHF to L-band) ultra-wideband (UWB) synthetic aperture radar: detecting bombs and mines buried under rough surfaces. (3) General object classification: face, owers, objects, dogs, indoor scenes, etc.