Sparse Representation of Signals and Dictionary Learning, Applied to Hyperspectral and Multispectral Images

Abstract

Imaging technologies, especially hyperspectral and multispectral imaging, are playing significant roles in the applications in numerous fields, including computer vision, remote sensing, medical imaging, security and surveillance, industrial inspection, etc. Spatial and spectral information carried by the images are exploited using machine learning algorithms for the detection and recognition of objects, classification, action recognition, etc., in various fields. Among signal representation techniques in machine learning, being used for different applications, sparse representation of signals is gaining remarkable interest in its analysis and appli cation domains. In practice, an overcomplete dictionary consisting of atoms is constructed and a signal is represented as the linear combination of a few atoms of the dictionary. Sparse representation of signals extracts essential features re quired for the application and reduces redundancy, noise, and dimensionality of the data. Dictionary composition and sparse representation for a particular do main of signals is represented as a constrained problem and different algorithms such as K-SVD (K-Singular Value Decomposition), MOD (Method of Optimal Directions), etc., are used to solve the problem. Algorithms such as Orthogonal Matching Pursuit (OMP), Least Absolute Shrinkage and Selection Operator (LASSO), Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), Basis Pursuit (BP), Matching Pursuit (MP), etc. are used for computing sparse codes for a signal over a given overcomplete dictionary. This dissertation addresses the key problems related to imaging technology used in machine learning models for different applications, including object detection and classification, face recognition, action recognition, and manipulation of adversarial examples. It attempts to solve the problems in various applications associated with the use of hyperspectral imaging such as hyperspectral image classification, fusion of hyperspectral and multispectral images, and issues of spectral variabilities. All these problems have been addressed in a sequence of papers published or submitted at prestigious venues. This dissertation explains the use of dictio naries and sparse codes to address these problems while defining the models for the application of imaging technologies. It explains the formulation of Bayesian networks and associated conditional probabilities, and the integration of dictionaries and sparse coefficients to set up problem models. These Bayesian models use a Non-parametric Bayesian framework coupled with Beta-Bernoulli processes to induce strongly joint and discriminative behavior in the posterior parameters of the problems. Moreover, the Stochastic Variational Inference (SVI) technique has been introduced to solve the models encompassing Bayesian dictionary and sparse representation learning approach. SVI has reduced the training time of our models of the order of 100 to 400. A shared weights approach in joint learning of the dictionary and classifier has also been introduced to increase the accuracy of the classifier. In this approach, the dictionary and the classifier are learned with the same representations (weights) of the training examples and the corresponding labels respectively, contrary to the traditional approaches which use different weights. Consequently, at the prediction stage, weights of a test sample computed over the learned dictionary and fed to the classifier will map to the corresponding label with a high chance. Hyperspectral images are spectrally superior to multispectral images, and multispectral images are spatially superior to hyperspectral images. They need to be fused to generate a super-resolution image that represents both the images, hyperspectral and multispectral, equal in terms of spectral resolution and spatial resolution respectively. This dissertation explains the design of a Bayesian network and the use of a Non-parametric Bayesian approach with Beta-Bernoulli processes that represent the underlying degradation model for fusion addressing also the spectral variability issue. This model induced a strong coupling among the reflectance scaling factors matrix, the spectral dictionary, and spectral sparse coefficients. The sparse representation power of the Bayesian dictionary learning approach has been also exploited for generating adversarial examples for attacking convolutional neural networks (CNN) while keeping the adversarial examples imperceptible.Demonstration has been presented for the approaches by performing experiments on the standard datasets and performance has been compared with state-of-the-art approaches. The approaches presented in this dissertation beat other approaches not only in accuracy but also in training time.