Joint Modeling and Learning Approaches for Hyperspectral Imaging and Changepoint Detection

In the era of artificial intelligence, there has been a growing consensus that solutions to complex science and engineering problems require novel methodologies that can integrate interpretable physics-based modeling approaches with machine learning techniques, from stochastic optimization to deep neural networks. This thesis aims to develop new methodological and applied frameworks for combining the advantages of physics-based modeling and machine learning, with special attention to two important signal processing tasks: solving inverse problems in hyperspectral imaging and detecting changepoints in time series. The first part of the thesis addresses learning priors in model-based optimization for solving inverse problems in hyperspectral imaging systems. First, we introduce a tuning-free Plug-and-Play algorithm for hyperspectral image deconvolution (HID). Specifically, we decompose the optimization problem into two iterative sub-problems, learn deep priors to solve the blind denoising sub-problem with neural networks, and estimate hyperparameters with a measure of the statistical whiteness of the residual. Second, we introduce an original hyperspectral and multispectral image fusion (HMIF) method. It leverages neural networks to learn image priors from data to solve the optimization problem accounting for inter-image variability. We also propose a zero-shot strategy to learn the image-specific priors in an unsupervised manner. The second part of the thesis focuses on modeling changes in data distribution and learning knowledge of time series signals to detect changepoints. First, we propose a changepoint detection (CPD) method using an online approach based on neural networks and continual learning to directly estimate the density ratio between current and reference windows of the data stream. Second, we introduce a non-parametric algorithm for online CPD in manifold-valued data and provide theoretical bounds on the detection and false alarm rate performances using a new result on the non-asymptotic convergence of the stochastic Riemannian gradient descent. Finally, we extend this algorithm to distributed CPD in streaming manifold-valued signals over graphs with a parallel implementation of a graph filter. This significantly improves the detection of changepoints in unknown communities of networks.