High-Dimensional Imaging Data Analysis

This book provides a comprehensive, modern treatment of Principal Component Analysis (PCA) and its robust extensions for high-dimensional data analysis, with a particular emphasis on image data, machine learning (ML) and artificial intelligence (AI) applications, and optimization-based methods. Classical PCA remains a foundational tool for dimensionality reduction, outlier detection, feature extraction, and data image visualization and reconstruction; however, its sensitivity to outliers, noise, missing data, and gross corruption severely limits its applicability in real-world problems. This book addresses these limitations by developing a unified and rigorous framework for Robust PCA and its advanced variants. The scope of the book spans from classical PCA to state-of-the-art robust low-rank modelling techniques, including Robust PCA with weighted nuclear norm, norm-based robustness, truncated weighted nuclear norm RPCA, and tensor robust PCA for high-dimensional imaging data.. Particular attention is given to ADMM and related optimization strategies that enable scalable solutions for high-dimensional problems. The core arguments of the book are threefold. First, robustness is essential not optional in modern data analysis, especially for high-dimensional image and tensor data contaminated by outliers, occlusions, and structured noise. Second, carefully incorporated regularization, such as weighted and truncated nuclear norms and structured sparsity via the  norm, substantially improves recovery accuracy and interpretability compared with standard RPCA. Third, many seemingly distinct methods in machine learning and AI, and low-rank modelling can be understood within a unified optimization framework, enabling principled algorithm design and theoretical insight.