Advances in Noise-Robust Hyperspectral Unmixing: From Random Matrix Theory to Dictionary Learning and Deep Models

Abstract: Hyperspectral unmixing (HU) is a core challenge in remote sensing, where the goal is to decomposeeach mixed pixel into a set of pure spectral signatures (endmembers) and their associated proportions(abundances). In practice, HU is complicated by diverse noise sources that degrade performance. Earlystudies employed Random Matrix Theory (RMT) to distinguish signal and noise subspaces, providingrigorous tools for intrinsic dimensionality estimation. While effective under Gaussian noise and linear mixingassumptions, RMT-based models often fail in real-world conditions. Advances in sparse regression anddictionary learning (DL) have introduced adaptability by learning data-driven bases that better capturespectral variability and structured noise. More recently, robust and deep dictionary learning frameworkshave extended HU to nonlinear, complex environments, improving resilience to outliers and noise. Thisreview traces the evolution from RMT-driven models to modern dictionary learning approaches, highlightingtheir strengths, limitations, and adoption trends. We also outline future research frontiers, including deepdictionary learning, hybrid unmixing strategies, and integration with emerging AI-driven remote sensingworkflows.