Hyperspectral Unmixing using Least Squares Optimization Methods

Abstract

Hyperspectral imaging, with its capability of capturing information beyond the visible spectrum, can offer detailed spectral signatures that are critical in various applications, ranging from environmental monitoring to medical diagnostics. However, a significant challenge arises when dealing with hyperspectral data due to the mixed-pixel phenomenon, where a single pixel contains spectral signatures from multiple materials. To solve this problem, hyperspectral unmixing (HU) is used to decompose mixed pixels into their constituent endmembers and their corresponding abundances. This study
introduces a novel approach that utilizes least squares optimization methods under various constraints for abundance estimation, specifically using quadratic programming (QP). Additionally, a Principal Component Analysis (PCA) based k-means clustering method is presented for endmember extraction. The research also explores the potential of using Weighted Total Least Squares (WTLS) to refine the estimation process iteratively for the abundance and endmember solutions. The results demonstrate that the type of constraints, whether Weighted Constraints (WC) or Hard Constraints (HC), significantly
influences the accuracy of abundance estimation. The QP model, when optimized with appropriate regularization and constraints, showed substantial improvements compared to standard unconstrained least squares methods. The newly proposed PCA method for endmember estimation outperforms traditional methods such as Vertex Component Analysis (VCA). Furthermore, while the WTLS method was sensitive to initial inputs, it showed potential for further enhancing the solutions derived from the QP and PCA methods.