L₁ Sparsity-Constrained Archetypal Analysis Algorithm for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is widely used to process mixed pixels as an essential technology. Among them, the nonnegative matrix factorization (NMF)-based approach is one typical of the blind unmixing techniques, which can achieve endmembers and abundances simultaneously. Considering the physical meaning of the extracted endmembers, the archetypal analysis (AA) method constructs a new matrix decomposition structure with stronger interpretability than NMF. However, AA ignores the significant sparse property of abundance in unmixing. Therefore, we propose the L
₁
sparsity-constrained AA algorithm for HU. To solve the new optimization problem, we explore a new optimization method for optimizing abundance. The alternating direction method of multipliers (ADMM) is used to increase the strong convexity and convergence of the problem. Then the fast gradient method (FGM) instead of traditional gradient descent is used to speed up algorithm convergence. The experimental results in both the synthesized and real datasets show that the proposed method outperforms several sparse NMF-based and AA-based methods.