Hyperspectral unmixing using an active set algorithm

The inversion problem in hyperspectral unmixing involves solving a constrained least-squares problem. Several solutions have been proposed, often based on convex optimization techniques, such as alternating optimization strategies, projection onto convex sets, augmenting positively constrained optimization algorithms, or quadratic programming. One of the most popular techniques, fully-constrained least-squares unmixing, is based on extending the Lawson-Hanson non-negatively constrained least-squares algorithm with an extra weighted term that takes the sum-to-one constraint into account. In this paper, we present an alternative active-set algorithm, inspired by the Lawson-Hanson algorithm, which solves the unmixing problem exactly, and does not require any weighting parameters. The resulting algorithm always finds the correct solution, and works an order of magnitude faster than the fully-constrained least-squares algorithm.