On Using Projection Onto Convex Sets for Solving the Hyperspectral Unmixing Problem

We present a new algorithm for solving the fully constrained least-squares problem in hyperspectral unmixing, based on the Dykstra algorithm for projections onto convex sets, integrated with a solution validation phase based on the Kolmogorov criterion. We first show the equivalence between the fully constrained least-squares problem and the convex set projection problem. Next, an alternating projections algorithm is designed that can be used for this projection operation. A validation phase is built in the algorithm, so that the iteration can be terminated early when the projection has been found. The resulting algorithm yields abundance maps that are similar to those obtained with state-of-the-art methods, with runtimes that are competitive compared to several other techniques. Furthermore, the simple nature of the algorithm allows for efficient implementations on specialized hardware.