Identifiable Solutions to Foreground Signature Extraction from Hyperspectral Images in an Intimate Mixing Scenario

The problem of foreground material signature extraction in an intimate (nonlinear) mixing setting is considered. It is possible for a foreground material signature to appear in combination with multiple background material signatures. We explore a framework for foreground material signature extraction based on a patch model that accounts for such background variation. We identify data conditions under which a foreground material signature can be extracted up to scaling and elementwise-inverse variations. We present algorithms based on volume minimization and endpoint member identification to recover foreground material signatures under these conditions. Numerical experiments on real and synthetic data illustrate the efficacy of the proposed algorithms.