Foreground Signature Extraction for an Intimate Mixing Model in Hyperspectral Image Classification

The hyperspectral unmixing problem arises in remote sensing, chemometrics, and biomedical engineering applications. The spectral signature of a single pixel in a hyperspectral cube can be represented as a non-negative combination of non-negative signatures from various materials contained in the physical region corresponding to the pixel (linear mixing). A less studied problem is associated with foreground extraction in an intimate (nonlinear) mixing model. We introduce a framework for foreground signature extraction based on a proposed patch model. We introduce identifiability conditions for the single and multiple patch cases. Using these conditions, we present an algorithm for the identifiable recovery of foreground signatures. Numerical experiments on real and synthetic data illustrate the efficacy of the proposed approach.