Hyperspectral unmixing from incomplete and noisy data

In hyperspectral images, once the pure spectra of the materials are known, hyperspectral unmixing seeks to find their relative abundances throughout the scene. We present a novel variational model for hyperspectral unmixing from incomplete noisy data, which combines a spatial regularity prior with the knowledge of the pure spectra. The material abundances are found by minimizing the resulting convex functional with a primal dual algorithm. This extends least squares unmixing to the case of incomplete data, by using total variation regularization and masking of unknown data. Numerical tests with artificial and real-world data demonstrate that our method successfully recovers the true mixture coefficients from heavily-corrupted data.