Hyperspectral Imaging allows quick remote classification of materials in areas such as sorting plastics, detection of residual chemicals or airborne surveillance of plant nutrition.
A hyperspectral camera records several hundred spectral channels at once, associating to each pixel a reflectance spectrum, which servers as fingerprint of the mixture of materials in that pixel.
This wealth of information needs to be processed to make it accessible to human perception.
Segmentation of hyperspectral images may be formulated as finding the material spectra present in a scene and decomposing the scene meaningfully into regions where individual materials dominate. Unmixing of hyperspectral images finds instead a fuzzy decomposition, that is, the concentrations of the materials throughout the scene.
In my PhD thesis I employ the methods of convex analysis and partial differential equations to develop robust and efficient algorithms for hyperspectral unmixing.
Further I study multiplicative and proximal algorithms and their convergence and variational convergence on manifolds.
Challenges in hyperspectral imaging include high mixing of materials, several kinds of noise, partially known data, occlusions and varying illumination.