February Fourier Talks 2019

Paul Gader

University of Florida


Inverse Problems for Nonlinear Spectral Unmixing


Hyperspectral images are images formed using an imaging spectrometer on a moving platform, such as an airplane or satellite. Visible, Near-InfraRed, and Short-Wave InfraRed (VisNIRSWIR) typically consist of measured power converted to estimated reflectance over hundreds of wavelength, or spectral bands. For example, the NASA Airborne Visible and Infrared Imaging Spectrometer - Next Generation (AVIRIS-NG) produces images with 426 spectral bands ranging from 380nm to 2500nm. Therefore, each pixel consists of a spectrum and materials can be identified by their spectrum. The small- bandwidth of each band gives rise to the need to have lower spectral resolution than RGB or multi- spectral data in order to provide sufficient Signal-to-Noise. Therefore, there are often multiple materials that are mixed into the measured light for each pixel. Moreover, multiple scattering at multiple scales produces nonlinear mixing of the spectra of materials. To identify materials in a scene therefore requires solving an inverse problem, namely: Given a mixture of light reflected from multiple materials in a scene, identify the materials and the proportion of each material in the scene. In this talk, physical models of microscopic mixing will be described and algorithms for inverting the models will be described and evaluated. A comparison will be made to model-free inversion.

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