Correlated maximum likelihood temperature/emissivity separation of hyperspectral images

We consider a model for temperature/emissivity separation in hyperspectral image processing. The emissivity is modulated by both the black body function and the atmospheric down- welling. This dual modulation has made it difficult to extract both temperature and emissivity, since offsets in one variable can be compensated by the other. Previous work with only a single wavelength is extended to the multiple wavelength (vector) case. Downwelling radiance is modeled as a Gaussian random vector. As before, the emissivity contributes to both the mean and variance of the observations. The covariance of the downwelling is assumed to have correlated elements, providing additional information beyond what is seen in the scalar case. Gradient ascent is used as an approach to find the maximum likelihood solution, demonstrating that a single maximum exists.