The goal of this research was to develop a new approach to solve the inverse problem of thermal remote sensing of the Earth. This problem falls under a large class of inverse problems that are ill-conditioned because there are many more unknowns than observations. The approach is based on a multivariate analysis technique known as Canonical Correlation Analysis (CCA). By collecting two ensembles of observations, it is possible to find the latent dimensionality where the data are maximally correlated. This produces a reduced and orthogonal space where the problem is not ill-conditioned. In this research, CCA was used to extract atmospheric physical parameters such as temperature and water vapor profiles from multispectral and hyperspectral thermal imagery. CCA was also used to infer atmospheric optical properties such as spectral transmission, upwelled radiance, and downwelled radiance. These properties were used to compensate images for atmospheric effects and retrieve surface temperature and emissivity. Results obtained from MODTRAN simulations, the MODerate resolution Imaging Spectrometer (MODIS) Airborne Sensor (MAS), and the MODIS and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) (MASTER) airborne sensor show that it is feasible to retrieve land surface temperature and emissivity with 1.0 K and 0.01 accuracies, respectively
