Resolution enhancement of hyperspectral imagery using coincident panchromatic imagery and a stochastic mixing model

A maximum a posteriori (MAP) estimation approach to the hyperspectral resolution enhancement problem is described for enhancing the spatial resolution of a hyperspectral image using a higher resolution, coincident, panchromatic image. The approach makes use of a stochastic mixing model (SMM) of the underlying spectral scene content to develop a cost function that simultaneously optimizes the estimated hyperspectral scene relative to the observed hyperspectral and panchromatic imagery, as well as the local statistics of the spectral mixing model. The incorporation of the stochastic mixing model is found to be the key ingredient to reconstructing subpixel spectral information in that it provides the necessary constraints that lead to a well-conditioned linear system of equations for the high resolution hyperspectral image estimate. The mathematical formulation of the method is described, and enhancement results are provided for a synthetically-generated hyperspectral image data set and compared to prior methods. In general, it is found that the MAP/SMM method is able to reconstruct sub-pixel information in several principal components of the high resolution hyperspectral image estimate, while the enhancement for conventional methods, like those based on least-squares estimation, is limited primarily to the first principal component (i.e., the intensity component).