Simulated annealing approach to temperature–emissivity separation in thermal remote sensing

Abstract

The method of simulated annealing is adapted to the temperature–emissivity separation problem. A patch of surface at the bottom of the atmosphere is assumed to be a graybody emitter with spectral emissivity ε(k)ε(k) describable by a mixture of spectral endmembers. We prove that a simulated annealing search conducted according to a suitable schedule converges to a solution maximizing the a-posteriori probability that spectral radiance detected at the top of the atmosphere originates from a patch with stipulated TT and ε(k)ε(k). Any such solution will be nonunique. The average of a large number of simulated annealing solutions, however, converges almost surely to a unique maximum a-posteriori (MAP) solution for TT and ε(k)ε(k).