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The method of simulated annealing is adapted to the temperature-emissivityseparation (TES) problem. A patch of surface at the bottom of the atmosphere isassumed to be a greybody emitter with spectral emissivity $\epsilon(k)$describable by a mixture of spectral endmembers. We prove that a simulatedannealing search conducted according to a suitable schedule converges to asolution maximizing the $\textit{A-Posteriori}$ probability that spectralradiance detected at the top of the atmosphere originates from a patch withstipulated $T$ and $\epsilon(k)$. Any such solution will be nonunique. Theaverage of a large number of simulated annealing solutions, however, convergesalmost surely to a unique Maximum A-Posteriori solution for $T$ and$\epsilon(k)$. The limitation to a stipulated set of endmember emissivities maybe relaxed by allowing the number of endmembers to grow without bound, and tobe generic continuous functions of wavenumber with bounded first derivativeswith respect to wavenumber.

Simulated Annealing Approach to the Temperature-Emissivity Separation Problem in Thermal Remote Sensing Part One: Mathematical Background