  The method of simulated annealing is adapted to the temperature-emissivity
separation (TES) problem. A patch of surface at the bottom of the atmosphere is
assumed to be a greybody emitter with spectral emissivity $\epsilon(k)$
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 $\textit{A-Posteriori}$ probability that spectral
radiance detected at the top of the atmosphere originates from a patch with
stipulated $T$ and $\epsilon(k)$. 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 solution for $T$ and
$\epsilon(k)$. The limitation to a stipulated set of endmember emissivities may
be relaxed by allowing the number of endmembers to grow without bound, and to
be generic continuous functions of wavenumber with bounded first derivatives
with respect to wavenumber.

Data Analysis, Statistics and Probability;Geophysics