Atmospheric correction of hyperspectral data over dark surfaces via simulated annealing

A method [atmospheric correction via simulated annealing (ACSA)] is proposed that enhances the atmospheric correction of hyperspectral images over dark surfaces. It is based on the minimization of a smoothness criterion to avoid the assumption of linear variations of the reflectance within gas absorption bands. We first show that this commonly used approach generally fails over dark surfaces when the signal to noise ratio strongly declines. In this case, important residual features highly correlated with the shape of gas absorption bands are observed in the estimated surface reflectance. We add a geometrical constraint to deal with this correlation. A simulated annealing approach is used to solve this constrained optimization problem. The parameters involved in the implementation of the algorithm (initial temperature, number of iterations, cooling schedule, and correlation threshold) are automatically determined by using a standard simulated annealing theory, reflectance databases, and sensor characteristics. Applied to a HyMap image with available ground truths, we verify that ACSA adequately recovers ground reflectance over clear land surfaces, and that the added spectral shape constraint does not introduce any spurious feature in the spectrum. The analysis of an AVIRIS image of Central Switzerland clearly shows the ability of the method to perform enhanced water vapor estimations over dark surfaces. Over a lake (reflectance equal to 0.02, low signal to noise ratio equal to about 6), ACSA retrieves unbiased water vapor amounts (2.86 cm±0.36 cm) in agreement with in situ measurements (2.97 cm±0.30 cm). This corresponds to a reduction of the standard deviation by a factor 3 in comparison with standard unconstrained procedures (1.95 cm±1.08 cm). Similar results are obtained using a Hyperion image of DoE ARM SGP test site containing a very dark area of the land surface.