Atmospheric correction with the Bayesian empirical line.

Atmospheric correction of visible/infrared spectra traditionally involves either (1) physics-based methods using Radiative Transfer Models (RTMs), or (2) empirical methods using in situ measurements. Here a more general probabilistic formulation unifies the approaches and enables combined solutions. The technique is simple to implement and provides stable results from one or more reference spectra. This makes empirical corrections practical for large or remote environments where it is difficult to acquire coincident field data. First, we use a physics-based solution to define a prior distribution over reflectances and their correction coefficients. We then incorporate reference measurements via Bayesian inference, leading to a Maximum A Posteriori estimate which is generally more accurate than pure physics-based methods yet more stable than pure empirical methods. Gaussian assumptions enable a closed form solution based on Tikhonov regularization. We demonstrate performance in atmospheric simulations and historical data from the "Classic" Airborne Visible Infrared Imaging Spectrometer (AVIRIS-C) acquired during the HyspIRI mission preparatory campaign.