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We discuss the estimation of ground reflectance from remotely-sensed measurements made by a satellite-borne instrument. The particular sensor under study includes a spatially-varying weighting of the ground values within overlapping, large, low-resolution image pixels. Thus the problem is one of estimating sub-pixel information from a low resolution observation. The observation process involves interaction with an unknown atmosphere, realistic modeling of which requires sophisticated and computationally expensive algorithms. These make it difficult to specify likelihood functions for use in a fully Bayesian approach to the inversion and so we work with atmospherically-corrected data in a penalized least-squares framework. We formulate realistic physical models for the observation process which can then be inverted using a forward modeling approach. This can be solved by using a stochastic optimization algorithm on a suitably chosen energy function, which regularizes the accuracy of reconstruction of the observed satellite data with our prior beliefs about spatial smoothness of the ground reflectance. A further complication is introduced as the sensor views the same ground point from two viewing angles at closely-spaced times. As the surface property of reflectance intrinsically varies with viewing angle, depending on the vegetation or ground cover, these two views allow us to jointly estimate two parameters of a suitable physical model for this variation. From this we can also derive other functionals of interest to environmental applications. This estimation can be considered as a form of image fusion, via the forward model of the observation process. We consider practical aspects of the smoothness priors, the forward model and its implications for the design of an energy function and stochastic inversion algorithms in this application. We compare their performance with an existing method, on some synthetic data, generated with the important sensor properties. We discuss a `stochastic refinement' algorithm, which improves on starting estimates, and is a computationally-cheap and effective alternative to full stochastic optimization when images are smooth.
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