  Synthetic aperture radar (SAR) is a day or night any-weather imaging modality
that is an important tool in remote sensing. Most existing SAR image formation
methods result in a maximum a posteriori image which approximates the
reflectivity of an unknown ground scene. This single image provides no
quantification of the certainty with which the features in the estimate should
be trusted. In addition, finding the mode is generally not the best way to
interrogate a posterior. This paper addresses these issues by introducing a
sampling framework to SAR image formation. A hierarchical Bayesian model is
constructed using conjugate priors that directly incorporate coherent imaging
and the problematic speckle phenomenon which is known to degrade image quality.
Samples of the resulting posterior as well as parameters governing speckle and
noise are obtained using a Gibbs sampler. These samples may then be used to
compute estimates, and also to derive other statistics like variance which aid
in uncertainty quantification. The latter information is particularly important
in SAR, where ground truth images even for synthetically-created examples are
typically unknown. An example result using real-world data shows that the
sampling-based approach introduced here to SAR image formation provides
parameter-free estimates with improved contrast and significantly reduced
speckle, as well as unprecedented uncertainty quantification information.
