Synthetic Aperture Radar Image Formation with Uncertainty Quantification

Abstract: 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.