Sampling-based Spotlight SAR Image Reconstruction from Phase History Data for Speckle Reduction and Uncertainty Quantification

. Spotlight mode airborne synthetic aperture radar (SAR) is a coherent imaging modality that is an 5 important tool in remote sensing. Existing methods for spotlight SAR image reconstruction from 6 phase history data typically produce a single image estimate which approximates the reflectivity 7 of an unknown ground scene, and therefore provide no quantification of the certainty with which 8 the estimate can be trusted. In addition, speckle affects all coherent imaging modalities causing a 9 degradation of image quality. Many point estimate image reconstruction methods incorrectly treat 10 speckle as additive noise resulting in an unnatural smoothing of the speckle that also reduces image 11 contrast. The purpose of this paper is to address the issues of speckle and uncertainty quantification 12 by introducing a sampling-based approach to SAR image reconstruction directly from phase history 13 data. In particular, a statistical model for speckle as well as a corresponding sparsity technique to 14 reduce it are directly incorporated into the model. Rather than a single point estimate, samples 15 of the resulting joint posterior density are efficiently obtained using a Gibbs sampler, which are in 16 turn used to derive estimates and other statistics which aid in uncertainty quantification. The latter 17 information is particularly important in SAR, where ground truth images even for synthetically-18 created examples are typically unknown. While similar methods have been deployed to process 19 formed images, this paper focuses on the integration of these techniques into image reconstruction 20 from phase history data. An example result using real-world data shows that, when compared with 21 existing methods, the sampling-based approach introduced provides parameter-free estimates with 22 improved contrast and significantly reduced speckle, as well as uncertainty quantification information. 23