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


  1. sampling-based image reconstruction
  2. Bayesian uncertainty quantification
  3. synthetic aperture radar

MSC codes

  1. 94A08
  2. 68U10
  3. 62F15
  4. 65C05
  5. 65F22
  6. 62G07
  7. 60J22

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Information & Authors


Published In

cover image SIAM/ASA Journal on Uncertainty Quantification
SIAM/ASA Journal on Uncertainty Quantification
Pages: 1225 - 1249
ISSN (online): 2166-2525


Submitted: 17 November 2020
Accepted: 6 April 2022
Published online: 28 September 2022


  1. sampling-based image reconstruction
  2. Bayesian uncertainty quantification
  3. synthetic aperture radar

MSC codes

  1. 94A08
  2. 68U10
  3. 62F15
  4. 65C05
  5. 65F22
  6. 62G07
  7. 60J22



Victor Churchill Contact the author
Department of Mathematics, The Ohio State University, Columbus, OH 43210 USA ([email protected]).

Funding Information

Division of Mathematical Sciences (DMS): DMS-1502640, DMS-1912685
This research was partially supported by NSF grants DMS-1502640 and DMS-1912685, the Air Force Office of Sponsored Research grant FA9550-18-1-0316, and the Office of Naval Research MURI grant N00014-20-1-2595.

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