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Optimization Methods for Synthetic Aperture Radar Imaging

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Handbook of Convex Optimization Methods in Imaging Science

Abstract

We review recent developments in Synthetic Aperture Radar (SAR) image formation from an optimization perspective. Majority of these methods can be viewed as constrained least squares problems exploiting sparsity. We reviewed analytic and large scale numerical optimization based approaches in both deterministic and Bayesian frameworks. These methods offer substantial improvements in image quality, suppression of noise and clutter. Analytic methods also have the advantage of computational efficiency.

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Notes

  1. 1.

    \(\mathcal{F}^{\dag }\mathcal{F}\) is a pseudo-differential operator.

  2. 2.

    For the deterministic case, we can consider a Gaussian model with large variance to obtain pseudo-inverse solutions.

  3. 3.

    \([\mathcal{I} -\alpha \nabla ^{2}V (\rho _{k})]\) can be expressed as a time-varying convolution and combined with Q, the kernel of the filter \(\mathcal{Q}\) in \(\mathcal{K}\).

  4. 4.

    The passive SAR forward model is formed by correlating two sets of bistatic measurements in fast-time. The resulting forward model is \(\tilde{\mathcal{F}} =\mathcal{ F}_{b}^{\dag }\mathcal{F}_{b}\) where \(\mathcal{F}_{b}\) is (4.1) with phase (4.4). The unknown is then modeled as \(\tilde{\rho }=\rho \otimes \rho\), where ⊗ denotes the tensor product. For the notational simplicity and uniformity \(\tilde{\mathcal{F}} \rightarrow \mathcal{ F}\) and \(\tilde{\rho }\rightarrow \rho\) in this section.

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Acknowledgements

This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-16-1-0234, and by the National Science Foundation (NSF) under Grant No. CCF-1421496.

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Authors and Affiliations

  1. Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, 110, 8th Street, Troy, NY, 12180, USA

    Eric Mason & Birsen Yazici

  2. Department of Electronics and Communications Engineering, Istanbul Technical University, Maslak, 34469, Istanbul, Turkey

    Ilker Bayram

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  1. Eric Mason
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  2. Ilker Bayram
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  3. Birsen Yazici
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Correspondence to Birsen Yazici .

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  1. The Pennsylvania State University, University Park, Pennsylvania, USA

    Vishal Monga

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Mason, E., Bayram, I., Yazici, B. (2018). Optimization Methods for Synthetic Aperture Radar Imaging. In: Monga, V. (eds) Handbook of Convex Optimization Methods in Imaging Science. Springer, Cham. https://doi.org/10.1007/978-3-319-61609-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-61609-4_4

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