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.
Notes
- 1.
\(\mathcal{F}^{\dag }\mathcal{F}\) is a pseudo-differential operator.
- 2.
For the deterministic case, we can consider a Gaussian model with large variance to obtain pseudo-inverse solutions.
- 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.
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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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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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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