Using a Kronecker decomposition from a sample covariance matrix to remove noise. Interesting !
Kronecker PCA Based Robust SAR STAP by Kristjan Greenewald, Edmund Zelnio, Alfred O. Hero III
In this work the detection of moving targets in multiantenna SAR is considered. As a high resolution radar imaging modality, SAR detects and identifies stationary targets very well, giving it an advantage over classical GMTI radars. Moving target detection is more challenging due to the "burying" of moving targets in the clutter and is often achieved using space-time adaptive processing (STAP) (based on learning filters from the spatio-temporal clutter covariance) to remove the stationary clutter and enhance the moving targets. In this work, it is noted that in addition to the oft noted low rank structure, the clutter covariance is also naturally in the form of a space vs time Kronecker product with low rank factors. A low-rank KronPCA covariance estimation algorithm is proposed to exploit this structure, and a separable clutter cancelation filter based on the Kronecker covariance estimate is proposed. Together, these provide orders of magnitude reduction in the number of training samples required, as well as improved robustness to corruption of the training data, e.g. due to outliers and moving targets. Theoretical properties of the proposed estimation algorithm are derived and the significant reductions in training complexity are established under the spherically invariant random vector model (SIRV). Finally, an extension of this approach incorporating multipass data (change detection) is presented. Simulation results and experiments using the real Gotcha SAR GMTI challenge dataset are presented that confirm the advantages of our approach relative to existing techniques.
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