Atomic Norm Minimization Based Fast Off-Grid Tomographic SAR Imaging With Nonuniform Sampling

The accuracy of the traditional compressed sensing (CS) based tomographic synthetic aperture radar (TomoSAR) imaging is limited by inappropriate grid partitioning. The atomic norm-based processing effectively solves this problem by implementing variable estimation in the continuous domain, that is, avoiding the undesired grid partitioning manipulation. Nevertheless, the performance of the atomic norm-based TomoSAR imaging is limited in two main aspects: limited geometry adaptability caused by the uniform sampling requirement and the high computational load. In this article, a novel atomic norm minimization (ANM) based off-grid TomoSAR imaging is proposed for fast processing with nonuniform sampling. The main technical contributions are twofold: first, the nonuniformly sampled data is resampled to be uniform where a new geometrical projection-based interpolation is used; second, the ANM problem is solved by using the nonsymmetric cone model to speed up the processing, reducing the computational load from
$O(N^{2})$
to
$O(N)$
. The proposed approaches have been verified by computer simulations and real data experiments.