  Synthetic aperture radar (SAR) tomography (TomoSAR) enables the
reconstruction and three-dimensional (3D) localization of targets based on
multiple two-dimensional (2D) observations of the same scene. The resolving
along the elevation direction can be treated as a line spectrum estimation
problem. However, traditional super-resolution spectrum estimation algorithms
require multiple snapshots and uncorrelated targets. Meanwhile, as the most
popular TomoSAR imaging method in modern years, compressed sensing (CS) based
methods suffer from the gridding mismatch effect which markedly degrades the
imaging performance. As a gridless CS approach, atomic norm minimization can
avoid the gridding effect but requires enormous computing resources. Addressing
the above issues, this paper proposes an improved fast ANM algorithm to TomoSAR
elevation focusing by introducing the IVDST-ANM algorithm, which reduces the
huge computational complexity of the conventional time-consuming semi-positive
definite programming (SDP) by the iterative Vandermonde decomposition and
shrinkage-thresholding (IVDST) approach, and retains the benefits of ANM in
terms of gridless imaging and single snapshot recovery. We conducted
experiments using simulated data to evaluate the performance of the proposed
method, and reconstruction results of an urban area from the SARMV3D-Imaging
1.0 dataset are also presented.
