Tomographic SAR Inversion by Atomic-Norm Minimization—The Gridless Compressive Sensing Approach

Synthetic aperture radar (SAR) tomography (TomoSAR) extends the synthetic aperture principle into the elevation direction for 3-D imaging. Due to the sparsity of the elevation signal, compressive sensing (CS) methods have been introduced for tomographic reconstruction. However, the limited irregular acquisitions and the dense sampling grids of the elevation cannot guarantee the sufficiently sparse reconstruction in the presence of noise. By constructing a complete set of atoms, the gridless sparse methods can directly recover the sparse signals in the continuous frequency space. In this article, we propose the atomic-norm minimization or the gridless CS approach for tomographic SAR inversion and compare it with the L1-norm-based optimization. The enhanced sparsity, the super-resolution capability, and the more accurate estimates are demonstrated using the numerical simulations and experiments with real data. A gridless CS reconstruction of an urban area of Shanghai from the TerraSAR-X data set is presented.