SAR Tomography Based on Atomic Norm Minimization in Urban Areas

Synthetic aperture radar (SAR) tomography (TomoSAR) is a powerful tool for the three-dimensional (3D) reconstruction of buildings in urban areas. At present, the compressed sensing (CS) technique has been widely used in the TomoSAR inversion of urban areas because of the sparsity of the backscattering power of buildings along the elevation direction. However, this algorithm discretizes the elevation and assumes that the scatterers are located on predetermined finite grids. In fact, scatterers can lie anywhere in the elevation direction, regardless of grid point constraints. The phenomenon of scatterer positioning errors due to elevation discretization is called the off-grid effect, which will affect the height estimation accuracy of TomoSAR. To overcome this problem, we proposed a TomoSAR reconstruction algorithm based on atomic norm minimization (Tomo-ANM) in this paper. Tomo-ANM employs ANM, a continuous compressed sensing technique, to obtain scatterer positions on the continuous dictionary, thus eliminating the off-grid effect. Baseline compensation is necessary to obtain the data of virtual uniform baselines or the samples of uniform data during preprocessing. A fast realization of ANM, IVDST, is utilized to accelerate the process. Tomo-ANM was tested through simulation experiments, and the results confirmed the validity of eliminating the influence of off-grid effects and exhibited an improved location accuracy and detection rate in less time compared with the on-grid TomoSAR algorithm SL1MMER. Real data experiments based on eight staring spotlight TerraSAR-X images showed that Tomo-ANM can improve the accuracy of building height estimation by 4.83% relative to its real height.