On the Performance of Reweighted $L_{1}$ Minimization for Tomographic SAR Imaging

L1 minimization has proven to be useful for tomographic synthetic aperture radar (SAR) imaging because it has super-resolution capability and produces no sidelobes. However, it cannot always derive the sparsest solution and often yields outliers in recovery. Consequently, it is usually difficult to extract true persistent scatterers straightforwardly in practice. To enhance the sparsity, we introduce iterative reweighted L1 minimization for sparse inversion. The weight factor is computed in each iteration, according to the previous tomographic magnitude to establish a more democratic penalization rule. Our simulation results indicate that the reweighted algorithm can achieve perfect recovery when noise is lower. Specifically, when the signal-to-noise ratio is equal to 5 dB, two reweighted iterations can improve the probability of true sparsity from 29.2% to 99.8% for single scatterers and from 0.2% to 95.4% for double scatterers. Due to the enhanced sparsity, we can directly identify scatterers without the need for further model selection. The method is validated using 44 TerraSAR-X/ TanDEM-X images. Single and double scatterers are detected in urban areas. Verification using light detection and ranging (LiDAR) data indicates that we achieve submeter accuracy of the height estimates.