Sparse reconstrcution techniques for SAR tomography

Tomographic SAR inversion, including SAR tomography and differential SAR tomography, is essentially a spectral analysis problem. The resolution in the elevation direction depends on the size of the elevation aperture, i.e. on the spread of orbit tracks. Since the orbits of modern meter-resolution space-borne SAR systems, like TerraSAR-X, are tightly controlled, the tomographic elevation resolution is at least an order of magnitude lower than in range and azimuth. Hence, super-resolution reconstruction algorithms are desired. The high anisotropy of the 3D tomographic resolution element renders the signals sparse in the elevation direction; only a few point-like reflections are expected per azimuth-range cell. Considering the sparsity of the signal in elevation, a compressive sensing based algorithm is proposed in this paper: “Scale-down by L₁ norm Minimization, Model selection, and Estimation Reconstruction” (SL1MMER, pronounced “slimmer”). It combines the advantages of compressive sensing, e.g. super-resolution capability, with the high amplitude and phase accuracy of linear estimators, and features a model order selection step which is demonstrated with several examples using TerraSAR-X spotlight data. Moreover, we investigate the ultimate bounds of the technique on localization accuracy and super-resolution power. Finally, a practical demonstration of the super resolution of SL1MMER for SAR tomographic reconstruction is provided.