Within the resolution cell: super-resolution in tomographic SAR imaging

Abstract

We address the problem of resolving two closely spaced complex-valued points from N irregular Fourier domain samples. Although this is a generic super-resolution problem, our target application is SAR tomography where typically the number of acquisitions is N = 10... 100 and SNR = 0 ...10dB. In this paper, a compressive sensing based algorithm is introduced for tomographic SAR inversion. It is named "Scale-down by L1 norm Minimization. Model selection, and Estimation Reconstruction" (SLIMMER, pronounced "slimmer"). SLIMMER combines the advantage of compressive sensing, e.g. high localization accuracy and super-resolution, and the radiometric accuracy of the linear estimator. Moreover, a systematic performance assessment of the SLIMMER algorithm is carried out regarding the elevation estimation accuracy and super-resolution. It is proven that SLIMMER is an efficient estimator; its super resolution factors are in the range of 1.5 to 25 for the aforementioned parameter ranges of TV and SNR. Our results are approximately applicable to nonlinear least-squares estimation, and hence can be considered as fundamental bounds for super-resolution of spectral estimators.