We address the problem of resolving two closely spaced complex-valued points from N irregular Fourier do- main samples. Although this is a generic super-resolution (SR) problem, our target application is SAR tomography (TomoSAR), where typically the number of acquisitions is N = 10 - 100 and SNR = 0-10 dB. As the TomoSAR algorithm, we introduce "Scale-down by LI norm Minimization, Model selection, and Estimation Reconstruction" (SL1MMER), which is a spectral estimation algorithm based on compressive sensing, model order selection, and final maximum likelihood parameter estimation. We investigate the limits of SLIMMER concerning the following questions. How accurately can the positions of two closely spaced scatterers be estimated? What is the closest distance of two scat- terers such that they can be separated with a detection rate of 50% by assuming a uniformly distributed phase difference? How many acquisitions N are required for a robust estimation (i.e., for separating two scatterers spaced by one Rayleigh resolution unit with a probability of 90%)? For all of these questions, we provide numerical results, simulations, and analytical approxima- tions. Although we take TomoSAR as the preferred application, the SLIMMER algorithm and our results on SR are generally applicable to sparse spectral estimation, including SR SAR focus- ing of point-like objects. Our results are approximately applicable to nonlinear least-squares estimation, and hence, although it is derived experimentally, they can be considered as a fundamental bound for SR of spectral estimators. We show that SR factors are in the range of 1.5-25 for the aforementioned parameter ranges of N and SNR.     «

We address the problem of resolving two closely spaced complex-valued points from N irregular Fourier do- main samples. Although this is a generic super-resolution (SR) problem, our target application is SAR tomography (TomoSAR), where typically the number of acquisitions is N = 10 - 100 and SNR = 0-10 dB. As the TomoSAR algorithm, we introduce "Scale-down by LI norm Minimization, Model selection, and Estimation Reconstruction" (SL1MMER), which is a spectral estimation algorithm based on compres...     »

Synthetic aperture radar, spectral estimation, Maximum likelihood estimation, Compressive sensing (CS), SL1MMER algorithm, Strontium, Fourier analysis, data acquisition, minimisation, probability, Fourier domain sample, Rayleigh resolution analysis, TomoSAR algorithm, compressive sensing robustness analysis, generic super-resolution problem, maximum likelihood parameter estimation, nonlinear least-squares estimation, numerical simulation, spaceborne SAR tomography, sparse spectral estimation, spectral estimation method, super-resolution power, uniformly distributed phase difference analysis, Minimization, Noise, SAR tomography (TomoSAR), super-resolution (SR), synthetic aperture radar (SAR), tomography, Estimation, Robustness, SL1MMER, image resolution, remote sensing by radar, geophysical techniques, spaceborne radar, least squares approximations     «

Synthetic aperture radar, spectral estimation, Maximum likelihood estimation, Compressive sensing (CS), SL1MMER algorithm, Strontium, Fourier analysis, data acquisition, minimisation, probability, Fourier domain sample, Rayleigh resolution analysis, TomoSAR algorithm, compressive sensing robustness analysis, generic super-resolution problem, maximum likelihood parameter estimation, nonlinear least-squares estimation, numerical simulation, spaceborne SAR tomography, sparse spectral estimation, sp...     »