Atomic Decomposition by Basis Pursuit
SIAM Review
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In this work Sparse Approximation methods for frequency estimation of complex exponentials in white Gaussian noise are evaluated and compared against classical frequency estimation approaches. We use a non-equidistant sampling scheme which allows reconstructing frequencies far beyond the Nyquist rate. The evaluation is done for signals composed of one single complex exponential or the sum of two complex exponentials. We show that for the latter case the SA methods outperform the classical approaches. Especially when only a small number of signal samples are available the performance gain becomes significant.