A Relationship Between the False Alarm Probability and the Atomic Norm Denoising Regularization Parameter for Line Spectral Estimation

Atomic norm denoising is an efficient approach for line spectral estimation. Contrary to other classical sparse methods it operates without the need to discretize the parameter space and avoids the corresponding gridding error. In this letter, we provide an accurate asymptotic expression that links its regularization parameter to the false alarm probability when the latter is low, in presence of white Gaussian noise. Numerical results confirm the accuracy of the proposed expression that allows to tune the regularization parameter accordingly.