Abstract:

To estimate the line spectrum of data corrupted with outliers, a robust atomic norm denoising method is proposed. In the method, an optimization problem jointly estimating the outliers and the original signal is formulated. By adding an l₁ norm penalty on the outliers and an atomic norm penalty on the signal to the cost function, the sparsity in the outliers and the signal own characteristics are constrained. Once the optimization problem is solved, the existed spectral estimation algorithms can be used to estimate the spectrum of the denoised signal. The simulation results indicate that when the observed data are corrupted with outliers, the proposed method can acquire a more accurate original signal estimation, thus the spectral estimation will be of higher precision and resolution.