Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise
Abstract
The aim of two-dimensional line spectral estimation is to super-resolve the spectral point sources of the signal from time samples. In many associated applications such as radar and sonar, due to cut-off and saturation regions in electronic devices, some of the numbers of samples are corrupted by spiky noise. To overcome this problem, we present a new convex program to simultaneously estimate spectral point sources and spiky noise in two dimensions. To prove uniqueness of the solution, it is sufficient to show that a dual certificate exists. Construction of the dual certificate imposes a mild condition on the separation of the spectral point sources. Also, the number of spikes and detectable sparse sources are shown to be a logarithmic function of the number of time samples. Simulation results confirm the conclusions of our general theory.
Keywords
Cite
@article{arxiv.1807.01185,
title = {Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise},
author = {Iman Valiulahi and Farzan Haddadi and Arash Amini},
journal= {arXiv preprint arXiv:1807.01185},
year = {2020}
}