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arXiv · 1807.01185

Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise

Iman Valiulahi·Farzan Haddadi·Arash Amini
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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.

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Iman Valiulahi, Farzan Haddadi, Arash Amini. 2018-07-03. Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise. https://doi.org/10.1109/tsp.2019.2951220

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