Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise

TL;DR

This paper introduces a convex optimization method for two-dimensional line spectral estimation that effectively handles spiky noise, with theoretical guarantees and confirmed by simulations.

Contribution

A novel convex program that jointly estimates spectral sources and spiky noise, with mild separation conditions and logarithmic bounds on spikes and sources.

Findings

Dual certificate existence guarantees solution uniqueness.

Number of spikes and sources scales logarithmically with samples.

Simulation results validate theoretical predictions.

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.