Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise
arXiv:1807.01185 · doi:10.1109/TSP.2019.2951220
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.
References in corpus (8)
- On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data
- Robust Spectral Compressed Sensing via Structured Matrix Completion
- Super-Resolution Delay-Doppler Estimation for OFDM Passive Radar
- Super-Resolution Sparse MIMO-OFDM Channel Estimation Based on Spatial and Temporal Correlations
- On the efficiency of techniques for the reduction of impulsive noise in astronomical images
- Two-Dimensional Super-Resolution via Convex Relaxation
- Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise
- Off-the-grid Two-Dimensional Line Spectral Estimation With Prior Information