Frequency estimation without missing measurements under impulsive noise

The frequency recovery problem from impulse noise corrupted signal is considered by exploring the signal sparse property. Through creating a DFT-like matrix, the frequency sparsity is revealed in the frequency domain, and then utilized to formulate a sparsity-inspired frequency estimation approach. Special treatment is required when it comes to impulsive noise corrupted signal. Thanks to the exciting finding of the nearly-sparse property of the impulsive noise in the time domain, the noise reduction approach is designed to explore its sparsity to cancel the noise. By utilizing the sparsity of both frequency and noise, a joint frequency estimation and impulsive noise reduction approach is achieved. Numerical studies demonstrate that joint estimate offers robust and consistent results compared to the non-joint estimate (without noise reduction).