Robust Time-Frequency Analysis Based on the L-Estimation and Compressive Sensing

The L-estimate transforms and time-frequency representations are presented within the framework of compressive sensing. The goal is to recover signal or local auto-correlation function samples corrupted by impulse noise. The signal is assumed to be sparse in a transform domain or in a joint-variable representation. Unlike the standard L-statistics approach, which suffers from degraded spectral characteristics due to the omission of samples, the compressive sensing in combination with the L-estimate permits signal reconstruction that closely approximates the noise free signal representation.