Improved higher order robust distributions based on compressive sensing reconstruction

A general form of compressive sensing (CS)-based higher order time-frequency distributions (TFDs) is proposed. Non-linear time-varying spectrum analysis requires higher order TFDs, but they cannot produce efficient result in the presence of strong noisy pulses. Consequently, the time-frequency analysis needs to be combined with the L-statistics. When applied to the higher order local auto-correlation function, the L-statistics removes all possibly corrupted samples and just a small number of samples remains for distribution calculation. In the proposed approach the discarded information can be completely recovered using CS reconstruction. Owing to the use of higher order local auto-correlation function, the signal becomes locally sparse in the transform domain. Hence, the idea is to cast all noisy samples as missing ones, then reconstruct the entire information and produce highly concentrated representation in the transform domain. The proposed CS-based distribution form provides significantly improved performance compared to the existing standard and L-estimate forms. It is proven by various experiments.