Low-Rank Hankel Matrix Completion for Robust Time-Frequency Analysis

Abstract

In this paper, we develop a novel method to enable robust sparsity-based time-frequency representation of multi-component frequency modulated signals in the presence of burst missing samples, where the amplitudes of the different signal components are generally different. Unlike existing methods which require cross-term presence to be sparse in the time-frequency domain, the proposed method permits effective time-frequency representation reconstruction even when undesired cross-terms take a high occupancy. A key enabling procedure is the high-fidelity missing entry recovery of the instantaneous autocorrelation function that is insensitive to cross-terms. By designing instantaneous autocorrelation function patches such that their Doppler-frequency domain representation is sparse, we formulate the instantaneous autocorrelation function recovery problem as a patch-based low-rank block Hankel matrix completion problem. This approach effectively suppresses the effects of burst missing data samples and is robust to the amplitude differences. A data-adaptive time-frequency kernel is then applied to further mitigate the undesired cross-terms and the residual artifacts due to the burst missing samples. We prove the superiority of the proposed method over the state of the art for both multi-component linear and nonlinear frequency modulated signals. Simulation results confirm that the proposed method outperforms the state of the art for different types of frequency modulated signals with varying signal-to-noise ratios and missing sample rates.