Robust sparse time-frequency analysis for data missing scenarios

Sparse time-frequency analysis (STFA) can precisely achieve the spectrum of the local truncated signal. However, when the signal is disturbed by unexpected data loss, STFA cannot distinguish effective signals from missing data interferences. To address this issue and establish a robust STFA model for time-frequency analysis (TFA) in data loss scenarios, a stationary Framelet transform-based morphological component analysis is introduced in the STFA. In the proposed model, the processed signal is regarded as a sum of the cartoon, texture and data-missing parts. The cartoon and texture parts are reconstructed independently by taking advantage of the stationary Framelet transform. Then, the signal is reconstructed for STFA. The forward-backwards splitting method is employed to split the robust STFA model into the data recovery and robust time-frequency imaging stages. The two stages are then solved separately by using the alternating direction method of multipliers (ADMM). Finally, several experiments are conducted to show the performance of the proposed robust STFA method under different data loss levels, and it is compared with some existing state-of-the-art time-frequency methods. The results indicate that the proposed method outperforms the compared methods in obtaining the sparse spectrum of the effective signal when data are missing. The proposed method has a potential value in TFA in scenarios where data is easily lost.