A fast threshold OMP based on self-learning dictionary for propeller signal reconstruction

The acquisition of propeller signals can be applied to localization and fault diagnosis, etc. However, recording a large amount of propeller signals results in higher costs. Compressive sensing (CS) is an effective approach to processing large data. CS algorithms work well for sparse signals, but propeller signals are non-sparse in both the time and frequency domains. Therefore, the traditional fixed dictionary, such as discrete cosine transform (DCT), has a limited sparse representation of propeller signals. We propose a self-learning dictionary in this study, the self-learning dictionary uses the propeller signal as input to train the dictionary, and the trained dictionary can be stored and used for sparse representation of propeller signals. Based on the self-learning dictionary, we propose a threshold orthogonal matching pursuit based on QR decomposition (TOMP-QR) algorithm. We use the ratio of two energy thresholds as the stopping condition of the TOMP-QR algorithm, which is more robust under arbitrary noise. Then, we use QR decomposition to reduce the complexity of the algorithm. The simulation results verify the effectiveness of the proposed method in signal reconstruction accuracy and running time. Based on DCT, discrete wavelet transform (DWT) and self-learning dictionary, we compare the TOMP-QR algorithm with TOMP, OMP, sparsity adaptive matching pursuit (SAMP) and stage wise OMP (StOMP) algorithm to reconstruct propeller signals in the experiment, the results show that the effectiveness and superiority of the self-learning dictionary and TOMP-QR algorithm.