Two robust approaches to multicomponent signal reconstruction from STFT ridges. (15th January 2019) - Zhu, Xiangxiang; Zhang, Zhuosheng; Gao, Jinghuai; Li, Wenting
Highlights: Two robust signal reconstruction approaches by STFT ridges are proposed. Adaptive weights are assigned to different ridge points. SPRR can avoid a bad reconstruction in the presence of missing observations. The proposed methods have high reconstruction accuracy and noise robustness. The methods can be effectively applied to the weak fault feature extraction. Abstract: The problem of how to accurately reconstruct the multicomponent signal from the ridges of the short-time Fourier transform (STFT) is considered. Especially when time-frequency representations contain strong noise corruption and crossed components, exact reconstruction becomes more difficult. In this paper, we propose two robust ridge reconstruction approaches, i.e., weighted ridge reconstruction (WRR) and self-paced ridge reconstruction (SPRR). The former is aim to select a more robust loss function to eliminate the influence of the strong noise and outliers. A half-quadratic optimization algorithm is developed to solve the proposed problem efficiently. The latter incorporates self-paced learning (SPL) method into ridge reconstruction model to sequentially include ridge points into signal reconstruction from easy to complex, which not only can suppress noise and outliers, but also can avoid a bad result in the presence of missing observations. Simulation and real-life signals are employed to show the effectiveness and practicability of the proposed approaches.