Two robust approaches to multicomponent signal reconstruction from STFT ridges

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.