Time-frequency manifold histogram matching for transient signal detection

Time-frequency manifold (TFM) is learned from the time-frequency distribution (TFD) of an analyzed signal by addressing manifold learning on multiple TFDs in a reconstructed phase space. This paper explores the probability distribution property of the TFM by using the image histogram concept, and proposes a TFM histogram matching method to build a relationship between the original TFD and the learned TFM. The proposed method provides a novel idea to modify the time-frequency representation by employing the histogram matching concept in image processing. It is to build a gray transform function to modify the TFD so that its histogram matches that of the TFM. With the TFM matching function built from a short signal, the TFM result can be then approximately achieved for a long transient signal. Consequently, a TFM analysis and synthesis scheme is constructed for detection of transient signal corrupted by noise. The proposed scheme is a data-driven approach and the detected result could keep the intrinsic time-frequency structure of the transient signal and remove the in-band noise. A case study verifies the excellent performance of the proposed method.