Period Extraction Algorithm of Astronomical Light Curve Signal Based on Mahalanobis Distance Weighted Path Graph

Astronomical light curve signal is a signal to measure the change of celestial radiation flux with time, which is characterized by multi period, non-uniformity, large interval and noise. The period extraction of light curve signal is helpful to reveal the physical mechanism behind celestial bodies. Traditional period extraction algorithms can't make full use of signals with large intervals, and will lose some information, leading to the inability to extract small periods of some light curve signals. The graph structure can implicitly express the relationship between data in the graph by establishing the connection relationship between nodes, fully mining the contact information between data, and obtaining the small period components that can't be extracted by traditional period extraction algorithms. In this paper, the graph signal processing (GSP) method is applied to the period extraction of light curve signals, and a period extraction algorithm based on Mahalanobis distance weighted path graph Fourier transform is proposed. The algorithm first converts the light curve signal into a path graph signal, then uses the Mahalanobis distance to weight the connected edges to represent the non-uniformity of signal sampling, and finally uses the Graph Fourier transform (GFT) to obtain the eigenvalue spectrum domain of the signal, and then extracts the periodic components of the signal. The analysis results of simulation data and real data show that the period extraction algorithm based on GFT and Mahalanobis distance weighting can accurately identify all the periodic components of the light curve signal.