Analysis of noisy transient signals based on Gaussian process regression

Abstract

Transient signals convey information on the state and function of the studied system. The estimation of characteristic parameters of transient signals is complicated by the noise in the records. The reduction of noise by filtering leads to certain signal distortion. Alternatively, the transient signal can be approximated by a mathematical function, if available. We introduce here the model-independent approximation method for general noisy transient signals based on the Gaussian process regression. The method was implemented in the software TransientAnalyzer, which detects transients in a record, finds their best approximation by the Gaussian process, constructs a surrogate spline function, and estimates specified signal parameters. The method and software were tested on a model of the calcium concentration transient, characterized by abrupt rise and slow decay, contaminated by various signal-to-noise ratios, and recorded at a low sampling frequency. Statistics of the analyzed data set revealed that the software estimates all signal parameters reliably. The error of estimation and the standard deviation of estimates were less than 10% for SNR ≥ 7. The software and its description are available on GitHub.