Analysis of Noisy Transient Signals Based on Gaussian Process Regression

Dynamic systems such as cells or tissues generate, either spontaneously or in response to stimuli, transient signals that carry information about the system. Characterization of recorded transients is often hampered by a low signal-to-noise ratio (SNR). Reduction of the noise by filtering has limited use due to partial signal distortion. Occasionally, transients can be approximated by a mathematical function, but such a function may not hold correctly if recording conditions change. We introduce here the model-independent approximation method for general noisy transient signals based on the Gaussian process regression (GPR). 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 cellular model of the calcium concentration transient corrupted by various SNR levels and recorded at a low sampling frequency. Statistical analysis of the model data sets provided the error of estimation <7.5% and the coefficient of variation of estimates <17% for peak SNR=5. The performance of GPR on signals of diverse experimental origin was even better than fitting by a function. The software and its description are available on GitHub. Statement of Significance Transient signals convey information on the state and function of the studied system. However, the estimation of their characteristic parameters is complicated by the noise present in the recordings. Methods used for noise reduction have various disadvantages, such as distortion of the time course by filtering, the difficult superposition of many transients for accurate averaging, or a lack of a model for data fitting. In this work, we present a general method for the automatic analysis of noisy transient signals based on Gaussian process regression and its implementation in Python. The method can analyze recorded transients reliably at peak SNR ≥ 2 with a precision equivalent to the model-fitting methods.