Hypersampling of pseudo-periodic signals by analytic phase projection

TL;DR

This paper introduces a hypersampling method for pseudo-periodic signals that significantly increases effective sampling rate, enabling detailed analysis of fast brain waveforms from MRI data and potentially other neural signals.

Contribution

The paper presents a novel hypersampling technique using analytic phase projection that enhances sampling rate based on a reference signal, improving analysis of pseudo-periodic signals.

Findings

Effective sampling rate increased by three orders of magnitude in MRI data

Method captures fast cerebral pulse waveforms with high fidelity

Numerical comparison shows advantages over retrospective gating

Abstract

A method to upsample insufficiently sampled experimental time series of pseudo-periodic signals is proposed. The result is an estimate of the pseudo-periodic cycle underlying the signal. This hypersampling requires a sufficiently sampled reference signal that defines the pseudo-periodic dynamics. The time series and reference signal are combined by projecting the time series values to the analytic phase of the reference signal. The resulting estimate of the pseudo-periodic cycle has a considerably higher effective sampling rate than the time series. The procedure is applied to time series of MRI images of the human brain. As a result, the effective sampling rate could be increased by three orders of magnitude. This allows for capturing the waveforms of the very fast cerebral pulse waves traversing the brain. Hypersampling is numerically compared to the more commonly used retrospective gating. An outlook regarding EEG and optical recordings of brain activity as the reference signal is provided.