Topological Time Frequency Analysis of Functional Brain Signals

TL;DR

This paper introduces a topological framework combining persistent homology with time-frequency analysis to extract noise-invariant features from brain signals, enhancing understanding of functional connectivity in neuroscience.

Contribution

It presents a novel method integrating topological data analysis with time-frequency analysis for brain signals, capturing multi-scale features.

Findings

Successfully applied to resting-state fMRI data

Identified topological patterns related to brain connectivity

Demonstrated robustness to noise and temporal misalignments

Abstract

We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that characterize the dynamic behavior of brain activity. This approach identifies 0D (connected components) and 1D (loops) topological structures in the signal's time-frequency domain, enabling robust extraction of features invariant to noise and temporal misalignments. The proposed method is demonstrated on resting-state functional magnetic resonance imaging (fMRI) data, showcasing its ability to discern critical topological patterns and provide insights into functional connectivity. This topological approach opens new avenues for analyzing complex brain signals, offering potential applications in neuroscience and clinical diagnostics.