Learning the Morphology of Brain Signals Using Alpha-Stable Convolutional Sparse Coding

TL;DR

This paper introduces a robust probabilistic convolutional sparse coding model using alpha-stable distributions to extract meaningful neural signal waveforms from noisy, artifact-laden brain recordings, advancing analysis in clinical and cognitive neuroscience.

Contribution

The study presents a novel alpha-stable convolutional sparse coding model with an efficient Monte Carlo EM algorithm, improving robustness and speed over existing methods for neural signal analysis.

Findings

Achieves state-of-the-art convergence speeds

More robust to artifacts than competing algorithms

Effectively extracts spike bursts, oscillations, and cross-frequency coupling

Abstract

Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such 'shift-invariant' atoms. Even though some success has been reported with existing algorithms, they are limited in applicability due to their heuristic nature. Moreover, they are often vulnerable to artifacts and impulsive noise, which are typically present in raw neural recordings. In this study, we address these issues and propose a novel probabilistic convolutional sparse coding (CSC) model for learning shift-invariant atoms from raw neural signals containing potentially severe artifacts. In the core of our model, which we call $\alpha$CSC, lies a family of heavy-tailed distributions called $\alpha$-stable distributions. We develop a novel, computationally efficient Monte Carlo expectation-maximization algorithm for inference. The maximization step boils down to a weighted CSC problem, for which we develop a computationally efficient optimization algorithm. Our results show that the proposed algorithm achieves state-of-the-art convergence speeds. Besides, $\alpha$CSC is significantly more robust to artifacts when compared to three competing algorithms: it can extract spike bursts, oscillations, and even reveal more subtle phenomena such as cross-frequency coupling when applied to noisy neural time series.