# Single-lead f-wave extraction using diffusion geometry

## TL;DR

This paper introduces DD-NLEM, a novel diffusion geometry-based algorithm for single-lead f-wave extraction that outperforms traditional methods in simulations and shows clinical potential.

## Contribution

The paper presents DD-NLEM, a new diffusion geometry framework for f-wave extraction, combining diffusion distance and non-local Euclidean median, improving over existing algorithms.

## Key findings

- DD-NLEM outperforms traditional algorithms in simulations.
- The algorithm shows promise in real Holter signals.
- A new performance evaluation score is introduced.

## Abstract

A novel single-lead f-wave extraction algorithm based on the modern diffusion geometry data analysis framework is proposed. The algorithm is essentially an averaged beat subtraction algorithm, where the ventricular activity template is estimated by combining a newly designed metric, the "diffusion distance," and the non-local Euclidean median based on the non-linear manifold setup. We coined the algorithm DD-NLEM. Two simulation schemes are considered, and the new algorithm DD-NLEM outperforms traditional algorithms, including the average beat subtraction, principal component analysis, and adaptive singular value cancellation, in different evaluation metrics with statistical significance. The clinical potential is shown in the real Holter signal, and we introduce a new score to evaluate the performance of the algorithm.