Decomposed Mean Euler-Poincaré Characteristic Model for a Non-Gaussian Physiological Random Field

Moises Ramos-Martinez,Christophe Corbier,Victor M Alvarado,Guadalupe Lopez Lopez

doi:10.1109/access.2020.3048712

Abstract

This paper introduces a new approach of the mean Euler-Poincare characteristic for non-Gaussian random fields (NGRF), which is based on the decomposition by a basic function named mother-wave . The method is proved for long-term recorded, noisy physiological signals. A pretreatment allows the signal to become smooth as the original one is fitted through a Random Algebraic Polynomials (RAP)-based scheme. After that, the polynomized signals are merged by thresholding the RAP function at different levels $u$ . In this way, it is formed a real-valued non-Gaussian physiological random field (NGPRF). Thereby, we deal with their geometric properties centered on their excursion sets $A_{u}(\Phi,\mathcal {T})$ and a topological invariant, such as the Euler Poincare Characteristic (EPC) $\varphi (A_{u}(\Phi,\mathcal {T}))$ . The highlight of this work is an explicit model, referred to as the decomposed mean Euler-Poincare characteristic (DMEPC). The proposed method produces a reduced model with a viable interpretation for different heart conditions investigated for data issued from Holter EKG recordings.

Highlights

Random Fields (RF) give a statistical description of complex random patterns of change and relationships from physical data sets [1]–[3]
Because limited cases can be defined in this way, and it is difficult to get a function F to encode the behavior of nonGaussian random fields (NGRF), we introduce an approach focused on the mean Euler-Poincaré characteristic (MEPC)
We propose a new characteristic through a decomposition that we refer to as the decomposed mean Euler-Poincaré characteristic (DMEPC)

Summary

Introduction

Random Fields (RF) give a statistical description of complex random patterns of change and relationships from physical data sets [1]–[3]. The geometry and regularity properties of RF have been largely discussed in the literature. These features have to do with continuity and differentiability notions [5] and still with the geometry generated by RF through their excursion sets over a level u [4]. Gaussian Random Fields (GRF) is a class of RF for which the finite-dimensional distributions are multivariable normal distributions that can be fully specified by expectations and covariances. A noticeable issue has been accessing information from biomedical images. In this case, Gaussian Markov Random Fields (GMRF) provide a spatial-contextual knowledge

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Conclusion