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

This paper introduces a new approach of the mean Euler-Poincaré 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 Poincaré Characteristic (EPC)
$\varphi (A_{u}(\Phi,\mathcal {T}))$
. The highlight of this work is an explicit model, referred to as the decomposed mean Euler-Poincaré 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.