A PDE-regularized smoothing method for space-time data over manifolds with application to medical data
Keywords
Statistical learning
Computational Medicine for the Cardiocirculatory System
Code:
76/2021
Title:
A PDE-regularized smoothing method for space-time data over manifolds with application to medical data
Date:
Sunday 28th November 2021
Author(s):
Ponti, L.; Perotto, S.; Sangalli, L.M.
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Abstract:
We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold.
The proposed approach consists of a regression model completed with a regularizing term based on the heat equation.
The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm.
This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with
massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool
in practical contexts by dealing with neuroimaging and hemodynamic data.