A PDE‐regularized smoothing method for space–time data over manifolds with application to medical data

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.