Robust Mean Signal Estimation and Inference for Imaging Data

In this paper, we propose a robust nonparametric method for learning and inferring from noisy imaging data by modeling it as contaminated functional data, which enables accurate estimation of the underlying signals and efficient detection and localization of significant effects.The proposed robust and smoothed M-estimator is based on bivariate penalized splines over triangulation, effectively addressing challenges posed by contaminated imaging data, spatial dependencies, and irregular domains commonly encountered in imaging applications.We establish the L2 convergence of the proposed M-based mean function estimator under certain regularity conditions and investigate its asymptotic normality.Additionally, we present a novel approach for constructing a simultaneous confidence corridor for the mean signal of a set of noisy imaging data.Extensive simulation studies and a real-data application with brain imaging data illustrate the effectiveness of the proposed robust methods.