A0664
Title: Reproducing kernel approach to tomographic data
Authors: Ho Yun - EPFL (Switzerland)
Alessia Caponera - LUISS Guido Carli (Italy) [presenting]
Victor Panaretos - EPFL (Switzerland)
Abstract: Many natural phenomena pose challenges wherein the function of interest cannot be directly measured. For instance, the density of a brain cannot be directly measured; rather, it can only be evaluated through 2D sectional images via computerized tomography (CT). Tomography refers to a technique employed to produce sectional images at various orientations using penetrating waves, representing a non-invertible linear operator that maps the original function to a lower-dimensional function, such as positron emission tomography (PET) and quantum state tomography (QST). In such a setup where the true random function is a latent feature, how can their mean function and covariance tensor be estimated using discretized tomographic data? The tomographic operator is considered an operator between reproducing kernel Hilbert spaces (RKHS), and representer theorems are established to address the problem of mean and covariance estimation. The uniform rates of convergence of the estimators are also presented with respect to the observation scheme, evaluating efficiency through simulation results across various tomographic configurations.
