Abstract

Functional data such as space curves, images, and surfaces are seldom sensed directly; curves are often noisily and discretely sampled, images are subject to blurring and deformation, and surfaces are often obtained via indirect linear measurements. Understanding the generation of the observations then requires modelling the act of acquisition, and solving an inverse problem in order to arrive at statistical inferences. This leads to a host of new research questions, from identifiability to trade-offs between statistical optimality and computational feasibility, which also make contact with signal processing and numerical analysis.