Wavelet functional data analysis - applications to images

Abstract

Functional data analysis has been pursued in various ways. A very competitive paradigm is given by statistical wavelet analysis of functional data. This is due for several reasons, such as: parsimony; asymptotic optimality; its natural representation of images and other stochastic processes; and computational efficiency. This project of undergraduate research assistantship aims the student to learn the elementary theory of wavelets, and the most important wavelet-based statistical tools. It is specially important to learn the numerical aspects of its application to real data sets, as well as the specificities of applying them to image analysis. The student shows great potential for graduate studies. She has the second best GPA in her year, almost double of the overall GPA for her class. This project would be an excellent form of her initiating her academic career. The just edited book from the supervisor (Morettin, Pinheiro and Vidakovio, 2017) would be one of the theretical bases for the project, along with papers from the state of the art on the areas of application (Kim et al., 201r and Morettin, Pinheiro and Vidakovic, 2017), as well as four classic monographs: Vidakovic (1999); Wojtaszczyk (1999); Ramsay and Silverman (2002, 2005); e Morettin (2014).