The focus of this thesis is the construction and analysis of efficient representations in nonlinear signal processing, and the applications of these structures to inverse problems in a variety of fields. The work is composed of three major sections, each associated with a different form of data: - Regression and Distance Estimation on Graphs and Riemannian Manifolds. - Instantaneous Time-Frequency Analysis via Synchrosqueezing. - Multiscale Dictionaries of Slepian Functions on the Sphere.
@article{arxiv.2109.09625,
title = {Efficient Representations of Signals in Nonlinear Signal Processing with Applications to Inverse Problems},
author = {Eugene Brevdo},
journal= {arXiv preprint arXiv:2109.09625},
year = {2021}
}