| 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: (1) Regression and Distance Estimation on Graphs and Riemannian Manifolds. (2) Instantaneous Time-Frequency Analysis via Synchrosqueezing. (3) Multiscale Dictionaries of Slepian Functions on the Sphere. |
