Efficient Representations of Signals in Nonlinear Signal Processing with Applications to Inverse Problems

Abstract

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.

References in corpus (9)

• Finding and evaluating community structure in networks
• Sparsity and Incoherence in Compressive Sampling
• Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples
• Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifolds
• On Low Rank Matrix Approximations with Applications to Synthesis Problem in Compressed Sensing
• On Verifiable Sufficient Conditions for Sparse Signal Recovery via ${\ell }_1$ Minimization
• An Analysis of the Convergence of Graph Laplacians
• Slepian functions and their use in signal estimation and spectral analysis
• Incoherent dictionaries and the statistical restricted isometry property

Cited by in corpus (1)

• Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion