Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.
Author(s): Götz E. Pfander (ed.)
Series: Applied and Numerical Harmonic Analysis
Edition: 1
Publisher: Birkhäuser
Year: 2015
Language: English
Pages: 532
Tags: Information and Communication, Circuits; Signal, Image and Speech Processing; Approximations and Expansions; Appl.Mathematics/Computational Methods of Engineering; Functions of a Complex Variable
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Estimation in High Dimensions: A Geometric Perspective....Pages 3-66
Convex Recovery of a Structured Signal from Independent Random Linear Measurements....Pages 67-101
Low Complexity Regularization of Linear Inverse Problems....Pages 103-153
Front Matter....Pages 155-155
Noise-Shaping Quantization Methods for Frame-Based and Compressive Sampling Systems....Pages 157-184
Fourier Operators in Applied Harmonic Analysis....Pages 185-215
The Fundamentals of Spectral Tetris Frame Constructions....Pages 217-266
Front Matter....Pages 267-267
System Approximations and Generalized Measurements in Modern Sampling Theory....Pages 269-305
Entire Functions in Generalized Bernstein Spaces and Their Growth Behavior....Pages 307-329
Sampling in Euclidean and Non-Euclidean Domains: A Unified Approach....Pages 331-359
A Sheaf-Theoretic Perspective on Sampling....Pages 361-399
Front Matter....Pages 401-401
How To Best Sample a Solution Manifold?....Pages 403-435
On the Stability of Polynomial Interpolation Using Hierarchical Sampling....Pages 437-458
Front Matter....Pages 459-459
OperA: Operator-Based Annihilation for Finite-Rate-of-Innovation Signal Sampling....Pages 461-484
Digital Adaptive Calibration of Data Converters Using Independent Component Analysis....Pages 485-517
Back Matter....Pages 519-532
