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Sampling Theory, a Renaissance: Compressive Sensing and Other Developments (Applied and Numerical Harmonic Analysis)

Editat de Götz E. Pfander
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en Limba Engleză Carte Hardback – 18 Dec 2015
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.
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Specificații

ISBN-13: 9783319197487
ISBN-10: 3319197487
Pagini: 532
Ilustrații: 29 schwarz-weiße und 38 farbige Abbildungen, 1 schwarz-weiße Tabellen, Bibliographie
Dimensiuni: 155 x 235 x 27 mm
Greutate: 10.39 kg
Ediția: 1st ed. 2015
Editura: Springer
Colecția Birkhäuser
Seria Applied and Numerical Harmonic Analysis

Locul publicării: Cham, Switzerland

Public țintă

Research

Cuprins

Part I: Sparsity Models.- Estimation in High Dimensions: A Geometric Perspective.- Convex Recovery of a Structured Signal from Independent Random Linear Measurements.- Low Complexity Regularization of Linear Inverse Problems.- Part II: Frames with Benefits.- Noise-shaping Quantization Methods for Frame-based and Compressive Sampling Systems.- Fourier Operations in Applied Harmonic Analysis.- The Fundamentals of Spectral Tetris Frame Constructions.- Part III: Bandlimitation Recast.- System Approximation and Generalized Measurements in Modern Sampling Theory.- Entire Functions in Generalized Bernstein Spaces and Their Growth Behavior.- Sampling and Geometry.- A Sheaf-theoretic Perspective on Sampling.- Part IV: Solutions of Parametric PDEs.- How to Best Sample a Solution Manifold?.- On the Stability of Polynomial Interpolation using Hierarchical Sampling.- Part V: Implementation.- OperA: Operator-based Annihilation for Finite-Rate-of-Innovation Signal Sampling.- Digital Adaptive Calibration of Data Converters using Independent Component Analysis.

Textul de pe ultima copertă

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.

Caracteristici

Tutorial style articles on new high-impact topics in sampling and applications
Offers experts in sampling theory (mathematicians and engineers) new insights into the wide area of sampling theory
Includes a great breadth of topics ranging from the analysis of real world analog, to digital converters, to generalizations of sampling theory in abstract geometry