Overview

The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.

Full Product Details

Author:   Willi Freeden ,  M. Zuhair Nashed
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.299kg
ISBN:  

9781470473457

ISBN 10:   1470473453
Pages:   491
Publication Date:   30 November 2023
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Introductory remarks: Constituents of the univariate antenna problem Regularization tools: Functional and Fourier analytic auxiliaries Regularization methodologies: Matricial methodologies of resolution Compact operator methodologies of resolution Example realizations light: Univariate differentiation Reconstruction and regularization methods Regularization examples: Regularization methodologies in geotechnology Sampling tools: Lattice point and special function theoretic auxiliaries Sampling methodologies: Sampling over continuously connected pointsets Sampling over discretely given pointsets Polyharmonic finite bandwidth sampling Polyharmonic infinite bandwidth sampling Polymetaharmonic finite bandwidth sampling Polymetaharmonic infinite bandwidth sampling Sampling examples: Sampling methodologies in technology Concluding remarks: Recovery as interconnecting whole List of symbols Bibliography Index

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Author Information

Willi Freeden, University of Kaiserslautern, Germany. M. Zuhair Nashed, University of Central Florida, Orlando, FL.

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