- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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.
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
