Recovery methodologies: regularization and sampling
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 betwee...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2023]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 274 |
| Schlagworte: | |
| Online-Zugang: | Verlagsinformation |
| Zusammenfassung: | 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. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xii, 490 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470473457 |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 274 | |
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| 520 | 3 | |a 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. | |
| 653 | 0 | |a Sampling (Statistics) | |
| 653 | 0 | |a Inverse problems (Differential equations) / Numerical solutions | |
| 653 | 0 | |a Numerical analysis -- Numerical analysis in abstract spaces -- Improperly posed problems; regularization | |
| 653 | 0 | |a Statistics -- Sampling theory, sample surveys -- Sampling theory, sample surveys | |
| 653 | 0 | |a Numerical analysis -- Integral equations, integral transforms -- Inverse problems | |
| 653 | 0 | |a Optics, electromagnetic theory -- General -- Antennas, wave-guides | |
| 653 | 0 | |a Information and communication, circuits -- Communication, information -- Sampling theory | |
| 653 | 0 | |a Geophysics -- Geophysics -- Inverse problems | |
| 700 | 1 | |a Nashed, M. Zuhair |d 1936- |e Verfasser |0 (DE-588)141023589 |4 aut | |
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| id | DE-604.BV049488861 |
| illustrated | Illustrated |
| index_date | 2024-07-03T23:19:21Z |
| indexdate | 2024-07-10T10:08:42Z |
| institution | BVB |
| isbn | 9781470473457 |
| language | English |
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| physical | xii, 490 Seiten Illustrationen, Diagramme |
| publishDate | 2023 |
| publishDateSearch | 2023 |
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| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
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| spelling | Freeden, Willi 1948- Verfasser (DE-588)121167259 aut Recovery methodologies regularization and sampling Willi Freeden, M. Zuhair Nashed Providence, Rhode Island American Mathematical Society [2023] xii, 490 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 274 Includes bibliographical references and index 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. Sampling (Statistics) Inverse problems (Differential equations) / Numerical solutions Numerical analysis -- Numerical analysis in abstract spaces -- Improperly posed problems; regularization Statistics -- Sampling theory, sample surveys -- Sampling theory, sample surveys Numerical analysis -- Integral equations, integral transforms -- Inverse problems Optics, electromagnetic theory -- General -- Antennas, wave-guides Information and communication, circuits -- Communication, information -- Sampling theory Geophysics -- Geophysics -- Inverse problems Nashed, M. Zuhair 1936- Verfasser (DE-588)141023589 aut Erscheint auch als Online-Ausgabe 978-1-4704-7451-5 Mathematical surveys and monographs Volume 274 (DE-604)BV000018014 274 https://bookstore.ams.org/view?ProductCode=SURV/274 Verlagsinformation |
| spellingShingle | Freeden, Willi 1948- Nashed, M. Zuhair 1936- Recovery methodologies regularization and sampling Mathematical surveys and monographs |
| title | Recovery methodologies regularization and sampling |
| title_auth | Recovery methodologies regularization and sampling |
| title_exact_search | Recovery methodologies regularization and sampling |
| title_exact_search_txtP | Recovery methodologies regularization and sampling |
| title_full | Recovery methodologies regularization and sampling Willi Freeden, M. Zuhair Nashed |
| title_fullStr | Recovery methodologies regularization and sampling Willi Freeden, M. Zuhair Nashed |
| title_full_unstemmed | Recovery methodologies regularization and sampling Willi Freeden, M. Zuhair Nashed |
| title_short | Recovery methodologies |
| title_sort | recovery methodologies regularization and sampling |
| title_sub | regularization and sampling |
| url | https://bookstore.ams.org/view?ProductCode=SURV/274 |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT freedenwilli recoverymethodologiesregularizationandsampling AT nashedmzuhair recoverymethodologiesregularizationandsampling |