Variational Methods in Imaging

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With its mathematically rigorous presentation, this book is a detailed treatment of the approach from an inverse problems point of view. It is geared towards graduate students and researchers in applied mathematics and can serve as a text for graduate courses.
This book focuses on variational methods in imaging science. Many numerical examples accompany the theory throughout the text. This systematic presentation includes additional material and images available on the website. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.
Fundamentals of Imaging.- Case Examples of Imaging.- Image and Noise Models.- Regularization.- Variational Regularization Methods for the Solution of Inverse Problems.- Convex Regularization Methods for Denoising.- Variational Calculus for Non-convex Regularization.- Semi-group Theory and Scale Spaces.- Inverse Scale Spaces.- Mathematical Foundations.- Functional Analysis.- Weakly Differentiable Functions.- Convex Analysis and Calculus of Variations.
This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.
Autor: Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, Frank Lenzen
Editiert von: S.S. Antman, J. E. Marsden, L. Sirovich
RezensionFrom the reviews:"Imaging is a wide area of applied mathematics which covers inverse problems, data filtering. medical diagnosis, etc. The book is structured in a logical manner, starting with motivating examples and building on them. One of the strengths of this book is its real-life applications and analytical and numerical results presented at each step, keeping the content real. This is. a book for the seasoned researchers or graduate students who look to deepen their understanding of the subject." (Bogdan G. Nita, Mathematical Reviews, Issue 2009 j)"The book is mainly devoted to variational methods in imaging. It is divided into three parts. The book is interesting in particular for its rigorous presentation of many proved mathematical results, and is. important for the image processing community." (Alessandro Duci, Zentralblatt MATH, Vol. 1177, 2010)
Autor: Otmar Scherzer
ISBN-13:: 9780387309316
ISBN: 0387309314
Erscheinungsjahr: 01.11.2008
Verlag: Springer-Verlag GmbH
Gewicht: 597g
Seiten: 320
Sprache: Englisch
Sonstiges: Buch, 245x162x23 mm, 40 schw.-w. Abb., 40 schw.-w. Zeichn.