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© 2008

An Introduction to Mathematics of Emerging Biomedical Imaging

Benefits

  • First book about emerging techniques such as multi-scales and multi-physics approaches

  • Moreover, most recent mathematical and numerical results are described in readable and informative manner

  • Contains also recent results on time-reversal, electrical impedance tomography, and brain imaging

Book

Part of the MathéMatiques & Applications book series (MATHAPPLIC, volume 62)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Mathematical Tools

  3. General Reconstruction Algorithms

  4. Anomaly Detection Algorithms

    1. Pages 127-149
    2. Pages 151-166
  5. Hybrid Imaging Techniques

  6. Back Matter
    Pages 189-198

About this book

Introduction

Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics.

This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so.

The volume is suitable for a graduate-level course in applied mathematics and  helps prepare the reader for a deeper understanding of research areas in biomedical imaging.

Keywords

algorithms anomaly detection biomedical imaging image reconstruction inverse problems linear optimization reconstruction algorithms

Authors and affiliations

  1. 1.Centre de Mathématiques AppliquéesÉcole Polytechnique91128France

About the authors

Habib Ammari (born in June 1969) received the B.S., M.S., and Ph.D. degrees in mathematics from École Polytechnique Palaiseau in 1992, 1993, and 1995, respectively, and the Habilitation Degree from Université Pierre et Marie Curie (Paris 6), in 1999. He is currently Director of Research at the French Center of Scientific Research (CNRS). His current research interests include biomedical imaging, electrical impedance tomography, inverse problems, and electromagnetic modelling. He has contributed over 100 peer-reviewed articles and book chapters, authored four books and edited three others. He is serving as an editor of several mathematical journals. Habib Ammari has been invited to more than 30 international conferences. He produced 10 Ph.D. students and served as adviser for 10 post-docs.

Bibliographic information

Industry Sectors
Pharma
Health & Hospitals
Biotechnology
Electronics
Internal Medicine & Dermatology

Reviews

From the reviews:

“This book consists of an introductive chapter, four parts, a bibliography, and an index. … The book may be useful for non-specialists … . Students may use this book … .” (Alexander G. Ramm, Zentralblatt MATH, Vol. 1181, 2010)

“This monograph presents an overview of medical imaging techniques based on many different modalities (X-rays, magnetic fields, ultrasound, microwaves, elasticity and others). The treatment is fairly concise … . The book can be used as a basis of a graduate course, or read as a survey of cutting-edge research in biomedical imaging.”­­­ (Fritz Keinert, Mathematical Reviews, Issue 2010 j)