An introduction to mathematics of emerging biomedical imaging
Preface
This book has grown out of lecture notes for a course on mathematical methods
in biomedical imaging at Ecole Polytechnique.
Biomedical imaging is a fascinating research area to applied mathematicians.
It is quite a hot topic that appeals to many students. Challenging
imaging problems arise and they often trigger the investigation of fundamental
problems in various branches of mathematics (including inverse problems,
PDEs, harmonic analysis, complex analysis, numerical analysis, optimization,
image analysis). Many applied mathematicians have experienced a great feeling
of accomplishment when they saw their work having a real impact on
medical and clinical decision making.
In this book, we underscore the importance of mathematical aspects of
emerging biomedical imaging. We acknowledge that biomedical technology
has already had success in performing imaging in many different contexts,
however in this book we highlight the most recent developments in emerging,
non standard, techniques that are not yet established as standard imaging
tools. The contents of this book introduce the reader to the basic mathematical
concepts of biomathematical imaging and lay the ground for advanced issues
in innovative techniques in the field.
This book may be used for a graduate-level course in applied mathematics
and should help prepare the reader for a deeper understanding of research
areas in biomedical imaging. Some background knowledge of PDEs is assumed.
I thank Frank Bauer, Natacha B´ereux, Yves Capdeboscq, and Darko
Volkov for reading an early version of this book and making a number of
helpful suggestions. I am also indebted to Sylvain Baillet and Mickael Tanter
for providing me with some of the illustrations presented in this book. Finally,
I would like to acknowledge the support by the ANR project EchoScan
(AN-06-Blan-0089).
Paris, June 2007 Habib Ammari
Download
http://s18.alxa.net/s18/srvs2/02/003...al.imaging.rar
Preface
This book has grown out of lecture notes for a course on mathematical methods
in biomedical imaging at Ecole Polytechnique.
Biomedical imaging is a fascinating research area to applied mathematicians.
It is quite a hot topic that appeals to many students. Challenging
imaging problems arise and they often trigger the investigation of fundamental
problems in various branches of mathematics (including inverse problems,
PDEs, harmonic analysis, complex analysis, numerical analysis, optimization,
image analysis). Many applied mathematicians have experienced a great feeling
of accomplishment when they saw their work having a real impact on
medical and clinical decision making.
In this book, we underscore the importance of mathematical aspects of
emerging biomedical imaging. We acknowledge that biomedical technology
has already had success in performing imaging in many different contexts,
however in this book we highlight the most recent developments in emerging,
non standard, techniques that are not yet established as standard imaging
tools. The contents of this book introduce the reader to the basic mathematical
concepts of biomathematical imaging and lay the ground for advanced issues
in innovative techniques in the field.
This book may be used for a graduate-level course in applied mathematics
and should help prepare the reader for a deeper understanding of research
areas in biomedical imaging. Some background knowledge of PDEs is assumed.
I thank Frank Bauer, Natacha B´ereux, Yves Capdeboscq, and Darko
Volkov for reading an early version of this book and making a number of
helpful suggestions. I am also indebted to Sylvain Baillet and Mickael Tanter
for providing me with some of the illustrations presented in this book. Finally,
I would like to acknowledge the support by the ANR project EchoScan
(AN-06-Blan-0089).
Paris, June 2007 Habib Ammari
Download
http://s18.alxa.net/s18/srvs2/02/003...al.imaging.rar