**NONLINEAR INVERSE**

**PROBLEMS IN IMAGING**

ISBN: 978-0-470-66942-6

This companion website to the book is to provide further
examples and solutions, experimental data sets, open problems, teaching
material such as lecture notes and PowerPoint slides, and software including
MATLAB m files.
Click on the link below to access downloadable
resources.

Mathematical
techniques in science and engineering have evolved to expand our ability to
visualize various physical phenomena of interest and their characteristics in
detail. Many significant applied and
basic research questions today are interdisciplinary in nature, involving
mathematics, physics, engineering and biomedical science. A large variety of
natural phenomena occurring in real life
applications from science and engineering to medical imaging fields are described by means of partial
differential equations. Developing mathematical models with practical significance and
value requires fusing the knowledge and
techniques of the traditional engineering fields with pure and applied
mathematics. Many problems are intrinsically nonlinear. Finding
solutions with practical significance and value requires in-depth understanding
of the underlying physical phenomena with data acquisition systems as well as
implementation details of algorithms. Experiences over the last three decades
showed that symbiotic interplay among theories and experiments is crucial for
understanding and solving these realistic model problems.

This book
provides researchers and engineers in the imaging field with the skills they
need to effectively deal with nonlinear inverse problems associated with
different imaging modalities, including impedance imaging, elastography, and
electrical source imaging. Focusing on numerically implementable methods, the
book bridges the gap between theory and applications, helping readers tackle
problems in applied mathematics and engineering. Complete, self-contained
coverage includes basic concepts, models, computational methods, numerical
simulations, examples, and case studies.

** Lecture Notes & Slides**

l
[Linear Algebra, chap
2] Lecture slide (Text book:
Strang's Computational Science & Engineering) , Lecture slide (Text book Strang's Computational
Science & Engineering)

l
[PDE & Analysis, chap 3,4,8] Lecture slide (Text book:
Real Analysis by Marsden) , Lecture slide (Measure theory)
, Lecture
notes: Harmonic analysis by R. Brown , Sobolev space by
Shkoller , Methods
of Applied Math. by Arbogast & Bona, Fundamentals
of Fluid mechanics by CH Lee

l
[Numerical Method,
chap 5] Multi-scale
modeling & stabilization by EJ Park

l
[CT, MRI & Image processing problems,
chap 6] LV
contour-ultrasound, Dental CT, Compressed
Sensing: A Tutorial by Romberg & Wakin , Image Processing
webpage by Terence Tao., Convex and
Optimization by Boyd & Vandenebrghe

l
[EIT, MREIT chap 7, 9] EIT Overview, MREIT forward
simulation, EIT&MREIT
by Seo , MR-based EIT Wave
length effect by Woo , MREIT(NFSI2011)
by Woo, MREIT(ISMRM2011)
by Woo, D-bar method by Siltannen

l
[MRI] Theory of RF Reciprocity by
Greig Scott , Basics in
MRI

**Experim****ental data sets**

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[EIT, chap 7] Data by KHU

l
[MREIT, chap 9] Data by KHU

l
[MRE, chap 10] Data

**Software
including MATLAB m files**

l
[Numerical Method, chap 5] C,C++,Fortran,matlab,JAVA,Latex,Python
codes for various problems

l
[EIT, chap 7] EIDORS

l
[MREIT, chap 9] Matlab Toolkit COREHA

**Further examples and solutions**** **

**Open problems**

**Useful links**

l [MRE,
chap 10] GE-Elastography

l [EIT, chap 7] PulmoVista @500, Drager.
Technology for life , Electrical
Impedance Mammography