PROBLEMS IN IMAGING
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 [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
Experimental data sets
l [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
l [MRE, chap 10] GE-Elastography