An Introduction to Mathematics of Emerging Biomedical Imaging (Mathématiques et Applications Book 62)

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. Front Matter....Pages i-xii Biomedical Imaging Modalities....Pages 3-13 Preliminaries....Pages 17-41 Layer Potential Techniques....Pages 43-92 Tomographic Imaging with Non-Diffracting Sources....Pages 95-106 Tomographic Imaging with Diffracting Sources....Pages 107-115 Biomagnetic Source Imaging....Pages 117-123 Small Volume Expansions....Pages 127-149 Imaging Techniques....Pages 151-166 Magnetic Resonance Electrical Impedance Tomography....Pages 169-175 Impediography....Pages 177-182 Magnetic Resonance Elastography....Pages 183-187 Back Matter....Pages 189-198