This book highlights recent mathematical developments in emerging biomedical imaging techniques, with a focus is on multi-physics and multi-scales imaging approaches. It provides the basic mathematical concepts and tools for image reconstruction.

Mathematical Tools.- Biomedical Imaging Modalities.- Preliminaries.- Layer Potential Techniques.- General Reconstruction Algorithms.- Tomographic Imaging with Non-Diffracting Sources.- Tomographic Imaging with Diffracting Sources.- Biomagnetic Source Imaging.- Anomaly Detection Algorithms.- Small Volume Expansions.- Imaging Techniques.- Hybrid Imaging Techniques.- Magnetic Resonance Electrical Impedance Tomography.- Impediography.- Magnetic Resonance Elastography.

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.

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)

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 Includes supplementary material: sn.pub/extras