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An Introduction to Mathematics of Emerging Biomedical Imaging [electronic resource] /by Habib Ammari.

by Ammari, Habib [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: MathéMatiques & Applications: 62Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: online resource.ISBN: 9783540795537.Subject(s): Mathematics | Differential Equations | Differential equations, partial | Potential theory (Mathematics) | Biology -- Mathematics | Mathematics | Mathematical Biology in General | Potential Theory | Partial Differential Equations | Ordinary Differential EquationsDDC classification: 570.151 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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