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The Mathematics of Medical Imaging [electronic resource] : A Beginner’s Guide / by Timothy G. Feeman.

By: Feeman, Timothy G [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Undergraduate Texts in Mathematics and Technology: Publisher: New York, NY : Springer New York, 2010Description: X, 141p. 20 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387927121.Subject(s): Mathematics | Radiology, Medical | Computer science | Computer vision | Functional analysis | Integral Transforms | Biomedical engineering | Mathematics | Functional Analysis | Imaging / Radiology | Integral Transforms, Operational Calculus | Math Applications in Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Biomedical EngineeringDDC classification: 515.7 Online resources: Click here to access online
Contents:
X-rays -- The Radon Transform -- Back Projection -- Complex Numbers -- The Fourier Transform -- Two Big Theorems -- Filters and Convolution -- Discrete Image Reconstruction -- Algebraic Reconstruction Techniques -- MRI—An Overview.
In: Springer eBooksSummary: A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography – the CT scan – for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. The text is self-contained with a range of practical exercises, topics for further study, and an ample bibliography, making it ideal for use in an undergraduate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of their field.
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X-rays -- The Radon Transform -- Back Projection -- Complex Numbers -- The Fourier Transform -- Two Big Theorems -- Filters and Convolution -- Discrete Image Reconstruction -- Algebraic Reconstruction Techniques -- MRI—An Overview.

A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography – the CT scan – for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. The text is self-contained with a range of practical exercises, topics for further study, and an ample bibliography, making it ideal for use in an undergraduate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of their field.

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