Abstract
In this chapter, Fourier transforms of dimension greater than one (i.e., 2-D, 3-D, etc.) are considered, and the specific application of magnetic resonance imaging is employed to demonstrate their use and relevance in biomedical sciences. First, a brief introduction to the physical basis of nuclear magnetic resonance (NMR) is presented. This should provide an intuitive understanding of basic events in an NMR experiment. Next, the concept of magnetic field gradients is developed, and their use in magnetic resonance imaging (MRI) described. The relationship between the received signal in MRI and the Fourier transform of the object being imaged is the focus of this section. Having established the Fourier view of MRI, this chapter concludes with a discussion of two advanced topics, magnetic resonance spectroscopic imaging (MRSI) and motion effects in MRI. The purpose of these sections is to illustrate the simplifying and unifying powers of a Fourier perspective in MRI.
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Pike, G.B. (1998). Multidimensional Fourier Transforms in Magnetic Resonance Imaging. In: Peters, T.M., Williams, J. (eds) The Fourier Transform in Biomedical Engineering. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0637-8_4
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DOI: https://doi.org/10.1007/978-1-4612-0637-8_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6849-9
Online ISBN: 978-1-4612-0637-8
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