Abstract
This chapter will introduce the k-space formalism used in MR imaging for data encoding and image reconstruction via Fourier transforms (FT). Essentially, this formalism is a mathematical construct that allows for the description of acquired MRI data in a domain described as spatial-frequency space, or k-space, which is related to the desired image space representation via the Fourier transform. Representing the data as k-space converts the time varying signal acquired with the MR receiving coils into a 2D or 3D data space that can be readily reconstructed into an image representation by applying the well-known Fourier transform. Understanding MRI acquisitions and reconstructions in terms of k-space is a crucial step in understanding the basic relationships between the acquisition and the reconstructed images, most acceleration and reconstruction techniques, sources of artifacts and their appearance, and advanced acquisition strategies.
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Abbreviations
- AD converter:
-
Analog-to-digital converter
- CT:
-
Computed tomography
- EPI:
-
Echo-planar imaging
- FID:
-
Free induction decay
- FOV:
-
Field-of-view
- FT:
-
Fourier transform
- Rf:
-
Radio frequency
- SNR:
-
Signal-to-noise ratio
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Loecher, M., Wieben, O. (2015). k-Space. In: Syed, M., Raman, S., Simonetti, O. (eds) Basic Principles of Cardiovascular MRI. Springer, Cham. https://doi.org/10.1007/978-3-319-22141-0_2
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DOI: https://doi.org/10.1007/978-3-319-22141-0_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22140-3
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