Image Processing Reference
In-Depth Information
3
Parallel MRI: Concepts
and Methods
Walid Elias Kyriakos and W. Scott Hoge
CONTENTS
3.1 Introduction ................................................................................................57
3.2 History of Parallel MRI .............................................................................58
3.3 Formulation of the Problem .......................................................................61
3.3.1 Fourier Encoding ............................................................................62
3.3.2 Sampling at the Nyquist Rate and Equation
Independence ..................................................................................63
3.3.3 Parallel Imaging Methods ..............................................................64
3.3.3.1 Coil-Sensitivity Estimation..............................................64
3.3.3.2 Parallel MR Image Reconstruction
Techniques ........................................................................65
3.3.3.3 K-Space Approaches........................................................65
3.3.3.4 Image Domain Approaches .............................................70
3.4 Examples ....................................................................................................74
3.4.1 Example 1: Uniform Subsampling.................................................74
3.4.2 Example 2: Variable Subsampling .................................................76
3.4.3 Example 3: In vivo Applications ...................................................78
3.5 Summary.....................................................................................................79
References ...........................................................................................................80
3.1
INTRODUCTION
Throughout history, human nature's fascination with speed has constituted the main
driver for technological advancement. From the wheel to the space shuttle, the
pursuit of speed has been a defining attribute of our civilization, as the realization
of mortality pushes us to find faster ways to experience, understand, and interact
with our reality. Short of being an essay on the philosophy of speed, this chapter
pertains to increasing the speed of image acquisition in the medical imaging
modality of magnetic resonance imaging (MRI).
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