Advanced Image Reconstruction Methods in MRI - Advance Image Processing in Magnetic Resonance Imaging - page 37

2 Advanced Image

Reconstruction
Methods in MRI

Leslie Ying 1 and Zhi-Pei Liang

CONTENTS

2.1Introduction................................................................................................40
2.2Fourier Reconstruction..............................................................................40
2.3Constrained Image Reconstruction...........................................................43
2.3.1Nonparametric Methods................................................................43
2.3.2Parametric Methods.......................................................................45
2.3.3Application Examples...................................................................46
2.4Regularized Image Reconstruction in Parallel MRI.................................48
2.4.1Basic Reconstruction Methods......................................................48
2.4.2Regularized Reconstruction Methods...........................................50
2.4.2.1Construction of

ρ r

.........................................................50

.................................................................51
2.4.2.3 Sensitivity Analysis ........................................................52
2.4.3 Application Example .....................................................................53
2.5 Conclusion .................................................................................................54
References ...........................................................................................................55

2.4.2.2Selection of λ

This chapter provides a tutorial overview of advanced image reconstruction methods
used in MRI. The term “advanced” is used loosely to refer to the class of non-
Fourier reconstruction methods developed for handling the inverse problem with
limited Fourier samples. We will consider two specific cases: (a) the superresolution
reconstruction problem (associated with limited Fourier samples collected at the
Nyquist rate) and (b) the parallel imaging problem (arising when Fourier samples
are collected at sub-Nyquist rates, using multiple nonuniform receiver channels).
For notational convenience, we will consider only the one-dimensional case.
The following is a summary of notations used in this chapter.

ρ x

ˆ ()

() Desired image

Reconstructed image ρ x

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