MRI Essentials for Innovative Technologies
MRI Essentials for Innovative Technologies

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Magnetic resonance imaging (MRI) is recognized as one of the most advanced computerized imaging modalities. This imaging technology provides capabilities to reveal structure and function of the human body with a level of detail beyond that obtained with other diagnostic or its unique flexibility

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I Basic Concepts 1
1 Mathematical Tools 3
1.1 Frequency Encoding and Fourier Transform 3
1.2 FT Properties 12
1.3 Sampling, Interpolation, and Aliasing . 18
1.4 Instruments for Image Analysis . 24
2 MRI: Conventional Imaging Techniques and Instruments 27
2.1 Magnetic Resonance Phenomenon . 28
2.1.1 References Frames 31
2.1.2 Excitation and Resonance 32
2.1.3 Relaxation of Magnetization . 35
2.1.3.1 Longitudinal Relaxation 39
2.1.3.2 Transverse Relaxation . 40
2.1.4 Signal Detection . 43
2.2 Imaging Gradients 48
2.2.1 Frequency Encoding . 50
2.2.2 Phase Encoding . 50
2.2.3 Slice Selection 53
2.3 Conventional Imaging Techniques . 56
2.3.1 Spin Warp Imaging 56
2.3.2 Imaging from Projections 58
2.4 Bandwidth, Sampling, Resolution, and Sensitivity 64
2.5 An MRI Scanner . 67
2.6 Bloch Equations and Numerical MRI Simulators . 69
II Limitations of Conventional MRI 72
3 Limiting Artifacts for Advanced Applications 73
3.1 Magnetic Field Inhomogeneity . 74
3.2 Motion 81
3.3 Undersampling 83
3.4 Summary . 91
III Advanced Solutions 92
4 Methods for Magnetic Field Inhomogeneity Reduction 93
4.1 Introduction . 94
4.2 ConventionalMethods 95
4.2.1 FieldMapping 95
4.2.2 Field Gradients Modulation . 98
4.2.3 SomeRemarks 103
4.3 AnUnconventionalSolution 104
4.3.1 Spatial Encoding by Nonconstant Gradients 105
4.3.1.1 Numerical Simulations . 109
4.3.1.2 NoiseTolerance 112
4.4 Summary . 119
5 Methods to Handle Undersampling 121
5.1 Introduction . 121
5.2 SparseMethodswithoutRestoration . 123
5.3 SparseMethodswithRestoration . 129
5.3.1 Sample Adaptive Acquisition/Restoration Methods 129
5.3.1.1 Entropy-Based Adaptive Acquisition Method 130
5.3.1.2 Adaptive Acquisition Results . 134
5.3.1.3 An Adaptive Acquisition Improvement . 138
5.3.2 Sample Independent Acquisition/Restoration Methods 146
5.3.2.1 Compressed Sensing 147
5.3.2.1.1 Compressed Sensing Results 157
5.3.2.1.2 Some Remarks on Compressed SensinginMRI 159
5.3.2.2 Compressed Sensing on Adaptively Collected
Data 160
5.4 Summary . 169
IV The Future 170
6 Conclusions and perspectives 171
6.1 SomeHypothesis . 173

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