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E-raamat: Regularized Image Reconstruction in Parallel MRI with MATLAB

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  • Formaat: 322 pages
  • Ilmumisaeg: 05-Nov-2019
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351029254
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Regularized Image Reconstruction in Parallel MRI with MATLABSuurem pilt
  • Formaat: 322 pages
  • Ilmumisaeg: 05-Nov-2019
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351029254
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Regularization becomes an integral part of the reconstruction process in accelerated parallel magnetic resonance imaging (pMRI) due to the need for utilizing the most discriminative information in the form of parsimonious models to generate high quality images with reduced noise and artifacts. Apart from providing a detailed overview and implementation details of various pMRI reconstruction methods, Regularized image reconstruction in parallel MRI with MATLAB examples interprets regularized image reconstruction in pMRI as a means to effectively control the balance between two specific types of error signals to either improve the accuracy in estimation of missing samples, or speed up the estimation process. The first type corresponds to the modeling error between acquired and their estimated values. The second type arises due to the perturbation of k-space values in autocalibration methods or sparse approximation in the compressed sensing based reconstruction model.

Features:











Provides details for optimizing regularization parameters in each type of reconstruction.





Presents comparison of regularization approaches for each type of pMRI reconstruction.





Includes discussion of case studies using clinically acquired data.





MATLAB codes are provided for each reconstruction type.





Contains method-wise description of adapting regularization to optimize speed and accuracy.

This book serves as a reference material for researchers and students involved in development of pMRI reconstruction methods. Industry practitioners concerned with how to apply regularization in pMRI reconstruction will find this book most useful.
Preface xi
Acknowledgements xiii
Authors xv
1 Parallel MR Image Reconstruction
1(42)
1.1 Basics of MRI
1(6)
1.1.1 Basic Elements of an MR System
1(1)
1.1.2 Static Magnetic Field B0
1(1)
1.1.3 RF Magnetic Field B1
2(1)
1.1.4 RF Receiver
2(1)
1.1.5 Gradient Fields
2(1)
1.1.6 Slice Selection
3(1)
1.1.7 Generation of FID
4(1)
1.1.8 Imaging
4(3)
1.2 Nyquist Limit and Cartesian Sampling
7(2)
1.3 Pulse Sequencing and k-Space Filling
9(6)
1.3.1 Cartesian Imaging
9(2)
1.3.2 k-Space Features
11(2)
1.3.3 Non-Cartesian Imaging
13(1)
1.3.3.1 Data Acquisition and Pulse Sequencing
13(1)
1.3.3.2 Transformation from Non-Cartesian to Cartesian Data
14(1)
1.4 Parallel MRI
15(2)
1.4.1 Coil Combination
16(1)
1.5 MR Acceleration
17(4)
1.5.1 Acceleration Using Pulse Sequences
17(1)
1.5.2 Acceleration Using Sampling Schemes
18(1)
1.5.3 Under-Sampled Acquisition and Sampling Trajectories
19(1)
1.5.4 Artifacts Associated with Different Sampling Trajectories
20(1)
1.6 Parallel Imaging Reconstruction Algorithms
21(15)
1.6.1 Image-Based Reconstruction Methods
22(1)
1.6.1.1 Sense
22(2)
1.6.2 k-Space Based Reconstruction Methods
24(1)
1.6.2.1 Smash
25(1)
1.6.2.2 Grappa
26(3)
1.6.2.3 Spirit
29(1)
1.6.2.4 Regularization in Auto-calibrating Methods
30(1)
1.6.3 CS MRI
31(1)
1.6.3.1 CS-Based MR Image Reconstruction Model
32(1)
1.6.3.2 Sparsity-Promoting Regularization
33(1)
1.6.4 CS Recovery Using Low-Rank Priors
34(1)
1.6.4.1 Low-Rank CS-Based MR Image Reconstruction Model
34(2)
References
36(7)
2 Regularization Techniques for MR Image Reconstruction
43(42)
2.1 Regularization of Inverse Problems
43(1)
2.2 MR Image Reconstruction as an Inverse Problem
44(1)
2.3 Well-Posed and Ill-Posed Problems
45(2)
2.3.1 Moore-Penrose Pseudo-Inverse
45(1)
2.3.2 Condition Number
45(1)
2.3.3 Picard's Condition
46(1)
2.4 Types of Regularization Approaches
47(1)
2.4.1 Regularization by Reducing the Search Space
47(1)
2.4.2 Regularization by Penalization
47(1)
2.5 Regularization Approaches Using l2 Priors
48(8)
2.5.1 Tikhonov Regularization
48(2)
2.5.2 Conjugate Gradient Method
50(2)
2.5.3 Other Krylov Sub-space Methods
52(1)
2.5.3.1 Arnoldi Process
52(1)
2.5.3.2 Generalized Minimum Residual (GMRES) Method
53(2)
2.5.3.3 Conjugate Residual (CR) Algorithm
55(1)
2.5.4 Landweber Method
55(1)
2.6 Regularization Approaches Using l1 Priors
56(11)
2.6.1 Solution to l1-Regularized Problems
58(1)
2.6.1.1 Sub-gradient Methods
59(1)
2.6.1.2 Constrained Log-Barrier Method
60(1)
2.6.1.3 Unconstrained Approximations
61(6)
2.7 Linear Estimation in pMRI
67(7)
2.7.1 Regularization in GRAPPA-Based pMRI
69(1)
2.7.1.1 Tailored GRAPPA
69(1)
2.7.1.2 Discrepancy-Based Adaptive Regularization
70(1)
2.7.1.3 Penalized Coefficient Regularization
71(1)
2.7.1.4 Regularization in GRAPPA Using Virtual Coils
71(1)
2.7.1.5 Sparsity-Promoting Calibration
72(2)
2.7.1.6 KS-Based Calibration
74(1)
2.8 Regularization in Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT)
74(1)
2.9 Regularization for Compressed Sensing MRI (CSMRI)
75(4)
Appendix
79(1)
References
79(6)
3 Regularization Parameter Selection Methods in Parallel MR Image Reconstruction
85(34)
3.1 Regularization Parameter Selection
85(2)
3.2 Parameter Selection Strategies for Tikhonov Regularization
87(8)
3.2.1 Discrepancy Principle
88(1)
3.2.2 Generalized Discrepancy Principle (GDP)
89(1)
3.2.3 Unbiased Predictive Risk Estimator (UPRE)
90(1)
3.2.4 Stein's Unbiased Risk Estimation (SURE)
90(1)
3.2.5 Bayesian Approach
91(1)
3.2.6 GCV
92(1)
3.2.7 Quasi-optimality Criterion
93(1)
3.2.8 L-Curve
94(1)
3.3 Parameter Selection Strategies for Truncated SVD (TSVD)
95(2)
3.4 Parameter Selection Strategies for Non-quadratic Regularization
97(22)
3.4.1 Parameter Selection for Wavelet Regularization
97(2)
3.4.1.1 VisuShrink
99(1)
3.4.1.2 SUREShrink
99(2)
3.4.1.3 NeighBlock
101(1)
3.4.1.4 SUREblock
101(1)
3.4.1.5 False Discovery Rate
102(1)
3.4.1.6 Bayes Factor Thresholding
103(1)
3.4.1.7 BayesShrink
104(1)
3.4.1.8 Ogden's Methods
105(1)
3.4.1.9 Cross-validation
106(1)
3.4.1.10 Wavelet Thresholding
106(1)
3.4.2 Methods for Parameter Selection in Total Variation (TV) Regularization
106(1)
3.4.2.1 PDE Approach
107(1)
3.4.2.2 Duality-Based Approaches
108(4)
3.4.2.3 Prediction Methods
112(7)
References 114(155)
4 Multi-filter Calibration for Auto-calibrating Parallel MRI
119(28)
4.1 Problems Associated with Single-Filter Calibration
119(1)
4.2 Effect of Noise in Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) Calibration
119(1)
4.3 Monte Carlo Method for Prior Assessment of the Efficacy of Regularization
120(1)
4.4 Determination of Cross-over
121(7)
4.4.1 Perturbation of ACS Data for Determination of Cross-over
121(1)
4.4.2 First Order Update of Singular Values
122(1)
4.4.3 Application of GDP
122(1)
4.4.4 Determination of Cross-over
123(5)
4.5 Multi-filter Calibration Approaches
128(13)
4.5.1 MONKEES
129(3)
4.5.2 SV-GRAPPA
132(1)
4.5.3 Reconstruction Using FDR
133(3)
4.5.3.1 Implementation of FDR Reconstruction
136(5)
4.6 Effect of Noise Correlation
141(2)
Appendix
143(1)
References
143(4)
5 Parameter Adaptation for Wavelet Regularization in Parallel MRI
147(34)
5.1 Image Representation Using Wavelet Basis
147(1)
5.2 Structure of Wavelet Coefficients
147(3)
5.2.1 Statistics of Wavelet Coefficients
148(2)
5.3 CS Using Wavelet Transform Coefficients
150(5)
5.3.1 Structured Sparsity Model
151(1)
5.3.1.1 Model-Based RIP
151(1)
5.3.1.2 Model-Based Signal Recovery
152(2)
5.3.2 Wavelet Sparsity Model
154(1)
5.4 Influence of Threshold on Speed of Convergence and Need for Iteration-Dependent Threshold Adaptation
155(1)
5.4.1 Selection of Initial Threshold
156(1)
5.5 Parallelism to the Generalized Discrepancy Principle (GDP)
156(3)
5.6 Adaptive Thresholded Landweber
159(15)
5.6.1 Level-Dependent Adaptive Thresholding
161(1)
5.6.2 Numerical Simulation of Wavelet Adaptive Shrinkage CS Reconstruction Problem
161(2)
5.6.3 Illustration Using Single-Channel MRI
163(2)
5.6.4 Application to pMRI
165(1)
5.6.4.1 Update Calculation Using Error Information from Combined Image (Method I)
165(1)
5.6.4.2 Update Calculation Using SoS of Channel-wise Errors (Method II)
165(1)
5.6.4.3 Update Calculation Using Covariance Matrix (Method III)
166(1)
5.6.4.4 Illustration Using In Vivo Data
167(5)
5.6.4.5 Illustration Using Synthetic Data
172(2)
Appendix
174(2)
References
176(5)
6 Parameter Adaptation for Total Variation-Based Regularization in Parallel MRI
181(32)
6.1 Total Variation-Based Image Recovery
181(1)
6.2 Parameter Selection Using Continuation Strategies
182(1)
6.3 TV Iterative Shrinkage Based Reconstruction Model
183(4)
6.3.1 Derivative Shrinkage
185(1)
6.3.2 Selection of Initial Threshold
186(1)
6.4 Adaptive Derivative Shrinkage
187(2)
6.5 Algorithmic Implementation for Parallel MRI (pMRI)
189(9)
Appendix
198(11)
References
209(4)
7 Combination of Parallel Magnetic Resonance Imaging and Compressed Sensing Using L1-SPIRiT
213(26)
7.1 Combination of Parallel Magnetic Resonance Imaging and Compressed Sensing
213(1)
7.2 L1-SPIRiT
214(3)
7.2.1 Reconstruction Steps for Non-Cartesian SPIRIT
216(1)
7.3 Computational Complexity in L1-SPIRiT
217(1)
7.4 Faster Non-Cartesian SPIRiT Using Augmented Lagrangian with Variable Splitting
218(7)
7.4.1 Regularized Non-Cartesian SPIRiT Using Split Bregman Technique
219(1)
7.4.2 Iterative Non-Cartesian SPIRiT Using ADMM
220(2)
7.4.3 Fast Iterative Cartesian SPIRiT Using Variable Splitting
222(3)
7.5 Challenges in the Implementation of L1-SPIRiT
225(2)
7.5.1 Effect of Incorrect Parameter Choice on Reconstruction Error
226(1)
7.6 Improved Calibration Framework for L1-SPIRiT
227(1)
7.6.1 Modification of Polynomial Mapping
227(1)
7.6.2 Regularization Parameter Choice
228(1)
7.7 Automatic Parameter Selection for L1-SPIRiT Using Monte Carlo SURE
228(1)
7.8 Continuation-Based Threshold Adaptation in L1-SPIRiT
229(5)
7.8.1 L1-SPIRiT Examples
230(4)
7.9 Sparsity and Low-Rank Enhanced SPIRiT (SLR-SPIRiT)
234(2)
References
236(3)
8 Matrix Completion Methods
239(30)
8.1 Introduction
239(1)
8.2 Matrix Completion Problem
239(1)
8.3 Conditions Required for Accurate Recovery
240(1)
8.3.1 Matrix Completion under Noisy Condition
241(1)
8.4 Algorithms for Matrix Completion
241(7)
8.4.1 SVT Algorithm
242(1)
8.4.2 FPCA Algorithm
243(1)
8.4.3 Projected Landweber (PLW) Method
243(1)
8.4.4 Alternating Minimization Schemes
244(1)
8.4.4.1 Non-linear Alternating Least Squares Method
245(1)
8.4.4.2 ADMM with Nonnegative Factors
246(1)
8.4.4.3 ADMM for Matrix Completion without Factorization
246(2)
8.5 Methods for pMRI Acceleration Using Matrix Completion
248(11)
8.5.1 Simultaneous Auto-calibration and k-Space Estimation
249(4)
8.5.2 Low-Rank Modeling of Local k-Space Neighborhoods
253(2)
8.5.3 Annihilating Filter-Based Low-Rank Hankel Matrix Approach
255(4)
8.6 Non-convex Approaches for Structured Matrix Completion Solution for CS-MRI
259(3)
8.6.1 Solution Using IRLS Algorithm
260(1)
8.6.2 Solution Using Extension of Soft Thresholding
261(1)
8.7 Applications to Dynamic Imaging
262(3)
8.7.1 RPCA
263(1)
8.7.2 Solution Using ADMM
263(2)
References
265(4)
Matlab Codes 269(32)
Index 301
Joseph Suresh Paul

Joseph Suresh Paul is currently a Professor at the Indian Institute of Information Technology and Management- Kerala (IIITM-K), India. He obtained his Ph.D. degree in Electrical Engineering from the Indian Institute of Technology, Madras, India in the year 2000. His research is focused on MR imaging from the perspective of accelerating image acquisition, with the goal of enhancing clinically relevant features using filters integrated into the reconstruction process. His other interests include mathematical applications to problems in MR image reconstruction, compressed sensing, and super resolution techniques for MRI. He has published a number of articles in peer-reviewed international journals of high repute.

Raji Susan Mathew

Raji Susan Mathew is currently pursuing her Ph.D. degree in the area of MR image reconstruction. She received bachelor degree in Electronics and Communication Engineering from the Mahatma Gandhi university, Kottayam and master's degree in signal processing from the Cochin university of science and technology, Kochi in 2011 and 2013. She is a recipient of the Maulana Azad National Fellowship (MANF) by the University Grants Commission (UGC), India. Her research interests include regularization techniques for MR image reconstruction and Compressed Sensing.
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