Regularized image reconstruction in parallel MRI with MATLAB

✍ Scribed by Mathew, Raji Susan; Paul, Joseph Suresh

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 323
• Category: Library

✦ Synopsis

Parallel MR image reconstruction -- Regularization techniques for MR image reconstruction -- Regularization parameter selection methods in parallel MR image reconstruction -- Multi-filter calibration for autocalibrating parallel MRI -- Parameter adaptation for wavelet regularization in parallel MRI -- Parameter adaptation for total variation based regularization in parallel MRI -- Combination of parallel magnetic resonance imaging and compressed sensing using L1-SPIRiT -- Matrix completion methods -- MATLAB codes.;"This book provides a detailed discussion on the issues and challenges relating to choice and usage of regularization methods applied to pMRI reconstruction algorithms. The book summarizes aspects required for judiciously choosing regularization parameters for artifact and noise free reconstruction with relevance to specific reconstruction variant"--

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 12
Acknowledgements......Page 14
Authors......Page 16
1.1.2 Static Magnetic Field B0......Page 18
1.1.5 Gradient Fields......Page 19
1.1.6 Slice Selection......Page 20
1.1.8 Imaging......Page 21
1.2 Nyquist Limit and Cartesian Sampling......Page 24
1.3.1 Cartesian Imaging......Page 26
1.3.2 k-Space Features......Page 28
1.3.3.1 Data Acquisition and Pulse Sequencing......Page 30
1.3.3.2 Transformation from Non-Cartesian to Cartesian Data......Page 31
1.4 Parallel MRI......Page 32
1.4.1 Coil Combination......Page 33
1.5.1 Acceleration Using Pulse Sequences......Page 34
1.5.2 Acceleration Using Sampling Schemes......Page 35
1.5.3 Under-Sampled Acquisition and Sampling Trajectories......Page 36
1.5.4 Artifacts Associated with Different Sampling Trajectories......Page 37
1.6 Parallel Imaging Reconstruction Algorithms......Page 38
1.6.1.1 SENSE......Page 39
1.6.2 k-Space Based Reconstruction Methods......Page 41
1.6.2.1 SMASH......Page 42
1.6.2.2 GRAPPA......Page 43
1.6.2.3 SPIRiT......Page 46
1.6.2.4 Regularization in Auto-calibrating Methods......Page 47
1.6.3 CS MRI......Page 48
1.6.3.1 CS-Based MR Image Reconstruction Model......Page 49
1.6.3.2 Sparsity-Promoting Regularization......Page 50
1.6.4.1 Low-Rank CS-Based MR Image Reconstruction Model......Page 51
References......Page 53
2.1 Regularization of Inverse Problems......Page 60
2.2 MR Image Reconstruction as an Inverse Problem......Page 61
2.3.2 Condition Number......Page 62
2.3.3 Picard’s Condition......Page 63
2.4.2 Regularization by Penalization......Page 64
2.5.1 Tikhonov Regularization......Page 65
2.5.2 Conjugate Gradient Method......Page 67
2.5.3.1 Arnoldi Process......Page 69
2.5.3.2 Generalized Minimum Residual (GMRES) Method......Page 70
2.5.4 Landweber Method......Page 72
2.6 Regularization Approaches Using l1 Priors......Page 73
2.6.1 Solution to l1-Regularized Problems......Page 75
2.6.1.1 Sub-gradient Methods......Page 76
2.6.1.2 Constrained Log-Barrier Method......Page 77
2.6.1.3 Unconstrained Approximations......Page 78
2.7 Linear Estimation in pMRI......Page 84
2.7.1.1 Tailored GRAPPA......Page 86
2.7.1.2 Discrepancy-Based Adaptive Regularization......Page 87
2.7.1.4 Regularization in GRAPPA Using Virtual Coils......Page 88
2.7.1.5 Sparsity-Promoting Calibration......Page 89
2.8 Regularization in Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT)......Page 91
2.9 Regularization for Compressed Sensing MRI (CSMRI)......Page 92
References......Page 96
3.1 Regularization Parameter Selection......Page 102
3.2 Parameter Selection Strategies for Tikhonov Regularization......Page 104
3.2.1 Discrepancy Principle......Page 105
3.2.2 Generalized Discrepancy Principle (GDP)......Page 106
3.2.4 Stein’s Unbiased Risk Estimation (SURE)......Page 107
3.2.5 Bayesian Approach......Page 108
3.2.6 GCV......Page 109
3.2.7 Quasi-optimality Criterion......Page 110
3.2.8 L-Curve......Page 111
3.3 Parameter Selection Strategies for Truncated SVD (TSVD)......Page 112
3.4.1 Parameter Selection for Wavelet Regularization......Page 114
3.4.1.2 SUREShrink......Page 116
3.4.1.4 SUREblock......Page 118
3.4.1.5 False Discovery Rate......Page 119
3.4.1.6 Bayes Factor Thresholding......Page 120
3.4.1.7 BayesShrink......Page 121
3.4.1.8 Ogden’s Methods......Page 122
3.4.2 Methods for Parameter Selection in Total Variation (TV) Regularization......Page 123
3.4.2.1 PDE Approach......Page 124
3.4.2.2 Duality-Based Approaches......Page 125
3.4.2.3 Prediction Methods......Page 129
References......Page 131
4.2 Effect of Noise in Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) Calibration......Page 136
4.3 Monte Carlo Method for Prior Assessment of the Efficacy of Regularization......Page 137
4.4.1 Perturbation of ACS Data for Determination of Cross-over......Page 138
4.4.3 Application of GDP......Page 139
4.4.4 Determination of Cross-over......Page 140
4.5 Multi-filter Calibration Approaches......Page 145
4.5.1 MONKEES......Page 146
4.5.2 SV-GRAPPA......Page 149
4.5.3 Reconstruction Using FDR......Page 150
4.5.3.1 Implementation of FDR Reconstruction......Page 153
4.6 Effect of Noise Correlation......Page 158
References......Page 160
5.2 Structure of Wavelet Coefficients......Page 164
5.2.1 Statistics of Wavelet Coefficients......Page 165
5.3 CS Using Wavelet Transform Coefficients......Page 167
5.3.1.1 Model-Based RIP......Page 168
5.3.1.2 Model-Based Signal Recovery......Page 169
5.3.2 Wavelet Sparsity Model......Page 171
5.4 Influence of Threshold on Speed of Convergence and Need for Iteration-Dependent Threshold Adaptation......Page 172
5.5 Parallelism to the Generalized Discrepancy Principle (GDP)......Page 173
5.6 Adaptive Thresholded Landweber......Page 176
5.6.2 Numerical Simulation of Wavelet Adaptive Shrinkage CS Reconstruction Problem......Page 178
5.6.3 Illustration Using Single-Channel MRI......Page 180
5.6.4.2 Update Calculation Using SoS of Channel-wise Errors (Method II)......Page 182
5.6.4.3 Update Calculation Using Covariance Matrix (Method III)......Page 183
5.6.4.4 Illustration Using In Vivo Data......Page 184
5.6.4.5 Illustration Using Synthetic Data......Page 189
Appendix......Page 191
References......Page 193
6.1 Total Variation–Based Image Recovery......Page 198
6.2 Parameter Selection Using Continuation Strategies......Page 199
6.3 TV Iterative Shrinkage Based Reconstruction Model......Page 200
6.3.1 Derivative Shrinkage......Page 202
6.3.2 Selection of Initial Threshold......Page 203
6.4 Adaptive Derivative Shrinkage......Page 204
6.5 Algorithmic Implementation for Parallel MRI (pMRI)......Page 206
Appendix......Page 215
References......Page 226
7.1 Combination of Parallel Magnetic Resonance Imaging and Compressed Sensing......Page 230
7.2 L1-SPIRiT......Page 231
7.2.1 Reconstruction Steps for Non-Cartesian SPIRiT......Page 233
7.3 Computational Complexity in L1-SPIRiT......Page 234
7.4 Faster Non-Cartesian SPIRiT Using Augmented Lagrangian with Variable Splitting......Page 235
7.4.1 Regularized Non-Cartesian SPIRiT Using Split Bregman Technique......Page 236
7.4.2 Iterative Non-Cartesian SPIRiT Using ADMM......Page 237
7.4.3 Fast Iterative Cartesian SPIRiT Using Variable Splitting......Page 239
7.5 Challenges in the Implementation of L1-SPIRiT......Page 242
7.5.1 Effect of Incorrect Parameter Choice on Reconstruction Error......Page 243
7.6.1 Modification of Polynomial Mapping......Page 244
7.7 Automatic Parameter Selection for L1-SPIRiT Using Monte Carlo SURE......Page 245
7.8 Continuation-Based Threshold Adaptation in L1-SPIRiT......Page 246
7.8.1 L1-SPIRiT Examples......Page 247
7.9 Sparsity and Low-Rank Enhanced SPIRiT (SLR-SPIRiT)......Page 251
References......Page 253
8.2 Matrix Completion Problem......Page 256
8.3 Conditions Required for Accurate Recovery......Page 257
8.4 Algorithms for Matrix Completion......Page 258
8.4.1 SVT Algorithm......Page 259
8.4.3 Projected Landweber (PLW) Method......Page 260
8.4.4 Alternating Minimization Schemes......Page 261
8.4.4.1 Non-linear Alternating Least Squares Method......Page 262
8.4.4.3 ADMM for Matrix Completion without Factorization......Page 263
8.5 Methods for pMRI Acceleration Using Matrix Completion......Page 265
8.5.1 Simultaneous Auto-calibration and k-Space Estimation......Page 266
8.5.2 Low-Rank Modeling of Local k-Space Neighborhoods......Page 270
8.5.3 Annihilating Filter–Based Low-Rank Hankel Matrix Approach......Page 272
8.6 Non-convex Approaches for Structured Matrix Completion Solution for CS-MRI......Page 276
8.6.1 Solution Using IRLS Algorithm......Page 277
8.6.2 Solution Using Extension of Soft Thresholding......Page 278
8.7 Applications to Dynamic Imaging......Page 279
8.7.2 Solution Using ADMM......Page 280
References......Page 282
MATLAB Codes......Page 286
Index......Page 318

✦ Subjects

Image processing;Image reconstruction--Mathematical models;Magnetic resonance imaging;MATLAB;Image reconstruction -- Mathematical models