Magnetic Resonance Image Reconstruction: Theory, Methods and Applications presents the fundamental concepts of MR image reconstruction, including its formulation as an inverse problem, as well as the most common models and optimization methods for reconstructing MR images. The book discusses approaches for specific applications such as non-Cartesian imaging, under sampled reconstruction, motion correction, dynamic imaging and quantitative MRI. This unique resource is suitable for physicists, engineers, technologists and clinicians with an interest in medical image reconstruction and MRI.
1. Introduction - p. xxi 2. Basics of MRI Reconstruction - p. xxii 3. Chapter 1: Brief Introduction to MRI Physics - p. 3 4. Chapter 2: MRI Reconstruction as an Inverse Problem - p. 37 5. Chapter 3: Optimization Algorithms for MR Reconstruction - p. 59 6. Chapter 4: Non-Cartesian MRI Reconstruction - p. 73 7. Chapter 5: “Early” Constrained Reconstruction Methods - p. 105 8. Reconstruction of Undersampled MRI Data - p. 125 9. Chapter 6: Parallel Imaging - p. 129 10. Chapter 7: Simultaneous Multislice Reconstruction - p. 159 11. Chapter 8: Sparse Reconstruction - p. 189 12. Chapter 9: Low-Rank Matrix and Tensor–Based Reconstruction - p. 223 13. Abstract - p. 223 14. 9.1 Introduction - p. page223 15. 9.2 Problem formulation - p. page223 16. 9.3 Matrix-based approaches - p. 224 17. 9.4 Tensor-based approaches - p. 235 18. 9.5 Summary - p. page243 19. References - p. page243 20. Chapter 10: Dictionary, Structured Low-Rank, and Manifold Learning-Based Reconstruction - p. 249 21. Chapter 11: Machine Learning for MRI Reconstruction - p. 281 22. Abstract - p. 281 23. 11.1 Introduction - p. page281 24. 11.2 Organization of this chapter - p. 282 25. 11.3 Machine learning definitions - p. 283 26. 11.4 Task definition for MR reconstruction - p. 289 27. 11.5 Core concepts: layers - p. page292 28. 11.6 Network architectures for MRI reconstruction - p. page305 29. 11.7 How to build an ML model for MR reconstruction - p. page305 30. 11.8 Summary - p. page310 31. 11.9 Further resources and tutorials - p. page310 32. 11.10 Exercises - p. page311 33. References - p. page317 34. Reconstruction Methods for Non-linear Forward Models in MRI - p. 323 35. Chapter 12: Imaging in the Presence of Magnetic Field Inhomogeneities - p. 327 36. Chapter 13: Motion-Corrected Reconstruction - p. 355 37. Chapter 14: Chemical Shift Encoding-Based Water-Fat Separation - p. 391 38. Chapter 15: Model-Based Parametric Mapping Reconstruction - p. 419 39. Chapter 16: Quantitative Susceptibility-Mapping Reconstruction - p. 441 40. Appendix A: Linear Algebra Primer - p. 469 41. Index - p. 479
Magnetic Resonance Image Reconstruction: Theory, Methods and Applications presents the fundamental concepts of MR image reconstruction, including its formulation as an inverse problem, as well as the most common models and optimization methods for reconstructing MR images. The book discusses approaches for specific applications such as non-Cartesian imaging, under sampled reconstruction, motion correction, dynamic imaging and quantitative MRI. This unique resource is suitable for physicists, engineers, technologists and clinicians with an interest in medical image reconstruction and MRI.
1. Introduction - p. xxi 2. Basics of MRI Reconstruction - p. xxii 3. Chapter 1: Brief Introduction to MRI Physics - p. 3 4. Chapter 2: MRI Reconstruction as an Inverse Problem - p. 37 5. Chapter 3: Optimization Algorithms for MR Reconstruction - p. 59 6. Chapter 4: Non-Cartesian MRI Reconstruction - p. 73 7. Chapter 5: “Early” Constrained Reconstruction Methods - p. 105 8. Reconstruction of Undersampled MRI Data - p. 125 9. Chapter 6: Parallel Imaging - p. 129 10. Chapter 7: Simultaneous Multislice Reconstruction - p. 159 11. Chapter 8: Sparse Reconstruction - p. 189 12. Chapter 9: Low-Rank Matrix and Tensor–Based Reconstruction - p. 223 13. Abstract - p. 223 14. 9.1 Introduction - p. page223 15. 9.2 Problem formulation - p. page223 16. 9.3 Matrix-based approaches - p. 224 17. 9.4 Tensor-based approaches - p. 235 18. 9.5 Summary - p. page243 19. References - p. page243 20. Chapter 10: Dictionary, Structured Low-Rank, and Manifold Learning-Based Reconstruction - p. 249 21. Chapter 11: Machine Learning for MRI Reconstruction - p. 281 22. Abstract - p. 281 23. 11.1 Introduction - p. page281 24. 11.2 Organization of this chapter - p. 282 25. 11.3 Machine learning definitions - p. 283 26. 11.4 Task definition for MR reconstruction - p. 289 27. 11.5 Core concepts: layers - p. page292 28. 11.6 Network architectures for MRI reconstruction - p. page305 29. 11.7 How to build an ML model for MR reconstruction - p. page305 30. 11.8 Summary - p. page310 31. 11.9 Further resources and tutorials - p. page310 32. 11.10 Exercises - p. page311 33. References - p. page317 34. Reconstruction Methods for Non-linear Forward Models in MRI - p. 323 35. Chapter 12: Imaging in the Presence of Magnetic Field Inhomogeneities - p. 327 36. Chapter 13: Motion-Corrected Reconstruction - p. 355 37. Chapter 14: Chemical Shift Encoding-Based Water-Fat Separation - p. 391 38. Chapter 15: Model-Based Parametric Mapping Reconstruction - p. 419 39. Chapter 16: Quantitative Susceptibility-Mapping Reconstruction - p. 441 40. Appendix A: Linear Algebra Primer - p. 469 41. Index - p. 479
