臺灣博碩士論文加值系統

擴散磁振造影為目前臨床上唯一能造影神經纖維方向之非侵入式神經影像技術，其中，擴散頻譜磁振造影因具有解析三維空間中水分子擴散機率之能力，已被驗證能提供良好之神經纖維方向鑑別率。然而，受限於擴散頻譜磁振造影之造影原理，需沿著q空間與k空間共計六個維度進行大量之資料擷取，始能重建全腦中每個像素之水分子擴散機率分布，導致擴散頻譜磁振造影之掃描時間過長，大幅降低其臨床應用之可行性。因此，如何能夠縮短擴散頻譜磁振造影之掃描時間且使其能被廣泛應用於於臨床研究與診斷中已逐漸成為一重要之課題。

壓縮感測技術於近十年來快速發展，目前已廣泛被應用於巨維訊號處理上，例如像是資料壓縮、即時影像錄放、與無線通訊網路上。壓縮感測之原理建立於訊號本身所具備之稀疏度，由訊號所分解之基底中擷取高係數權重之係數，即可重建還原完整之訊號資料。由於壓縮感測技術能大幅縮短資料擷取之時間，並重建出近似之資料品質，已逐漸被應用於各種生醫影像技術中。

由於擴散磁振造影之q空間亦具有稀疏之特性，於應用壓縮感測於擴散頻譜磁振造影上，目前已有相關研究提出使用小波轉換原理進行資料重建，但其加速倍率受限於資料原始稀疏度。此外，先前研究亦有使用字典式基底之壓縮感測技術重建減少資料取樣之擴散頻譜磁振造影，亦能有效重建三維水分子擴散機率，並造影神經纖維之方向。雖然結合壓縮感測與擴散頻譜磁振造影已初步驗證其可行性，目前仍欠缺一有系統之分析架構以評估其效能與準確度，此外，取像參數、訊噪比及分析參數亦需進一步之探討。

此論文之主要之目的為發展快速之擴散頻譜磁振造影技術，並藉由建立字典式基底之壓縮感測技術，以重建完整之q空間訊號，並造影三維空間中水分子之擴散機率分布與方向機率分布。此外，我們提出不同之離散型字典訓練方法以及q空間資料取樣方式，以探討於不同加速倍率下之重建效能，最後並進一步探討擴散頻譜磁振造影之掃描參數對不同壓縮感測訓練模式之影響。本研究建立一套完整之量化誤差分析架構，除可提供未來於臨床應用上最佳化參數之參考外，亦希望能透過結合字典式基底之壓縮感測技術，進一步縮短擴散頻譜磁振造影於臨床系統上之掃描時間，增進其於大腦神經科學研究與臨床腦部疾病診斷之可行性。

Diffusion Spectrum Imaging (DSI) is one of the diffusion MRI techniques and has the highest accuracy of resolving complex fiber orientations in human brain. However, due to the large data sampling and resulting long scan time, its clinical feasibility has not been verified yet on clinical MRI applications. To reduce the data sampling and accelerate the scan time, a signal processing approach is highly needed without any additional cost of hardware improvement.

Compressive Sensing (CS) technique can moderate huge data information well based on the theory that extracts all the high coefficients from signal bases. This technique has been widely employed in a variety of research fields, such as data mining, wireless network communication, video and image processing. Although implementation of CS technique on DSI has been proposed in previous studies, a systematic and quantitative analysis framework is still lacking.

Therefore, this thesis aimed to establish a dictionary-based CS-DSI technique and quantitative evaluation framework. We developed a multiple-slice dictionary learning method and focused on investigating the improvement on white matter structures. We also discussed the influences of DSI sequence parameters on its performance, such as maximum b-value and signal-to-noise ratio. The framework of multiple-slice learning is verified to has higher accuracy of reconstructing probability distribution function and orientation distribution function. We expect this thesis could provide more useful information for facilitating the development of CS-DSI technology as well as utilizing this technique on neuroscience researches and clinical applications.

List of Figures …………………………...………….. xi
List of Tables ………………………………………… xv
Chapter 1 - Introduction ……………………………………1
1.1 Preface …………………………………………………2
1.2 Background …………………………………………… 6
1.2.1 Compressive Sensing on MRI (CS-MRI) ………………………..6
1.2.2 Compressive Sensing on Diffusion MRI (CS-dMRI) ……………8
1.3 Motivation ……………………………………………..11
1.4 Purpose …………………………………………………12
1.5 Thesis Overview …………………………………………13
Chapter 2 - Theory …………………………………………..15
2.1 Theory of dMRI …………………………………………16
2.1.1 Diffusion-Weighted MRI (DWI) ………………………………….17
2.1.2 Diffusion Spectrum MRI (DSI) ……………………………………21
2.2 Dictionary-based Compressive Sensing on DSI …………24
2.2.1 Architecture and Workflow ………………………………………..26
2.2.2 Dictionary Training using K-SVD ………………………………... 27
2.3 Sampling Pattern Design …………………………………31
2.3.1 Variable Density Pattern ……………………………………………31
2.3.2 Uniform Angular Pattern ……………………………………………32
Chapter 3 - Method ……………………………………………37
3.1 Experimental Data …………………………………………38
3.1.1 Simulated DSI Data ………………………………………………….38
3.1.2 MRI Experiments and Real DSI515 Dataset …………………………40
3.1.3 Undersampled Data Generation ………………………………………42
3.2 Implementation of Dictionary-based CS on DSI Data ……..46
3.2.1 Dictionary Generation …………………………………………………46
3.2.3 Reconstruction of ODF ………………………………………………..51
3.3 Quantitative Evaluation …………………………………….52
3.3.1 Quantification of Reconstruction Accuracy …………………………..52
3.3.2 Comparisons of MRI parameters ………………………………………53
Chapter 4 - Results ………………………………………………57
4.1 Results of Simulated DSI Datasets ………………………….58
4.1.1 Dictionary Training Using Simulated DSI Datasets ……………………58
4.1.2 Dictionary Training Using Real DSI Datasets ………………………….70
4.2 Results of Real DSI Datasets …………………………………78
4.2.1 DKSVD and DPDF ………………………………………………………82
4.2.2 Single-slice and Multiple-slice Dictionaries ……………………………..82
4.2.3 Whole-brain and High-GFA Dictionaries ………………………………..82
4.3 Variable Density and Uniform Angular Patterns ……………..92
Chapter 5 - Discussion …………………………………………….93
5.1 Simulation Study ………………………………………………94
5.1.1 Standard Deviation of RMSE …………………………………………….94
5.1.2 Angular Error of ODF …………………………………………………….96
5.1.3 Comparison of Real Training Dataset ……………………………………100
5.2 Study of Real DSI Datasets ……………………………………102
5.2.1 Inter-subject Difference ……………………………………………………102
5.2.2 Impact of RMSE and AE Results …………………………………………104
5.2.3 AE in Whole-brain, White-matter and Gray-matter Regions ……………..104
5.2.4 The Voxel Histogram of AE Values in Various Cases ……………………104
5.3 Optimal Lambda Decision ……………………………………..114
5.4 TIK vs LASSO Reconstruction …………………………………116
5.5 Limitations ………………………………………………………117
Chapter 6 - Conclusion ………………………………………………119
6.1 Conclusion ……………………………………………………….120
6.2 Future Works …………………………………………………….121
Bibliography ………………………………………………………….123

[1] D. S. Tuch, T. G. Reese, M. R. Wiegell, N. Makris, J. W. Belliveau, and V. J. Wedeen,
“High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity,”
Magnetic Resonance in Medicine, vol. 48, no. 4, pp. 577-582, 2002.
[2] D. S. Tuch, “Q‐ball imaging,” Magnetic Resonance in Medicine, vol. 52, no. 6, pp.
1358-1372, 2004.
[3] J. Tournier, F. Calamante, D. G. Gadian, and A. Connelly, “Direct estimation of the fiber orientation
density function from diffusion-weighted MRI data using spherical
deconvolution,” NeuroImage, vol. 23, no. 3, pp. 1176-1185, 2004.
[4] V. J. Wedeen, P. Hagmann, W. Y. I. Tseng, T. G. Reese, and R. M. Weisskoff, “Mapping
complex tissue architecture with diffusion spectrum magnetic resonance imaging,” Magnetic
Resonance in Medicine, vol. 54, no. 6, pp. 1377-1386, 2005.
[5] K. Setsompop, J. Cohen-Adad, B. Gagoski, T. Raij, A. Yendiki, B. Keil, V. J. Wedeen, and
L. L. Wald, “Improving diffusion MRI using simultaneous multi-slice echo planar imaging,”
Neuroimage, vol. 63, no. 1, pp. 569-580, 2012.
[6] P. Hagmann, L. Jonasson, P. Maeder, J.-P. Thiran, V. J. Wedeen, and R. Meuli, “Understanding
Diffusion MR Imaging Techniques: From Scalar Diffusion-weighted Imaging to
Diffusion Tensor Imaging and Beyond 1,” Radiographics, vol. 26, no. suppl_1, pp. S205-
S223, 2006.
[7] V. J. Wedeen, R. Wang, J. D. Schmahmann, T. Benner, W. Tseng, G. Dai, D. Pandya, P.
Hagmann, H. D'Arceuil, and A. J. de Crespigny, “Diffusion spectrum magnetic resonance
imaging (DSI) tractography of crossing fibers,” Neuroimage, vol. 41, no. 4, pp.
1267-1277, 2008.
[8] L.-W. Kuo, J.-H. Chen, V. J. Wedeen, and W.-Y. I. Tseng, “Optimization of diffusion spectrum
imaging and q-ball imaging on clinical MRI system,” Neuroimage, vol. 41, no. 1, pp.
7-18, 2008.
[9] H.-E. Assemlal, D. Tschumperlé, L. Brun, and K. Siddiqi, “Recent advances in diffusion
MRI modeling: Angular and radial reconstruction,” Medical image analysis, vol. 15, no. 4,
pp. 369-396, 2011.
[10] M. I. Menzel, E. T. Tan, K. Khare, J. I. Sperl, K. F. King, X. Tao, C. J. Hardy, and L. Marinelli,
“Accelerated diffusion spectrum imaging in the human brain using compressed sensing,”
Magnetic Resonance in Medicine, vol. 66, no. 5, pp. 1226-1233, 2011.
[11] D. L. Donoho, “Compressed sensing,” Information Theory, IEEE Transactions on, vol. 52,
no. 4, pp. 1289-1306, 2006.
[12] E. J. Candès, and M. B. Wakin, “An introduction to compressive sampling,” Signal Processing
Magazine, IEEE, vol. 25, no. 2, pp. 21-30, 2008.
[13] M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed
sensing,” Preprint, vol. 93, 2011.[14] E. J. Candes, “The restricted isometry property and its implications for compressed sensing,”
Comptes Rendus Mathematique, vol. 346, no. 9, pp. 589-592, 2008.
[15] S. Merlet, and R. Deriche, “Compressed sensing for accelerated EAP recovery in diffusion
MRI,” CDMRI'10, 2010.
[16] S. Merlet, E. Caruyer, and R. Deriche, "Impact of radial and angular sampling on multiple
shells acquisition in diffusion mri," Medical Image Computing and Computer-Assisted Intervention–
MICCAI 2011, pp. 116-123: Springer, 2011.
[17] S. Merlet, J. Cheng, A. Ghosh, and R. Deriche, "Spherical polar fourier eap and odf reconstruction
via compressed sensing in diffusion mri." pp. 365-371.
[18] B. Bilgic, K. Setsompop, J. Cohen‐Adad, A. Yendiki, L. L. Wald, and E. Adalsteinsson, “Accelerated
diffusion spectrum imaging with compressed sensing using adaptive dictionaries,”
Magnetic Resonance in Medicine, vol. 68, no. 6, pp. 1747-1754, 2012.
[19] A. Gramfort, C. Poupon, and M. Descoteaux, "Sparse dsi: Learning dsi structure for denoising
and fast imaging," Medical Image Computing and Computer-Assisted Intervention–
MICCAI 2012, pp. 288-296: Springer, 2012.
[20] B. A. Landman, J. A. Bogovic, H. Wan, F. E. Z. ElShahaby, P.-L. Bazin, and J. L. Prince,
“Resolution of crossing fibers with constrained compressed sensing using diffusion tensor
MRI,” NeuroImage, vol. 59, no. 3, pp. 2175-2186, 2012.
[21] S. Merlet, E. Caruyer, and R. Deriche, "Parametric dictionary learning for modeling eap
and odf in diffusion mri," Medical Image Computing and Computer-Assisted Intervention–
MICCAI 2012, pp. 10-17: Springer, 2012.
[22] B. Bilgic, I. Chatnuntawech, K. Setsompop, S. Cauley, A. Yendiki, L. Wald, and E. Adalsteinsson,
“Fast dictionary-based reconstruction for diffusion spectrum imaging,” 2013.
[23] S. L. Merlet, and R. Deriche, “Continuous diffusion signal, EAP and ODF estimation via
Compressive Sensing in diffusion MRI,” Medical image analysis, vol. 17, no. 5, pp.
556-572, 2013.
[24] A. Gramfort, C. Poupon, and M. Descoteaux, “Denoising and fast diffusion imaging with
physically constrained sparse dictionary learning,” Medical image analysis, vol. 18, no. 1,
pp. 36-49, 2014.
[25] M. Paquette, S. Merlet, G. Gilbert, R. Deriche, and M. Descoteaux, “Comparison of sampling
strategies and sparsifying transforms to improve compressed sensing diffusion
spectrum imaging,” Magnetic Resonance in Medicine, 2014.
[26] M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: The application of compressed sensing
for rapid MR imaging,” Magnetic resonance in medicine, vol. 58, no. 6, pp.
1182-1195, 2007.
[27] M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” Signal
Processing Magazine, IEEE, vol. 25, no. 2, pp. 72-82, 2008.
[28] W. Ye, B. C. Vemuri, and A. Entezari, "An over-complete dictionary based regularized reconstruction
of a field of ensemble average propagators." pp. 940-943.
[29] K. T. Block, M. Uecker, and J. Frahm, “Undersampled radial MRI with multiple coils. Iterative
image reconstruction using a total variation constraint,” Magnetic resonance in medicine,
vol. 57, no. 6, pp. 1086-1098, 2007.
[30] J. Aelterman, H. Q. Luong, B. Goossens, A. Pižurica, and W. Philips, “Augmented Lagrangian
based reconstruction of non-uniformly sub-Nyquist sampled MRI data,” Signal
Processing, vol. 91, no. 12, pp. 2731-2742, 2011.
[31] N. Chauffert, P. Ciuciu, and P. Weiss, "Variable density compressed sensing in MRI. Theoretical
VS heuristic sampling strategies." pp. 298-301.
[32] M. Aharon, M. Elad, and A. Bruckstein, “K-svd: An algorithm for designing overcomplete
dictionaries for sparse representation,” Signal Processing, IEEE Transactions on, vol. 54,
no. 11, pp. 4311-4322, 2006.
[33] H. Lee, A. Battle, R. Raina, and A. Y. Ng, "Efficient sparse coding algorithms." pp. 801-808.
[34] E. J. Candes, Y. C. Eldar, D. Needell, and P. Randall, “Compressed sensing with coherent
and redundant dictionaries,” Applied and Computational Harmonic Analysis, vol. 31, no.
1, pp. 59-73, 2011.
[35] R. Otazo, and D. Sodickson, "Adaptive compressed sensing MRI." p. 4867.
[36] S. Ravishankar, and Y. Bresler, “MR image reconstruction from highly undersampled kspace
data by dictionary learning,” Medical Imaging, IEEE Transactions on, vol. 30, no.
5, pp. 1028-1041, 2011.
[37] E. Saint-Amant, and M. Descoteaux, "Sparsity characterisation of the diffusion
propagator." p. 2011.
[38] S. Merlet, E. Caruyer, A. Ghosh, and R. Deriche, “A computational diffusion MRI and
parametric dictionary learning framework for modeling the diffusion signal and its features,”
Medical image analysis, vol. 17, no. 7, pp. 830-843, 2013.
[39] D. Jones, M. Horsfield, and A. Simmons, “Optimal strategies for measuring diffusion in anisotropic
systems by magnetic resonance imaging,” Magn Reson Med, vol. 42, 1999.
[40] R. Deriche, J. Calder, and M. Descoteaux, “Optimal real-time Q-ball imaging using regularized
Kalman filtering with incremental orientation sets,” Medical image analysis, vol. 13,
no. 4, pp. 564-579, 2009.
[41] J. L. Paulsen, H. Cho, G. Cho, and Y.-Q. Song, “Acceleration of multi-dimensional propagator
measurements with compressed sensing,” Journal of Magnetic Resonance, vol.
213, no. 1, pp. 166-170, 2011.
[42] P. J. Basser, J. Mattiello, and D. LeBihan, “MR diffusion tensor spectroscopy and imaging,”
Biophysical journal, vol. 66, no. 1, pp. 259-267, 1994.
[43] D. S. Tuch, T. G. Reese, M. R. Wiegell, and V. J. Wedeen, “Diffusion MRI of complex neural
architecture,” Neuron, vol. 40, no. 5, pp. 885-895, 2003.
[44] E. L. Hahn, “Spin echoes,” Physical Review, vol. 80, no. 4, pp. 580, 1950.
[45] H. C. Torrey, “Bloch equations with diffusion terms,” Physical Review, vol. 104, no. 3, pp.
563, 1956.
[46] E. Stejskal, and J. Tanner, “Spin diffusion measurements: spin echoes in the presence of a
time‐dependent field gradient,” The journal of chemical physics, vol. 42, no. 1, pp.
288-292, 1965.
[47] P. T. Callaghan, Principles of nuclear magnetic resonance microscopy: Clarendon Press
Oxford, 1991.
[48] R. Ward, “Compressed sensing with cross validation,” Information Theory, IEEE Transactions
on, vol. 55, no. 12, pp. 5773-5782, 2009.
[49] R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical
Society. Series B (Methodological), pp. 267-288, 1996.
[50] M. A. Rasmussen, and R. Bro, “A tutorial on the Lasso approach to sparse modeling,”
Chemometrics and Intelligent Laboratory Systems, vol. 119, pp. 21-31, 2012.
[51] C. G. Koay, E. Özarslan, K. M. Johnson, and M. E. Meyerand, “Sparse and optimal acquisition
design for diffusion MRI and beyond,” Medical physics, vol. 39, no. 5, pp.
2499-2511, 2012.