|
|
|
| Higher Order Tensor Diffusion Magnetic Resonance Sparse ImagingBased on Compressed Sensing |
| FENG Yuan-Jing, WU Ye, ZHANG Gui-Jun, LIANG Rong-Hua |
| Institute of Information Processing and Automation, College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023 |
|
|
|
|
Abstract High Order Tensor (HOT) diffusion magnetic resonance imaging is an important method to reveal the microstructural information of living brain white matter. However, its time-consuming data acquisition and low fiber reconstructing resolution limit its clinical application.In this paper, a fiber orientation estimation method with weighted sparse is presented based on HOT model. Firstly, the HOT spherical deconvolution model for fiber orientation estimation is established. Then, a sparse representation method of fiber orientation is put forward. Finally, a l1-norm optimization model is built for the sparse constraint deconvolution. A computing method of applying the training results of sparse dictionary with lower order into the high-order problem is proposed to achieve the solution of the optimization problem. The experimental results on simulated and vivo data show that the fiber orientation estimation method improves the angular resolution of HOT tensor imaging method and reduces the angle recognition error.
|
|
Received: 06 June 2014
|
|
|
|
|
|
[1] Assaf Y, Pasternak O. Diffusion Tensor Imaging(DTI)-Based White Matter Mapping in Brain Research: A Review. Journal of Molecular Neuroscience, 2008, 34(1): 51-61
[2] Basser P J, Mattiello J, LeBihan D. MR Diffusion Tensor Spectroscopy and Imaging. Biophysical Journal, 1994, 66(1): 259-267
[3] Cheng J, Ghosh A, Deriche R, et al. Model-Free, Regularized, Fast, and Robust Analytical Orientation Distribution Function Estimation // Proc of the 13th Iternational Conference on Medical Image Computing and Computer-Assisted Intervention. Beijing, China, 2010: 648-656
[4] Malcolm J G, Shenton M E, Rathi Y. Filtered Multi-tensor Tractography. IEEE Trans on Medical Imaging, 2010, 29(9): 1664-1675
[5] Li R, Feng J Y, Shao K L, et al. Higher Order Tensor Imaging Model Feature Extraction Algorithm Based on Iterative Search. China Journal of Biomedical Engineering, 2012, 31(3): 365-373 (in Chinese)
(李 蓉,冯远静,邵开来,等.磁共振扩散高阶张量成像的脑白质纤维微结构模型及特征提取算法.中国生物医学工程学报, 2012, 31(3): 365-373)
[6] Hlawitschka M, Scheuermann G. Tracking Lines in Higher Order Tensor Fields // Hagen H, ed. Scientific Visualization: Advanced Concepts. Dagstuhl, Germany: Schloss Dagstuhl, 2010: 124-135
[7] zarslan E, Mareci T H. Generalized Diffusion Tensor Imaging and Analytical Relationships between Diffusion Tensor Imaging and High Angular Resolution Diffusion Imaging. Magnetic Resonance in Medicine, 2003, 50(5): 955-965
[8] Moakher M. On the Averaging of Symmetric Positive-Definite Tensors. Journal of Elasticity, 2006, 82(3): 273-296
[9] Moakher M, Norris A N. The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry. Journal of Elasticity, 2006, 85(3): 215-263
[10] Barmpoutis A, Hwang M S, Howland D, et al. Regularized Positive-Definite Fourth Order Tensor Field Estimation from DW-MRI. NeuroImage, 2009, 45(1): S153-S162
[11] Barmpoutis A, Jeffery H, Vemuri B C. Approximating Symmetric Positive Semidefinite Tensors of Even Order. SIAM Journal on Imaging Sciences, 2012, 5(1): 434-464
[12] Weldeselassie Y T, Barmpoutis A, Atkins M S. Symmetric Positive Semi-definite Cartesian Tensor Fiber Orientation Distributions(CT-FOD). Medical Image Analysis, 2012, 16(6): 1121-1129
[13] Jeurissen B, Leemans A, Tournier J D, et al. Estimating the Number of Fiber Orientations in Diffusion MRI Voxels: A Constrained Spherical Deconvolution Study // Proc of the International Society for Magnetic Resonance in Medicine. Stockholm, Sweden, 2010: 573
[14] Yeh F C, Tseng W Y I. Sparse Solution of Fiber Orientation Distribution Function by Diffusion Decomposition. PloS One, 2013. DOI: 10.1371/journal.pone.0075747
[15] Merlet S, Caruyer E, Deriche R. Parametric Dictionary Learning for Modeling EAP and ODF in Diffusion MRI // Proc of the 15th International Conference on Medical Image Computing and Compu-ter-Assisted Intervention. Nice, France, 2012: 10-17
[16] Donoho D L. Compressed Sensing. IEEE Trans on Information Theory, 2006, 52(4): 1289-1306
[17] Candès E J, Romberg J, Tao T. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information. IEEE Trans on Information Theory, 2006, 52(2): 489-509
[18] Anderson A W, Ding Z. Sub-voxel Measurement of Fiber Orientation Using High Angular Resolution Diffusion Tensor Imaging //Proc of the International Society for Magnetic Resonance in Medicine. Berkeley, USA, 2002: 440
[19] Rudin W. Sums of Squares of Polynomials. The American Mathematical Monthly, 2000, 107(9): 813-821
[20] Ghosh A, Tsigaridas E, Mourrain B, et al. A Polynomial App-roach for Extracting the Extrema of a Spherical Function and Its Application in Diffusion MRI. Medical Image Analysis, 2013, 17(5): 503-514
[21] Patel V, Shi Y G, Thompson P M, et al. Mesh-Based Spherical Deconvolution: A Flexible Approach to Reconstruction of Non-negative Fiber Orientation Distributions. NeuroImage, 2010, 51(3): 1071-1081
[22] Jiao F X, Gur Y, Johnson C R, et al. Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions // Proc of the 22nd International Conference on Information Processing in Medical Imaging. Kloster Irsee, Germany, 2011: 538-549
[23] Daducci A, Van de Ville D, Thiran J P, et al. Sparse Regularization for Fiber ODF Reconstruction: From the Suboptimality of 2 and 1 Priors to 0. Medical Image Analysis, 2014, 18(6): 820-833
[24] Schultz T. Learning a Reliable Estimate of the Number of Fiber Directions in Diffusion MRI // Proc of the 15th International Conference on Medical Image Computing and Computer-Assisted Intervention. Nice, France, 2012: 493-500
[25] Candès E J, Wakin M B, Boyd S P. Enhancing Sparsity by Reweighted 1 Minimization. Journal of Fourier Analysis and Applications, 2008, 14(5/6): 877-905
[26] Tournier J D, Calamante F, Connelly A. Robust Determination of the Fibre Orientation Distribution in Diffusion MRI: Non-negativity Constrained Super-Resolved Spherical Deconvolution. NeuroImage, 2007, 35(4): 1459-1472
[27] Tikhonov A N, Goncharsky A, Stepanov V V, et al. Numerical Methods for the Solution of Ill-Posed Problems. Dordrecht, The Netherlands: Springer-Science + Business Media, 1995
[28] Parker G D, Marshall D, Rosin P L, et al. A Pitfall in the Reconstruction of Fibre ODFs Using Spherical Deconvolution of Diffusion MRI Data. NeuroImage, 2013, 65: 433-448
[29] Sderman O, Jnsson B. Restricted Diffusion in Cylindrical Geometry. Journal of Magnetic Resonance: Series A, 1995, 117(1): 94-97 |
|
|
|
2015, Vol. 28 
