Using Perturbation theory to reduce noise in diffusion tensor fields

Medical Image Analysis

Volumn 13, Issue 4, 2009, Pages 580-597

  Bansal, Ravi ^a,b   Staib, Lawrence H ^d   Xu, Dongrong ^a,b   Laine, Andrew F ^c   Liu, Jun ^a,b   Peterson, Bradley S ^a,b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b NEW YORK STATE PSYCHIATRIC INSTITUTE   (United States)

^c Yale University ^*  (United States)

^d YALE UNIVERSITY   (United States)

Author keywords

Diffusion tensor; Markov Random Field; Perturbation theory; Riemannian distance; Simulated annealing

Indexed keywords

CLOSE-IN; DATA SETS; DIFFUSION OF WATER; DIFFUSION TENSOR; DIFFUSION TENSOR IMAGING; DIFFUSION WEIGHTED IMAGES; EIGENVALUES; EIGENVECTORS; FINE STRUCTURES; HOMOGENEOUS REGIONS; IN-DIFFUSION; IN-VIVO; LOW SIGNAL-TO-NOISE RATIO; MARKOV RANDOM FIELD; MARKOV RANDOM FIELDS; PERTURBATION THEORY; POSITIVE DEFINITE; QUANTITATIVE ANALYSIS; REAL-WORLD DATASETS; REDUCING NOISE; RIEMANNIAN DISTANCE; SPATIAL DIRECTION; SPATIAL RESOLUTION; TENSOR FIELDS; WHITE MATTER FIBERS;

ACOUSTIC INTENSITY; CHEMICAL ANALYSIS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; HIDDEN MARKOV MODELS; PERTURBATION TECHNIQUES; SIGNAL TO NOISE RATIO; SIMULATED ANNEALING;

TENSORS;

ANALYTIC METHOD; ANISOTROPY; ARTICLE; DIFFUSION; DIFFUSION TENSOR IMAGING; DIFFUSION WEIGHTED IMAGING; MATHEMATICAL COMPUTING; NOISE REDUCTION; PRIORITY JOURNAL; PROBABILITY; QUANTITATIVE ANALYSIS; RADIATION FIELD; RELIABILITY; SIGNAL NOISE RATIO; STATISTICAL ANALYSIS; VALIDITY;

ALGORITHMS; ARTIFACTS; BRAIN; DIFFUSION MAGNETIC RESONANCE IMAGING; ELECTROMAGNETIC FIELDS; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 70149086679     PISSN: 13618415     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.media.2009.05.001     Document Type: Article

References (74)

1. Alexander, D., Gee, J., Bajcsy, R., 1999. Similarity measures for matching diffusion tensor images. In: British Machine Vision Conference (BMVC'99).
2. Anderson A.W. Theoretical analysis of the effects of noise on diffusion tensor imaging. Magnetic Resonance in Medicine 46 (2001) 1174-1188
3. Arsigny V., Fillard P., Pennec X., and Ayache N. Fast and simple calculus on tensors in the log-Euclidean framework. In: Duncan J., and Gerig G. (Eds). Proceedings of Eighth International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2005. LNCS vol. 3749 (2005), Palm Springs, CA, USA 115-122
4. Bansal R., Staib L., Plessen K., Xu D., Royal J., and Peterson B. Voxel-wise comparisons in the morphology of diffusion tensors across groups of experimental subjects. Psychiatric Research, Neuroimaging 156 3 (2007) 225-245
5. Bansal R., Staib L., Xu D., Laine A., Royal J., and Peterson B. Using perturbation theory to compute the morphological similarity of diffusion tensors. IEEE Transactions on Medical Imaging 27 5 (2008) 589-607
6. Basser P. Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR in Biomedicine 8 7 (1995) 333-344
7. Basser P., Mattiello J., and LeBihan D. Estimation of the effective self-diffusion tensor from the NMR spin echo. Journal of Magnetic Resonance, Series B 103 (1994) 247-254
8. Basser P., Mattiello J., and LeBihan D. MR diffusion tensor spectroscopy and imaging. Biophysical Journal 66 (1994) 259-267
9. Basser, P., Pajevic, S., 1999. Method to reduce eigenvalue sorting bias in DT-MRI. In: 7th Annual ISMRM, Philadelphia, p. 1788.
10. Basser P., and Pajevic S. Statistical artifacts in diffusion tensor MRI (DT-MRI) caused by background noise. Magnetic Resonance in Medicine 44 1 (2000) 41-50
11. Basser P., and Pajevic S. A normal distribution for tensor-valued random variables: applications to diffusion tensor MRI. IEEE Transactions on Medical Imaging 22 7 (2003) 785-794
12. Batchelor P., Atkinson D., Hill D., Calamante F., and Connelly A. Anisotropic noise propagation in diffusion tensor MRI sampling schemes. Magnetic Resonance in Medicine 49 (2003) 1143-1151
13. Batchelor P., Moakher M., Atkinson D., Calamante F., and Connelly A. A rigorous framework for diffusion tensor calculus. Magnetic Resonance in Medicine 53 1 (2005) 221-225
14. Besag J. On the statistical analysis of dirty pictures. Journal of the Royal Statistical Society B 48 3 (1986) 259-302
15. Chen B., and Hsu E. Noise removal in magnetic resonance diffusion tensor imaging. Magnetic Resonance in Medicine 54 (2005) 393-407
16. Conturo T., Lori N., Cull T., Akbudak E., Snyder A., Shimnoy J., McKinstry R., Burton H., and Raichle M. Tracking neuronal fiber pathways in the living human brain. Proceedings of the National Academy of Sciences 96 18 (1999) 10422-10427
17. Coulon O., Alexander D., and Arridge S. Diffusion tensor magnetic resonance image regularization. Medical Image Analysis 8 1 (2004) 47-67
18. Crank J. The Mathematics of Diffusion (1975), Oxford University Press
19. Ding Z., Gore J., and Anderson A. Reduction of noise in diffusion tensor images using anisotropic smoothing. Magnetic Resonance in Medicine 53 (2005) 485-490
20. Ellis C., Simmons A., Jones D.K., Bland J., Dawson J.M., Horsfield M.A., Williams S., and Leigh P. Diffusion tensor MRI assesses corticospinal tract damage in ALS. Neurology 53 (1999) 1051-1058
21. Eriksson S.H., Rugg-Gunn F.J., Symms M.R., Baker G.J., and Duncan J.S. Diffusion tensor imaging in patients with epilepsy and maformations of cortical development. Brain 124 (2001) 617-626
22. Fillard, P., Gerig, G., 2003. Analysis tool for diffusion tensor MRI. In: MICCAI'03.
23. Fletcher, P., Joshi, S., 2004. Principal geodesic analysis on symmetric spaces: Statistics of diffusion tensors. In: Workshop on Computer Vision Approaches to Medical Image Analysis (CVAMIA), LNCS, vol. 3117, pp. 87-98.
24. Friston K., Holmes A., Worsley K., Polime J., Frith C., and Frackwiak R. Statistical parametric maps in functional imaging: a general linear approach. Human Brain Mapping 2 (1995) 189-210
25. Geman S., and Geman D. Stochastic relaxation, Gibbs distributions and the bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 6 (1984) 721-741
26. Gerig G., Kubler O., Kikinis R., and Jolesz F. Nonlinear anisotropic filtering of MRI data. IEEE Transactions on Medical Imaging 11 2 (1992) 221-232
27. Hastings W.K. Monte carlo sampling methods using markov chains and their applications. Biometrika 57 1 (1970) 97-109
28. Jones D., Horsfield M., and Simmons A. Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magnetic Resonance in Medicine 42 3 (1999) 515-525
29. Jones D., Simmons A., Williams S., and Horsfield M. Non-invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magnetic Resonance in Medicine 42 1 (1999) 37-41
30. Klingberg T., Hedehus M., Temple E., Salz T., Gabrieli J., Moseley M., and Poldrack R. Microstructure of temporo-parietal white matter as a basis for reading ability: evidence from diffusion tensor magnetic resonance imaging. Neuron 25 2 (2000) 493-500
31. Koay C., Carew J., Alexander A., Basser P., and Meyerand M. Investigation of anomalous estimates of tensor-derived quantities in diffusion tensor imaging. Magnetic Resonance in Medicine 55 (2006) 930-936
32. Lee, J., Chung, M., Oakes, T., Alexander, A., 2005. Anisotropic kernel smoothing of DTI data. International Society for Magnetic Resonance in Medicine (ISMRM).
33. Lim K., Hedehus M., Moseley M., de Crespigny A., Sullivan E., and Pfefferbaum A. Compromised white matter tract integrity in schizophrenia inferred from diffusion tensor imaging. Archives of General Psychiatry 56 (1999) 367-374
34. Lim K., and Helpern J. Neuropsychiatric applications of DTI - a review. NMR in Biomedicine 15 2 (2002) 587-593
35. Lu Y. Computing the logarithm of a symmetric positive definite matrix. Applied Numerical Mathematics 26 4 (1998) 483-496
36. Madden D., Whiting W., Huettel S., White L., MacFall J., and Provenzale J. Diffusion tensor imaging of adult age differences in cerebral white matter: relation to response time. NeuroImage 21 (2004) 1174-1181
37. Malvern L.E. Introduction to the Mechanics of a Continuous Medium (1969), Prentice-Hall, Inc., Englewood Cliffs, NJ
38. Mangin J., Poupon C., Clark C., Bihan D.L., and Bloch I. Distortion correction and robust tensor estimation for MR diffusion imaging. Medical Image Analysis 6 (2002) 191-198
39. Martin K., Papadakis N., Huang C., Hall L.D., and Carpenter T. The reduction of the sorting bias in the eigenvalues of the diffusion tensor. Magnetic Resonance in Imaging 17 6 (1999) 893-901
40. Martin-Fernandez, M., Alberola-Lopez, C., Ruiz-Alzola, J., Westin, C.-F., 2003. Regularization of diffusion tensor maps using a non-Gaussian Markov random field approach. In: Medical Image Computing and Computer-Assisted Intervention (MICCAI), LNCS, vol. 2879, pp. 92-100.
41. Martin-Fernandez, M., Westin, C., Alberola-Lopez, C., 2004. 3D Bayesian regularization of diffusion tensor MRI using multivariate gaussian markov random fields. In: Medical Image Computing and Computer-Assisted Intervention (MICCAI), LNCS, vol. 3216, pp. 351-359.
42. Mattiello J., Basser P., and LeBihan D. Analytical expression for the b matrix in NMR diffusion imaging and spectroscopy. Journal of Magnetic Resonance, Series A 108 (1994) 131-141
43. McGraw T., Vemuri B., Chen Y., Rao M., and Mareci T. DT-MRI denoising and neuronal fiber tracking. Medical Image Analysis 8 (2004) 95-111
44. Melhem E.R., Mori S., Mukundan G., Kraut M.A., Pomper M.G., and van Zijl P.C.M. Diffusion tensor MR imaging of the brain and white matter tractography. American Journal of Radiology (AJR) 178 (2002) 3-16
45. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. Equation of state calculations by fast computing machines. Journal of Chemical Physics 21 (1953) 1087-1092
46. Moakher M. A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications 26 3 (2005) 735-747
47. Moakher M. On the averaging of symmetric positive-definite tensors. Journal of Elasticity 82 (2006) 273-296
48. Mori S., Crain B., Chacko V., and Van Zijl P. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology 45 2 (1999) 265-269
49. Mori S., and Zhang J. Principles of diffusion tensor imaging and its applications to basic neuroscience research. Neuron 51 (2006) 527-539
50. Neeman M., Freyer J., and Sillerud L. Pulsed-gradient spin-echo studies in NMR imaging effects of the imaging gradients on the determination of diffusion coefficients. Journal of Magnetic Resonance 90 (1990) 303-313
51. Parker, P., Schnabel, J., Symms, M., D.J., W., Barker, G., 2000. Nonlinear smoothing for reduction of systematic and random errors in diffusion tensor imaging. J. of Magnetic Resonance Imaging 11, 702-710.
52. Peled S., Gudbjartsson H., Westin C., Kikinis R., and Jolesz F. Magnetic resonance imaging shows orientation and asymmetry of white matter fiber tracts. Brain Research 780 (1998) 27-33
53. Pennec X., Fillard P., and Ayache N. A Riemannian framework for tensor computing. International Journal of Computer Vision 66 1 (2006) 41-66
54. Pfefferbaum A., Sullivan E., Hedehus M., Lim K., Adalsteinsson E., and Moseley M. Age-related decline in brain white matter anisotropy measured with spatially corrected echo-planar diffusion tensor imaging. Magnetic Resonance in Medicine 44 2 (2000) 259-268
55. Pierpaoli C., Jezzard P., Basser P., Barnett A., and Chiro G. Diffusion tensor MR imaging of human brain. Radiology 201 3 (1996) 637-648
56. Plessen K.J., Gruner R., Lundervold A., Hirsch J., Xu D., Bansal R., Hammer T., Wentzel-Larsen T., Atle L.S., Peterson B., and Hugdahl K. Reduced white matter connectivity in the corpus callosum of children with Tourette syndrome. Journal of Child Psychology and Psychiatry 47 12 (2006) 1013-1022
57. Poupon C., Clark A., Frouin V., Regis J., Bihan D.L., Bloch I., and Manging J.F. Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. NeuroImage 12 (2000) 184-195
58. Poupon, C., Mangin, J.-F., Frouin, V., Regis, J., Poupon, F., Pachot-Clouard, M., Bihan, D.L., Bloch, I., 1998. Regularization of MR diffusion tensor maps for tracking brain white matter bundles. In: MICCAI'98, LNCS, vol. 1496, pp. 489-498.
59. Press W., Teukolsky S., Vetterling W., and Flannery B. Numerical Recipes in C. The Art of Scientific Computing (1992), Cambridge University Press
60. Rugg-Gunn F.J., Eriksson S.H., Symms M.R., Barker G.J., and Duncan J.S. Diffusion tensor imaging of cryptogenic and acquired partial epilepsies. Brain 124 (2001) 627-636
61. Sakurai J.J., and Fu Tuan S. Modern Quantum Mechanics (1994), Addison-Wesley. 0-201-53929-2
62. Schwartzman, A., 2006. Random Ellipsoids and False Discovery Rates: Statistics for Diffusion Tensor Imaging Data. Ph.D. Thesis, Stanford University.
63. Schwartzman A., Dougherty R., and Taylor J. Cross-subject comparison of principal diffusion direction maps. Magnetic Resonance in Medicine 53 (2005) 1423-1431
64. Skare S., Hedehus M., Moseley M., and Li T. Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI. Journal of Magnetic Resonance 147 2 (2000) 340-352
65. Song S., Sun S., Ramsbottom M., Chang C., Russell J., and Cross A. Dysmyelination revealed through MRI as an increased radial (but unchanged axial) diffusion of water. Neuroimage 17 (2002) 1429-1436
66. Tabelow K., Polzehl J., Spokoiny V., and Voss H. Diffusion tensor imaging: structural adaptive smoothing. NeuroImage 39 4 (2008) 1763-1773
67. In: Taylor C., and Noble J. (Eds). A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field from DWI. Information Processing in Medical Imaging (2003), Springer-Verlag, Heidelberg 600
68. Tench C., Morgan P., Blumhardt L., and Constantinescu C. Improved white matter fiber tracking using stochastic labeling. Magnetic Resonance in Medicine 48 (2002) 677-683
69. Tschumperle, D., Deriche, R., 2001. Constrained and unconstrained PDEs for vector image restoration. In: Proceeding of the 12th Scandinavian Conference on Image Analysis, pp. 92-105.
70. Tschumperle, D., Deriche, R., 2003. DT-MRI images: estimation, regularization and application. In: MICCAI'03, LNCS, vol. 2809, pp. 530-541.
71. Wang Z., Vemuri B., Chen Y., and Mareci T. A constrained variational principal for direct estimation and smoothing of the diffusion tensor field from complex DWI. IEEE Transactions on Medical Imaging 23 8 (2004) 930-939
72. Westin C., and Knutsson H. Tensor field regularization using normalized convolution. In: Diaz R.M., and Arencibia A.Q. (Eds). Computer Aided Systems Theory (EUROCAST'03). LNCS vol. 2809 (2003), Springer Verlag, Las Palmas de Gran Canaria, Spain 564-572
73. Westin C., Maier S., Mamata H., Navabi A., Jolesz F., and Kikinis R. Processing and visualization for diffusion tensor MRI. Medical Image Analysis 6 2 (2002) 93-108
74. Xu D., Mori S., Solaiyappan M., van Zijl P., and Davatzikos C. A framework for callosal fiber distribution analysis. NeuroImage 17 (2002) 1131-1143