Comparative Analysis of Diffusion Tensor Imaging Estimation Methods
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Abstract
Purpose: This topic focuses on a comprehensive evaluation of various diffusion tensor imaging (DTI) estimation methods, such as linear least squares (LLS), weighted linear least squares (WLLS), iterative re-weighted linear least squares (IRLLS) and non-linear least squares (NLS). The article will explore how each method performs in terms of accuracy, efficiency in estimating the diffusion tensor and robustness against noise.
Materials and Methods: The study compares the methods using simulated diffusion-weighted MRI data. Time complexity and performance were evaluated across key metrics such as TRMSE, RMSE, MSD and ΔSNR.
Results: The results of the study demonstrate that LLS and IRLLS consistently outperform other methods in terms of TRMSE, MSD and SNR, particularly in high-noise scenarios. NLS performs best in reducing RMSE but high noise causes it to fit to noise, so it is not robust. WLLS showed the weakest performance across all metrics.
Conclusion: LLS and IRLLS provide a balance between accuracy and computational efficiency, making them practical for use in DTI analysis.
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31- Arsigny V, "Fast and simple calculus on tensors in the Log-Euclidean framework." in MICCAI, (2005), pp. 115-22.
32- Y. Kong, Y. Li, J. Wu, and H. Shu, "Noise reduction of diffusion tensor images by sparse representation and dictionary learning." Biomed Eng Online, Vol. 15p. 5, Jan 13 (2016).
33- P. Fillard, X. Pennec, V. Arsigny, and N. Ayache, "Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics." IEEE Trans Med Imaging, Vol. 26 (No. 11), pp. 1472-82, Nov (2007).
34- Zhenhua Lin, Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition. (2019).
35- J. D. Tournier, "Mrtrix3: A fast, flexible and open software framework for medical image processing and visualization." Neuroimage, pp. 116-37, (2019).
36- P. Cook and et al, "Camino: Open-source diffusion-MRI reconstruction and processing." in 14th Scientific Meeting and Exhibition, (2006), pp. 27-59.
37- B. Geveci J. P. Ahrens, and C. C. Law, Paraview: An end-user tool for large-data visualization. (The Visualization Handbook). (2005).
38- A. Leemans, "ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data." (2009).
39- D. K. Jones, "White matter integrity, fiber count, and other fallacies: The do’s and don’ts of diffusion MRI." Neuroimage, (2012).
40- J. Veraart, "A comprehensive framework for accurate diffusion MRI parameter estimation." Magn Reson Med, (2012).
2- J. Mattiello P. Basser, and D. LeBihan, "Estimation of the effective self-diffusion tensor from the NMR spin echo." Journal of Magnetic Resonance, Vol. 103pp. 247-54, (1994).
3- P. J. Basser, "Inferring microstructural features and the physiological state of tissues from diffusion-weighted images." NMR Biomedicine, Vol. 8pp. 333–44, (1995).
4- D. L. Bihan, "Diffusion tensor imaging: Concepts and applications." Journal of Magnetic Resonance Imaging, (2001).
5- P. J. Basser, "Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor." Journal of Magnetic Resonance, Vol. 111pp. 209-19, (1996).
6- P. J. Basser, "Diffusion-tensor MRI: theory, experimental design and data analysis - a technical review." NMR in Biomedicine, Vol. 15pp. 456–67, (2002).
7- R. Salvador, A. Pena, D. K. Menon, T. A. Carpenter, J. D. Pickard, and E. T. Bullmore, "Formal characterization and extension of the linearized diffusion tensor model." Hum Brain Mapp, Vol. 24 (No. 2), pp. 144-55, Feb (2005).
8- C. G. Koay, L. C. Chang, J. D. Carew, C. Pierpaoli, and P. J. Basser, "A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging." J Magn Reson, Vol. 182 (No. 1), pp. 115-25, Sep (2006).
9- C. G. Koay, "Least squares approaches to diffusion tensor estimation." in Diffusion MRI, D. Jones, Ed. New York: Oxford University Press, (2011), pp. 281-343.
10- Veraart J., "Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls." NeuroImage pp. 335-46, (2013).
11- P. G. Nucifora, "Diffusion-tensor MR imaging and tractography: exploring brain microstructure and connectivity." Radiology, Vol. 2pp. 367-84, (2007).
12- A. Faria K. Oishi, P. van Zijl, and S. Mori, MRI Atlas of Human White Matter. Elsevier Science, (2010).
13- E. W. Lang, "Brain connectivity analysis: A short survey." Computational Intelligence and Neuroscience, Vol. 1(2012).
14- B. Bodini and O. Ciccarelli, "Diffusion MRI in neurological disorders." in Diffusion MRI: Academic Press, (2014), pp. 241-55.
15- T. Woo-Suk, "Current clinical applications of diffusion-tensor imaging in neurological disorders." Journal of Clinical Neurology (2018).
16- C. Cavaliere, "Diffusion tensor imaging and white matter abnormalities in patients with disorders of consciousness." Frontiers in Human Neuroscience, Vol. 8(2015).
17- M. Georgios, "Traumatic brain injuries and diffusion tensor imaging a review." Recent Patents on Medical Imaging, Vol. 2pp. 36-50, (2012).
18- D. B. Douglas, "Diffusion Tensor Imaging of TBI: Potentials and Challenges." Topics in magnetic resonance imaging : TMRI, pp. 241-51, (2015).
19- S. H. Jang, "Role of Diffusion Tensor Imaging in the Diagnosis of Traumatic Axonal Injury in Individual Patients with a Concussion or Mild Traumatic Brain Injury: A Mini-Review." Diagnostics, (2022).
20- O. Abe T. Shizukuishi, "Diffusion tensor imaging analysis for psychiatric disorders." Magnetic resonance in medical sciences : MRMS pp. 153-59, (2013).
21- T. White, "Diffusion tensor imaging in psychiatric disorders." Topics in magnetic resonance imaging: TMRI, pp. 97-109, (2008).
22- E. O. Stejskal and J. E. 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. 288-92, (1965).
23- A. L. Alexander, "A geometric analysis of diffusion tensor measurements of the human brain." Magnetic Resonance in Medicine, pp. 283-91, (2000).
24- Q. Collier, J. Veraart, B. Jeurissen, A. J. den Dekker, and J. Sijbers, "Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters." Magn Reson Med, Vol. 73 (No. 6), pp. 2174-84, Jun (2015).
25- Z. Wang, B. C. Vemuri, Y. Chen, and T. H. Mareci, "A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI." IEEE Trans Med Imaging, Vol. 23 (No. 8), pp. 930-9, Aug (2004).
26- C. G. Koay, J. D. Carew, A. L. Alexander, P. J. Basser, and M. E. Meyerand, "Investigation of anomalous estimates of tensor-derived quantities in diffusion tensor imaging." Magn Reson Med, Vol. 55 (No. 4), pp. 930-6, Apr (2006).
27- J. Nocedal, Numerical Optimization. Springer New York, (1999).
28- D. Tschumperle, "Variational frameworks for DT-MRI estimation, regularization and visualization." in Proceedings Ninth IEEE International Conference on Computer Vision, (2003), pp. 116-21.
29- M. Moakher, "A differential geometry approach to the geometric mean of symmetric positive-definite matrices." SIAM J Matrix Analy Applicat, pp. 734-47, (2005).
30- Xavier Pennec, Pierre Fillard, and Nicholas Ayache, "A Riemannian Framework for Tensor Computing." International Journal of Computer Vision, Vol. 66 (No. 1), pp. 41-66, 2006/01/01 (2006).
31- Arsigny V, "Fast and simple calculus on tensors in the Log-Euclidean framework." in MICCAI, (2005), pp. 115-22.
32- Y. Kong, Y. Li, J. Wu, and H. Shu, "Noise reduction of diffusion tensor images by sparse representation and dictionary learning." Biomed Eng Online, Vol. 15p. 5, Jan 13 (2016).
33- P. Fillard, X. Pennec, V. Arsigny, and N. Ayache, "Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics." IEEE Trans Med Imaging, Vol. 26 (No. 11), pp. 1472-82, Nov (2007).
34- Zhenhua Lin, Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition. (2019).
35- J. D. Tournier, "Mrtrix3: A fast, flexible and open software framework for medical image processing and visualization." Neuroimage, pp. 116-37, (2019).
36- P. Cook and et al, "Camino: Open-source diffusion-MRI reconstruction and processing." in 14th Scientific Meeting and Exhibition, (2006), pp. 27-59.
37- B. Geveci J. P. Ahrens, and C. C. Law, Paraview: An end-user tool for large-data visualization. (The Visualization Handbook). (2005).
38- A. Leemans, "ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data." (2009).
39- D. K. Jones, "White matter integrity, fiber count, and other fallacies: The do’s and don’ts of diffusion MRI." Neuroimage, (2012).
40- J. Veraart, "A comprehensive framework for accurate diffusion MRI parameter estimation." Magn Reson Med, (2012).
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| Issue | Vol 13 No 2 (2026) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/fbt.v13i2.21943 | |
| Keywords | ||
| DTI diffusion MRI tensor estimation method Cholesky decomposition | ||
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How to Cite
1.
Jabari S, Ghodousian A, Lashgari R, A. Ardekani B. Comparative Analysis of Diffusion Tensor Imaging Estimation Methods. Frontiers Biomed Technol. 2026;13(2):447-457.
