Regularized, fast, and robust analytical Q-ball imaging
Open accessAbstract
We propose a regularized, fast, and robust analytical solution for the Q‐ball imaging (QBI) reconstruction of the orientation distribution function (ODF) together with its detailed validation and a discussion on its benefits over the state‐of‐the‐art. Our analytical solution is achieved by modeling the raw high angular resolution diffusion imaging signal with a spherical harmonic basis that incorporates a regularization term based on the Laplace–Beltrami operator defined on the unit sphere. This leads to an elegant mathematical simplification of the Funk–Radon transform which approximates the ODF. We prove a new corollary of the Funk–Hecke theorem to obtain this simplification. Then, we show that the Laplace–Beltrami regularization is theoretically and practically better than Tikhonov regularization. At the cost of slightly reducing angular resolution, the Laplace–Beltrami regularization reduces ODF estimation errors and improves fiber detection while reducing angular error in the ODF maxima detected. Finally, a careful quantitative validation is performed against ground truth from synthetic data and against real data from a biological phantom and a human brain dataset. We show that our technique is also able to recover known fiber crossings in the human brain and provides the practical advantage of being up to 15 times faster than original numerical QBI method. Magn Reson Med 58:497–510, 2007. © 2007 Wiley‐Liss, Inc.
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The TDF model addresses well-established limitations of the standard single-tensor diffusion model, which cannot resolve complex profiles of WM architecture such as crossing or mixing fibers, present in up to 90% of WM voxels.
“The TDF model addresses well-established limitations of the standard single-tensor diffusion model—which cannot resolve complex profiles of WM architecture such as crossing or mixing fibers, present in up to 90% of WM voxels (Tournier et al., 2004; Descoteaux et al., 2007, 2009; Jeurissen et al., 2013).”
From Diffusion MRI Indices and Their Relation to Cognitive Impairment in Brain Aging: The Updated Multi-protocol Approach in ADNI3 (2019) · cites this paper as Descoteaux et al., 2007
The Introduction (page not available) describes DTI’s well-known limitations in regions with multiple fiber crossings, and Human Brain Data shows crossings recovered by Q-ball ODFs where DTI profiles are limited. This paper does not establish that crossing or mixing fibers occur in up to 90% of white-matter voxels, and it studies Q-ball imaging rather than the TDF model. (LLM, conf=0.88)
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- Authors
- Descoteaux, M., Angelino, E., Fitzgibbons, S., & Deriche, R.
- Affiliations
- Institut national de recherche en sciences et technologies du numérique (FR)
- Harvard University (US)
- Corresponding author
- Descoteaux, Maxime
- ORCID
- Descoteaux, Maxime
- Venue
- Magnetic Resonance in Medicine
- Publisher
- Wiley
- Published
- 2007-08-30
- Volume
- 58
- Issue
- 3
- Pages
- 497-510
- ISSN
- 0740-3194 (ISSN-L)
- 1522-2594
- OpenAlex
- W2111508341
- Cited by
- 850
- References
- 5
- Citations by year
- 2026: 20 · 2025: 37 · 2024: 32 · 2023: 30 · 2022: 28 · 2021: 41 · 2020: 46 · 2019: 46 · 2018: 40 · 2017: 31 · 2016: 39 · 2015: 66 · 2014: 46 · 2013: 55 · 2012: 66
- FWCI
- 40.23
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Magnetic Resonance in Medicine (publishedVersion)
- PubMed (publishedVersion)
- Funders
- McGill University
- Max-Planck-Institut für Kognitions- und Neurowissenschaften
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Keywords
- Q-ball imaging, orientation distribution function, high angular resolution diffusion imaging, Tikhonov regularization, tractography, analytical reconstruction, diffusion MRI
- MeSH terms
- Algorithms, Animals, Brain, Fourier Analysis, Humans, Image Enhancement, Image Processing, Computer-Assisted, Models, Theoretical, Nerve Fibers, Spinal Cord, Time Factors, Artifacts, Rats, Sprague-Dawley, Echo-Planar Imaging, Phantoms, Imaging, Models, Animal, Diffusion Magnetic Resonance Imaging, Rats
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