Convex Non-negative Spherical Factorization of Multi-Shell Diffusion-Weighted Images

Christiaens, Daan; Maes, Frederik; Sunaert, Stefan; Suetens, Paul

doi:10.1007/978-3-319-24553-9_21

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…In these approaches, the diffusion sensitization is applied along uniformly distributed directions for each of a set of distinct b ‐values. Characterizing the b ‐value domain in this way opens up new possibilities, for example by allowing for decomposition of the diffusion signal into distinct tissue types, each with its own orientation density function, or the fitting of higher order models . Disentangling multiple tissue types can also improve the estimation of the fODF itself by removing or modelling out signal contributions not related to fibre orientations, as proposed in recent multi‐shell spherical deconvolution implementations .…”

Section: Impact and Future Outlookmentioning

confidence: 99%

Modelling white matter with spherical deconvolution: How and why?

2018

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Since the realization that diffusion MRI can probe the microstructural organization and orientation of biological tissue in vivo and non-invasively, a multitude of diffusion imaging methods have been developed and applied to study the living human brain. Diffusion tensor imaging was the first model to be widely adopted in clinical and neuroscience research, but it was also clear from the beginning that it suffered from limitations when mapping complex configurations, such as crossing fibres. In this review, we highlight the main steps that have led the field of diffusion imaging to move from the tensor model to the adoption of diffusion and fibre orientation density functions as a more effective way to describe the complexity of white matter organization within each brain voxel. Among several techniques, spherical deconvolution has emerged today as one of the main approaches to model multiple fibre orientations and for tractography applications. Here we illustrate the main concepts and the reasoning behind this technique, as well as the latest developments in the field. The final part of this review provides practical guidelines and recommendations on how to set up processing and acquisition protocols suitable for spherical deconvolution.

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Section: Impact and Future Outlookmentioning

confidence: 99%

Modelling white matter with spherical deconvolution: How and why?

2018

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“…Another option is cross-validation (Owen and Perry, 2009). In our previous conference paper (Christiaens et al, 2015a), we applied BIC to suggest the required number of components. However, different model selection criteria are not always in agreement with each other, and which one to use remains an open question.…”

Section: Discussionmentioning

confidence: 99%

“…Extending our previous conference paper (Christiaens et al, 2015a), we made improvements to the initialization, the optimization, and the convergence criterion, improving the overall performance and speed of the algorithm. The accuracy and precision of our convexity- and nonnegativity-constrained spherical factorization (CNSF) technique are evaluated in Monte Carlo simulations at various noise levels.…”

Section: Introductionmentioning

confidence: 99%

Convexity-constrained and nonnegativity-constrained spherical factorization in diffusion-weighted imaging

et al. 2017

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Diffusion-weighted imaging (DWI) facilitates probing neural tissue structure non-invasively by measuring its hindrance to water diffusion. Analysis of DWI is typically based on generative signal models for given tissue geometry and microstructural properties. In this work, we generalize multi-tissue spherical deconvolution to a blind source separation problem under convexity and nonnegativity constraints. This spherical factorization approach decomposes multi-shell DWI data, represented in the basis of spherical harmonics, into tissue-specific orientation distribution functions and corresponding response functions, without assuming the latter as known thus fully unsupervised. In healthy human brain data, the resulting components are associated with white matter fibres, grey matter, and cerebrospinal fluid. The factorization results are on par with state-of-the-art supervised methods, as demonstrated also in Monte-Carlo simulations evaluating accuracy and precision of the estimated response functions and orientation distribution functions of each component. In animal data and in the presence of edema, the proposed factorization is able to recover unseen tissue structure, solely relying on DWI. As such, our method broadens the applicability of spherical deconvolution techniques to exploratory analysis of tissue structure in data where priors are uncertain or hard to define.

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“…The combined spherical harmonics and radial decomposition (SHARD) offers a bespoke signal representation across all shells, hence building a data-driven basis for the q-space signal in the images at hand. This approach is similar in spirit to other blind source separation methods in dMRI, such as sparse or convex nonnegative spherical factorization [23], [32], [33]. However, while nonnegativity constraints of the factorized orientation distribution functions (ODF) in those techniques are motivated on biophysical grounds, they also-by necessity-lead to increased residuals on the signal representation that may still contain relevant structure.…”

Section: Introductionmentioning

confidence: 99%

Learning Compact <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math> </inline-formula>-Space Representations for Multi-Shell Diffusion-Weighted MRI

Christiaens

Cordero‐Grande

Hutter

et al. 2019

IEEE Trans. Med. Imaging

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Diffusion-weighted MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q-space, typically acquired in one or more shells. Recent developments in microstructure imaging and multi-tissue decomposition have sparked renewed attention in the radial bvalue dependence of the signal. Applications in motion correction and outlier rejection therefore require a compact linear signal representation that extends over the radial as well as angular domain. Here, we introduce SHARD, a data-driven representation of the q-space signal based on spherical harmonics and a radial decomposition into orthonormal components. This representation provides a complete, orthogonal signal basis, tailored to the spherical geometry of q-space and calibrated to the data at hand. We demonstrate that the rank-reduced decomposition outperforms model-based alternatives in human brain data, whilst faithfully capturing the micro-and meso-structural information in the signal. Furthermore, we validate the potential of joint radialspherical as compared to single-shell representations. As such, SHARD is optimally suited for applications that require lowrank signal predictions, such as motion correction and outlier rejection. Finally, we illustrate its application for the latter using outlier robust regression.

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Convex Non-negative Spherical Factorization of Multi-Shell Diffusion-Weighted Images

Cited by 6 publications

References 14 publications

Modelling white matter with spherical deconvolution: How and why?

Modelling white matter with spherical deconvolution: How and why?

Convexity-constrained and nonnegativity-constrained spherical factorization in diffusion-weighted imaging

Learning Compact <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math> </inline-formula>-Space Representations for Multi-Shell Diffusion-Weighted MRI

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