Total Variation and Mean Curvature PDEs on the Space of Positions and Orientations

Duits, Remco; St-Onge, Etienne; Portegies, Jim; Smets, Bart M. N.

doi:10.1007/978-3-030-22368-7_17

Cited by 8 publications

(10 citation statements)

References 29 publications

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“…Nevertheless, our method can still be used on such data sets, but would not be aware of the relationship between DWIs beyond the angular domain. Other approaches to build the dictionary could be used to inform the algorithm and potentially increase performance on such data sets by explicitly modeling the spatial and angular relationship (Schwab et al, 2018) or using an adaptive weighting considering the b-values in the angular domain (Duits, St-Onge, Portegies, & Smets, 2019) amongst other possible strategies. This weighting strategy could be used for repeated acquisitions or if multishell data sets without an equal repartition of the data across shells needs to be harmonized instead of the strictly angular criterion we used in this manuscript.…”

Section: Limitations Of Our Algorithm and Possible Improvementsmentioning

confidence: 99%

Harmonization of diffusionMRIdata sets with adaptive dictionary learning

St-Jean

Viergever

Leemans

2020

Human Brain Mapping

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Diffusion magnetic resonance imaging can indirectly infer the microstructure of tissues and provide metrics subject to normal variability in a population. Potentially abnormal values may yield essential information to support analysis of controls and patients cohorts, but subtle confounds could be mistaken for purely biologically driven variations amongst subjects. In this work, we propose a new harmonization algorithm based on adaptive dictionary learning to mitigate the unwanted variability caused by different scanner hardware while preserving the natural biological variability of the data. Our harmonization algorithm does not require paired training data sets, nor spatial registration or matching spatial resolution. Overcomplete dictionaries are learned iteratively from all data sets at the same time with an adaptive regularization criterion, removing variability attributable to the scanners in the process. The obtained mapping is applied directly in the native space of each subject toward a scanner-space. The method is evaluated with a public database which consists of two different protocols acquired on three different scanners. Results show that the effect size of the four studied diffusion metrics is preserved while removing variability attributable to the scanner. Experiments with alterations using a free water compartment, which is not simulated in the training data, shows that the modifications applied to the diffusion weighted images are preserved in the diffusion metrics after harmonization, while still reducing global variability at the same time. The algorithm could help multicenter studies pooling their data by removing scanner specific confounds, and increase statistical power in the process.

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Section: Limitations Of Our Algorithm and Possible Improvementsmentioning

confidence: 99%

Harmonization of diffusionMRIdata sets with adaptive dictionary learning

St-Jean

Viergever

Leemans

2020

Human Brain Mapping

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“…-A proof for the theorem of the strong convergence, stability and accuracy of TV flows. This result was announced in [25] but not yet proven.…”

Section: Remark 2 (Additional Content In This Version)mentioning

confidence: 95%

“…This article is an extended version of the authors' SSVM article by the same name [25]. The following content is new:…”

Section: Remark 2 (Additional Content In This Version)mentioning

confidence: 99%

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Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations

Smets

Portegies

St-Onge³

et al. 2020

J Math Imaging Vis

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Two key ideas have greatly improved techniques for image enhancement and denoising: the lifting of image data to multi-orientation distributions and the application of nonlinear PDEs such as total variation flow (TVF) and mean curvature flow (MCF). These two ideas were recently combined by Chambolle and Pock (for TVF) and Citti et al. (for MCF) for two-dimensional images. In this work, we extend their approach to enhance and denoise images of arbitrary dimension, creating a unified geometric and algorithmic PDE framework, relying on (sub-)Riemannian geometry. In particular, we follow a different numerical approach, for which we prove convergence in the case of TVF by an application of Brezis–Komura gradient flow theory. Our framework also allows for additional data adaptation through the use of locally adaptive frames and coherence enhancement techniques. We apply TVF and MCF to the enhancement and denoising of elongated structures in 2D images via orientation scores and compare the results to Perona–Malik diffusion and BM3D. We also demonstrate our techniques in 3D in the denoising and enhancement of crossing fiber bundles in DW-MRI. In comparison with data-driven diffusions, we see a better preservation of bundle boundaries and angular sharpness in fiber orientation densities at crossings.

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“…Nevertheless, our method can still be used on such datasets, but would not be aware of the relationship between DWIs beyond the angular domain. Other approaches to build the dictionary could be used to inform the algorithm and potentially increase performance on such datasets by explicitly modeling the spatial and angular relationship (Schwab et al, 2018) or using an adaptive weighting considering the b-values in the angular domain (Duits et al, 2019) amongst other possible strategies. Modeling explicitly the angular part of the signal could also be used to sample new gradients directions directly, an aspect we covered in the original CDMRI challenge by using the spherical harmonics basis (Descoteaux et al, 2007).…”

Section: Limitationsmentioning

confidence: 99%

Harmonization of diffusion MRI datasets with adaptive dictionary learning

St-Jean

Viergever

Leemans

2019

Preprint

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Diffusion magnetic resonance imaging is a noninvasive imaging technique which can indirectly infer the microstructure of tissues and provide metrics which are subject to normal variability across subjects. Potentially abnormal values or features may yield essential information to support analysis of controls and patients cohorts, but subtle confounds affecting diffusion MRI, such as those due to difference in scanning protocols or hardware, can lead to systematic errors which could be mistaken for purely biologically driven variations amongst subjects. In this work, we propose a new harmonization algorithm based on adaptive dictionary learning to mitigate the unwanted variability caused by different scanner hardware while preserving the natural biological variability present in the data. Overcomplete dictionaries, which are learned automatically from the data and do not require paired samples, are then used to reconstruct the data from a different scanner, removing variability present in the source scanner in the process. We use the publicly available database from an international challenge to evaluate the method, which was acquired on three different scanners and with two different protocols, and propose a new mapping towards a scanner-agnostic space. Results show that the effect size of the four studied diffusion metrics is preserved while removing variability attributable to the scanner. Experiments with alterations using a free water compartment, which is not simulated in the training data, shows that the effect size induced by the alterations is also preserved after harmonization. The algorithm is freely available and could help multicenter studies in pooling their data, while removing scanner specific confounds, and increase statistical power in the process.

show abstract

Total Variation and Mean Curvature PDEs on the Space of Positions and Orientations

Cited by 8 publications

References 29 publications

Harmonization of diffusionMRIdata sets with adaptive dictionary learning

Harmonization of diffusionMRIdata sets with adaptive dictionary learning

Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations

Harmonization of diffusion MRI datasets with adaptive dictionary learning

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