Variational Frameworks for DT-MRI Estimation, Regularization and Visualization
نویسندگان
چکیده
We address three crucial issues encountered in DT-MRI (Diffusion Tensor Magnetic Resonance Imaging) : diffusion tensor Estimation, Regularization and fiber bundle Visualization. We first review related algorithms existing in the literature and propose then alternative variational formalisms that lead to new and improved schemes, thanks to the preservation of important tensor constraints (positivity, symmetry). We illustrate how our complete DT-MRI processing pipeline can be successfully used to construct and draw fiber bundles in the white matter of the brain, from a set of noisy raw MRI images.
منابع مشابه
Neuronal Fiber Delineation in Area of Edema from Diffusion Weighted MRI
Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a non invasive method for brain neuronal fibers delineation. Here we show a modification for DT-MRI that allows delineation of neuronal fibers which are infiltrated by edema. We use the Muliple Tensor Variational (MTV) framework which replaces the diffusion model of DT-MRI with a multiple component model and fits it to the signal attenuati...
متن کاملDT-MRI Images: Estimation, Regularization, and Application
Diffusion-Tensor MRI is a technique allowing the measurement of the water molecule motion in the tissues fibers, by the mean of rendering multiple MRI images under different oriented magnetic fields. This large set of raw data is then further estimated into a volume of diffusion tensors (i.e. 3 × 3 symmetric and positive-definite matrices) that describe through their spectral elements, the diff...
متن کاملTensor Field Visualization with PDE’s and Application to DT-MRI Fiber Visualization
We propose a PDE-based method to create textured representations of dense tensor-valued fields, for visualization purposes. Within the framework of anisotropic diffusion PDE’s, we focus on the general trace-based expressions (that we previously investigated in [39]) that are particularly well adapted to control the local smoothing performed by the regularization processes. Using this formalism,...
متن کاملAn inexact alternating direction method with SQP regularization for the structured variational inequalities
In this paper, we propose an inexact alternating direction method with square quadratic proximal (SQP) regularization for the structured variational inequalities. The predictor is obtained via solving SQP system approximately under significantly relaxed accuracy criterion and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...
متن کاملTutorial on variational approximation methods
Tutorial topics • A bit of history • Examples of variational methods • A brief intro to graphical models • Variational mean field theory – Accuracy of variational mean field – Structured mean field theory • Variational methods in Bayesian estimation • Convex duality and variational factorization methods – Example: variational inference and the QMR-DT Variational methods • Classical setting: " f...
متن کامل