We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with -type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoisin...

Several studies have shown that in tissues over an extended range of b-factors, the signal decay deviates significantly from the basic monoexponential model. The true nature of this departure has to date not been identified. For the current study, line scan diffusion images of brain suitable for biexponential diffusion tensor analysis were acquired in normal subjects on a clinical MR system. Fo...

Determination of axonal pathways provides an invaluable means to study the connectivity of the human brain and its functional network. Diffusion tensor imaging (DTI) is unique in its ability to capture the restricted diffusion of water molecules which can be used to infer the directionality of tissue components. In this paper, we introduce a white matter tractography method based on anisotropic...

A novel anisotropic diffusion filter is proposed in this work with application to cardiac ultrasonic images. It includes probabilistic models which describe the probability density function (PDF) of tissues and adapts the diffusion tensor to the image iteratively. For this purpose, a preliminary study is performed in order to select the probability models that best fit the stastitical behavior ...

Oriented structure enhancement plays important role in computer vision tasks, where the diffusion is encouraged along the preferred direction instead of perpendicular to it. By analyzing the differential geometric property of the oriented structure, a complementary tensor is proposed by combining the first and the second-order structure tensors as complementary descriptors, which can precisely ...

This paper presents a method for deformable registration of diffusion tensor (DT) images that integrates geometry and orientation features into a hierarchical matching framework. The geometric feature is derived from the structural geometry of diffusion and characterizes the shape of the tensor in terms of prolateness, oblateness, and sphericity of the tensor. Local spatial distributions of the...

Diffusion tensor magnetic resonance imaging (DT-MRI, shortened as DTI) produces, from a set of diffusion-weighted magnetic resonance images, tensor-valued images where each voxel is assigned a 3x3 symmetric, positive-definite matrix. This tensor is simply the covariance matrix of a local Gaussian process with zero mean, modelling the average motion of water molecules. We propose a three-dimensi...

A novel method for estimating a field of fiber orientation distribution (FOD) based on signal de-convolution from a given set of diffusion weighted magnetic resonance (DW-MR) images is presented. We model the FOD by higher order Cartesian tensor basis using a parametrization that explicitly enforces the positive semi-definite property to the computed FOD. The computed Cartesian tensors, dubbed ...

Diffusion tensor imaging provides structural information in medical images in the form of a symmetric positive matrix that provides, at each point, the covariance of water diffusion in the tissue. We here describe a new approach designed for smoothing this tensor by directly acting on the field of frames provided by the eigenvectors of this matrix. Using a representation of fields of frames as ...

In this paper we discuss work on the use of diffusion tensor MRIs for inter-subject brain matching. A multiresolution elastic matching algorithm, [2-4], for spatial normalisation of 3D image data, has been adapted for use with diffusion tensor data. The hope is that by exploitation of the added information contained in the diffusion tensor image, improved anatomical matches can be found, partic...