We present a unified framework for interpolation and regularisation of scalarand tensor-valued images. This framework is based on elliptic partial differential equations (PDEs) and allows rotationally invariant models. Since it does not require a regular grid, it can also be used for tensor-valued scattered data interpolation and for tensor field inpainting. By choosing suitable differential op...

Introduction: Processing of clinical diffusion weighted images (DWIs) for Diffusion Tensor Imaging (DTI) and other applications requires correction for motion, eddy current distortions [1], and susceptibility induced EPI distortions [2]. These corrections are obtained by image registration techniques followed by interpolation of the original images. Image interpolation, however, alters the nois...

Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new imaging modality in the field of medical imaging. This modality of imaging allows one to capture the structural connectivity if any between functionally meaningful regions for example, in the brain. The data however can be noisy and requires restoration. In this paper, we present a novel unified model for simultaneous smoo...

We present the case of a 14-month-old male infant who underwent diffusion tensor imaging within 24 hours of traumatic brain injury. Although conventional MR findings that included those of diffusion-weighted imaging were unremarkable, full-tensor diffusion imaging revealed striking abnormalities in regions of brain that subsequently developed overt swelling. This case engenders important hypoth...

A reoccurring theme in the diffusion tensor imaging literature is the per-voxel estimation of a symmetric 3 x 3 tensor describing the measured diffusion. In this work we attempt to generalize this approach by calculating 2 or 3 or up to k diffusion tensors for each voxel. We show that our procedure can more accurately describe the diffusion particularly when crossing fibers or fiber-bundles are...

The measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities, such as registration, regularization, interpolation, or statistical inference is based. In recent years a family of Riemannian tensor metrics based on geometric considerations has been introduced for this purpose. In this work we examine the properties ...

In magnetic resonance diffusion tensor imaging (DTI), the direction and magnitude of diffusion of water molecules is characterized by a diffusion tensor. In the central nervous system, the highly organized fibre structure of white matter fibre tracts causes the diffusion to be anisotropic. From the DTI data, one can calculate a vector field representing the preferred direction of diffusion at e...

Purpose. Diffusion tensor images (DTI) have been widely used to characterize the white matter microstructure. The incapacity of DTI to represent crossing pathways has motivated the developement of novel diffusion models, such as the multi-tensor models. However, to estimate a multi-tensor model, one needs to acquire the diffusion weighted images (DWI) at multiple b-values, unlike the common sin...

To estimate diffusion tensor MRI (DTI) measures, such as fractional anisotropy and fiber orientation, reliably, a large number of diffusion-encoded images is needed, preferably cardiac gated to reduce pulsation artifacts. However, the concomitant longer acquisition times increase the chances of subject motion adversely affecting the estimation of these measures. While correcting for motion arti...

The purpose of this article is to explain how the random walks of water molecules undergoing diffusion in living tissue may be exploited to garner information on the white matter of the human brain and its connections. We discuss the concepts underlying diffusion-weighted (DW) imaging, and diffusion tensor imaging before exploring fibre tracking, or tractography, which aims to reconstruct the t...