We present a novel structure tensor for matrix-valued images. It allows for user defined parameters that add flexibility to a number of image processing algorithms for the segmentation and smoothing of tensor fields. We provide a thorough theoretical derivation of the new structure tensor, including a proof of the equivalence of its unweighted version to the existing structure tensor from the l...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate s...

We present an algebraic solution to both direct and featurebased registration of diffusion tensor images under various local deformation models. In the direct case, we show how to linearly recover a local deformation from the partial derivatives of the tensor using the so-called Diffusion Tensor Constancy Constraint, a generalization of the brightness constancy constraint to diffusion tensor da...

This paper investigates the iterative reconstruction of tensor fields in diffusion tensor magnetic resonance imaging (MRI). The gradient constraints on eigenvalue and tensor component images of the diffusion tensor were exploited. A computer-generated phantom was used in order to simulate the diffusion tensor in a cardiac MRI study with a diffusion model that depends on the fiber structure of t...

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require matrixinversion; and (ii) they cannot (or at least is very difficult to) handle structured regularizations. We propose a new tensor factorization algorithm that circumven...

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures...

Tensors are higher order generalizations of matrices to model multi-aspect data, e.g., a set of purchase records with the schema (user id, product id, timestamp, feedback). Tensor factorization is a powerful technique for generating a model from a tensor, just like matrix factorization generates a model from a matrix, but with higher accuracy and richer information as more attributes are availa...

BACKGROUND Diffusion imaging tractography is increasingly used to trace critical fiber tracts in brain tumor patients to reduce the risk of post-operative neurological deficit. However, the effects of peritumoral edema pose a challenge to conventional tractography using the standard diffusion tensor model. The aim of this study was to present a novel technique using a two-tensor unscented Kalma...

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank matrix recovery is already well-developed, only few contributions on the low rank tensor recovery problem are available so far. In this paper, we introduce versi...