A second order tensor is usually used to describe the diffusion of water for each voxel within a Diffusion Tensor Magnetic Resonance (DT-MR) images. However, a second order tensor approximation fails to accurately represent complex local tissue structures such as crossing fibers. Therefore, higher order tensors are used to represent more complex diffusivity profiles. In this work we examine and...

‎‎The tensor product is the fundemental ingredient for extending one-dimensional techniques of filtering and compression in signal preprocessing to higher dimensions‎. ‎Woven frames play ‎ a crucial role in signal preprocessing and distributed data processing‎. Motivated by these facts, we have investigated the tensor product of woven frames and presented some of their properties. Besides...

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem is capturing some delay/shift-invariant structure. In this study, we consider a low-rank model in an embedded space of a tensor. For this purpose, we extend a...

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches focused on matrix and vector based methods to represent these higher-order data, more recently it has been shown that tensor decomposition methods are better equip...

Introduction: The limitation of the 2 order diffusion tensor model in the representation of voxels containing more than one dominant fiber direction have led to the development of more advanced representations. Here the focus is especially on higher order diffusion tensor models [1,2]. These more advanced diffusion models require datasets which provide diffusion information for a larger number ...

Estimation of local spatial structure has a long history and numerous analysis tools have been developed. A concept that is widely recognized as fundamental in the analysis is the structure tensor. However, precisely what it is taken to mean varies within the research community. We present a new method for structure tensor estimation which is a generalization of many of it’s predecessors. The m...

We present Tensor-Train RNN (TT-RNN), a novel family of neural sequence architectures for multivariate forecasting in environments with nonlinear dynamics. Long-term forecasting in such systems is highly challenging, since there exist long-term temporal dependencies, higher-order correlations and sensitivity to error propagation. Our proposed tensor recurrent architecture addresses these issues...

Semantic models are presented for two simple imperative languages with higher order constructs. In the rst language the interesting notion is that of second order assignment x := s, for x a procedure variable and s a statement. The second language extends this idea by a form of higher order communication, with statements c ! s and c ? x, for c a channel. We develop operational and denotational ...

We show that function types which have only initial algebras for regular functors in the domains, i.e. first order function types, can be represented by terminal coalgebras for certain nested functors. The representation exploits properties of ω-limits and local ω-colimits.