In this article we study the fan-beam Radon transform Dm of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc D as the operator, acting from the object space L2(D;Sm) to the data space L2([0, 2π) × [0, 2π)). The orthogonal polynomial basis s (±m) n,k of solenoidal tensor fields on the disc D was built with the help of Zernike polynomials and then a singular value decomp...

In order to make the speech perception hashing authentication algorithm has strong robustness and discrimination to content preserving operations and speech communication under the common background noise, a new robust speech perceptual hashing authentication algorithm based on spectral subtraction and multi-feature tensor was proposed. The proposed algorithm uses spectral subtraction method to...

We have proposed a novel numerical method to calculate accurately physical quantities of the ground state using the tensor network wave function in two dimensions. The tensor network wave function is determined by an iterative projection approach which uses the Trotter-Suzuki decomposition formula of quantum operators and the singular value decomposition of matrix. The norm of the wave function...

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensorSingular Value Decomposition (t-SVD)[1], which is a group theoretic framework for tensor decomposition. In contrast to popular existing tensor decomposition techniques such as higher-order SVD (HOSVD), t-SVD has optimality properties similar to t...

How can we find patterns and anomalies in a tensor, or multidimensional array, in an efficient and directly interpretable way? How can we do this in an online environment, where a new tensor arrives each time step? Finding patterns and anomalies in a tensor is a crucial problem with many applications, including building safety monitoring, patient health monitoring, cyber security, terrorist det...

In this paper, we provide two generalizations of the CUR matrix decomposition Y = CUR (also known as pseudo-skeleton approximation method [1]) to the case of N-way arrays (tensors). These generalizations, which we called Fiber Sampling Tensor Decomposition types 1 and 2 (FSTD1 and FSTD2), provide explicit formulas for the parameters of a rank-(R,R, ..., R) Tucker representation (the core tensor...

Volterra series is a powerful tool for blackbox macromodeling of nonlinear devices. However, the exponential complexity growth in storing and evaluating higher order Volterra kernels has limited so far its employment on complex practical applications. On the other hand, tensors are a higher order generalization of matrices that can naturally and efficiently capture multidimensional data. Signif...

Modeling multi-way data can be accomplished using tensors, which are data structures indexed along three or more dimensions. Tensors are increasingly used to analyze extremely large and sparse multi-way datasets in life sciences, engineering, and business. The canonical polyadic decomposition (CPD) is a popular tensor factorization for discovering latent features and is most commonly found via ...

Tensor valued data are frequently used in medical imaging. For a 3-dimensional second order tensor such data imply at least six degrees of freedom for each voxel. The operators ability to perceive this information is of outmost importance and in many cases a limiting factor for the interpretation of the data. In this paper we propose a decomposition of such tensor fields using the Tflash tensor...

We consider the problem of how to group information when multiple similarities are known. For a group of people, we may know their education, geographic location and family connections and want to cluster the people by treating all three of these similarities simultaneously. Our approach is to store each similarity as a slice in a tensor. The similarity measures are generated by comparing featu...