Related papers: Approximating Multi-Dimensional and Multiband Sign…
The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. However, it is well known that the low rank CPD approximation…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…
This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…
The 3GPP suggests to combine dual polarized (DP) antenna arrays with the double directional (DD) channel model for downlink channel estimation. This combination strikes a good balance between high-capacity communications and parsimonious…
Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e.,…
Approximate message passing (AMP) is an algorithmic framework for solving linear inverse problems from noisy measurements, with exciting applications such as reconstructing images, audio, hyper spectral images, and various other signals,…
Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear…
Efficient channel estimation is challenging in full-dimensional multiple-input multiple-output communication systems, particularly in those with hybrid digital-analog architectures. Under a compressive sensing framework, this letter first…
We report the experimental realization of perfect sound absorption by sub-wavelength monopole and dipole resonators that exhibit degenerate resonant frequencies. This is achieved through the destructive interference of two resonators'…
In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…
An analytical theory of non-uniformly doped or shaped PN-junction diodes submitted to large-signals at high frequencies is presented. The resulting expressions can be useful to evaluate the performance of semiconductor device modeling…
In this paper, we consider the Poisson equation on a "long" domain which is the Cartesian product of a one-dimensional long interval with a (d-1)-dimensional domain. The right-hand side is assumed to have a rank-1 tensor structure. We will…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…