Related papers: Tensor tomography: progress and challenges
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
Creating virtual models of real spaces and objects is cumbersome and time consuming. This paper focuses on the problem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant…
Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However,…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…
The solution of one Zamfiresku's problem was obtained. We discuss the unsolved questions related to the Mizel's problem.
Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…
The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear…
The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing…
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
Our purpose is to investigate the local boundedness, the upper semicontinuity, and the stability of the solution map of tensor complementarity problems. To do this, we focus on the set of R$_0$--tensors and show that this set plays an…
We consider the problem of recovering an orthogonally decomposable tensor with a subset of elements distorted by noise with arbitrarily large magnitude. We focus on the particular case where each mode in the decomposition is corrupted by…
Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these…