English
Related papers

Related papers: Efficient tensor tomography in fan-beam coordinate…

200 papers

This paper studies tensors that admit decomposition in the Extended Tensor Train (ETT) format, with a key focus on the case where some decomposition factors are constrained to be equal. This factor sharing introduces additional challenges,…

Numerical Analysis · Mathematics 2025-08-29 Alexander Molozhavenko , Maxim Rakhuba

Magnetized beams beam with significant canonical angular momentum are critical to electron cooling of hadron beams such as contemplated in next-generation hadron and electron-ion colliders. The transport of magnetized electron beams over…

In this article we study the fan-beam Radon transform ${\cal D}_m $ of symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc $\mathbb D$ as the operator, acting from the object space ${\mathbf L}_{2}(\mathbb D; {\bf…

Complex Variables · Mathematics 2007-05-23 Sergey G. Kazantsev , Alexandre A. Bukhgeim

We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the…

Differential Geometry · Mathematics 2019-09-06 Jere Lehtonen , Jesse Railo , Mikko Salo

We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused…

Analysis of PDEs · Mathematics 2010-04-12 Moritz Allmaras , Wolfgang Bangerth

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…

Computer Vision and Pattern Recognition · Computer Science 2018-04-06 Tatsuya Yokota , Burak Erem , Seyhmus Guler , Simon K. Warfield , Hidekata Hontani

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated…

Numerical Analysis · Mathematics 2018-06-13 François Monard , Donsub Rim

Diffraction imaging of non-equilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension.…

Strongly Correlated Electrons · Physics 2018-02-19 Kenneth R. Beyerlein

Photonic computing has emerged as a promising substrate for accelerating the dense linear-algebra operations at the heart of AI, yet adoption for large Transformer models remains in its infancy. We identify two bottlenecks: (1) costly…

Emerging Technologies · Computer Science 2025-10-03 Hanqing Zhu , Zhican Zhou , Shupeng Ning , Xuhao Wu , Ray Chen , Yating Wan , David Pan

This paper proposes a novel and fast self-supervised solution for sparse-view CBCT reconstruction (Cone Beam Computed Tomography) that requires no external training data. Specifically, the desired attenuation coefficients are represented as…

Image and Video Processing · Electrical Eng. & Systems 2022-09-30 Ruyi Zha , Yanhao Zhang , Hongdong Li

In this article, we establish that any symmetric $m$-tensor field can be recovered pointwise from partial data of the $k$-th weighted divergent ray transform for any $k \in \mathbb{Z}^{+} \cup\{0\}$. Using the unique continuation property…

Analysis of PDEs · Mathematics 2025-09-12 Shubham R. Jathar , Manas Kar , Venkateswaran P. Krishnan , Rahul Raju Pattar

The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…

Mathematical Physics · Physics 2013-01-11 M. Olive , N. Auffray

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…

Methodology · Statistics 2021-10-29 Jiaxin Hu , Chanwoo Lee , Miaoyan Wang

This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficiently compress third-order spatiotemporal data. Using the…

Numerical Analysis · Mathematics 2024-02-21 Fan Tian , Mirjeta Pasha , Misha E. Kilmer , Eric Miller , Abani Patra

Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…

Numerical Analysis · Mathematics 2023-07-25 Sara Pollock , Rhea Shroff

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Machine Learning · Statistics 2017-08-03 Masaaki Imaizumi , Takanori Maehara , Kohei Hayashi

This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance…

Optimization and Control · Mathematics 2007-05-23 Lekbir Afraites , Marc Dambrine , Djalil Kateb

In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of…

Differential Geometry · Mathematics 2016-09-14 Hanming Zhou

We present a versatile method for full-field, X-ray scattering tensor tomography that is based on energy conservation and is applicable to data obtained using different wavefront modulators. Using this algorithm, we pave the way for…

We study the problem of recovery both the attenuation $a$ and the source $f$ in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which…

Analysis of PDEs · Mathematics 2011-05-10 Plamen Stefanov