Related papers: General reconstruction of elastic strain fields fr…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…
In this article, we study Momentum Light Ray Transform (MLRT) on symmetric tensor fields. MLRT is an integral transform in time-space domain ($(t,x)\in \mathbb{R}^{1+n}$), which integrates a scalar function or a tensor field along the light…
We examine the well-posedness of inverse eigenstrain problems for residual stress analysis from the perspective of the non-uniqueness of solutions, structure of the corresponding null space and associated orthogonal range-null…
Recently, a number of reconstruction algorithms have been presented for residual strain tomography from Bragg-edge neutron transmission measurements. In this paper, we examine whether strain tomography can also be achieved from diffraction…
The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic…
We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition…
In \cite{Lei}, the author derived an exact rotation-strain model in two dimensions for the motion of incompressible viscoelastic materials via the polar decomposition of the deformation tensor. Based on the rotation-strain model, the author…
In this article we develop an image based rendering technique based on light field reconstruction from a limited set of perspective views acquired by cameras. Our approach utilizes sparse representation of epipolar-plane images in a…
A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of Integral Geometry is cast into a workable framework which allows the full determination of…
We develop a method to reconstruct, from measured displacements of an underlying elastic substrate, the spatially dependent forces that cells or tissues impart on it. Given newly available high-resolution images of substrate displacements,…
Strain engineering is used to obtain desirable materials properties in a range of modern technologies. Direct nanoscale measurement of the three-dimensional strain tensor field within these materials has however been limited by a lack of…
In this paper, a restricted transverse ray transform acting on vector and symmetric $m$-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric $m$-tensor fields in…
Evaluation of residual elastic strain within the bulk of engineering components or natural objects is a challenging task, since in general it requires mapping a six-component tensor quantity in three dimensions. A further challenge concerns…
Broadband longitudinal-to-transverse mode conversion under normal incidence remains difficult to achieve, especially with structurally simple designs. Numerical simulations show that a single periodic row of inclined long-slits near a free…
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…
We consider the problem of high-dimensional light field reconstruction and develop a learning-based framework for spatial and angular super-resolution. Many current approaches either require disparity clues or restore the spatial and…
The linear algorithm of the the full non-linear large scale structure of Gaussian random fields is extended here to to perform non-linear CRs. The procedure consists of: (1) Using linear CR of low resolution data to construct a high…
A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm…
Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…
This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large…