Related papers: A linear time approach to three-dimensional recons…

We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree…

To date, high-resolution (< 1 nm) imaging of extended objects in three-dimensions (3D) has not been possible. A restriction known as the Crowther criterion forces a tradeoff between object size and resolution for 3D reconstructions by…

We adapt a symmetric interior penalty discontinuous Galerkin method using a patch reconstructed approximation space to solve elliptic eigenvalue problems, including both second and fourth order problems in 2D and 3D. It is a direct…

The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This…

In a number of astrophysical applications one tries to determine the two-dimensional or three-dimensional structure of an object from a time series of measurements. While most methods used for reconstruction assume that object is static,…

In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…

In the context of $f(\mathcal{R})$ gravity, dark energy is a geometrical fluid with negative equation of state. Since the function $f(\mathcal{R})$ is not known \emph{a priori}, the need of a model independent reconstruction of its shape…

We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…

When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…

Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…

Recent works have demonstrated non-line of sight (NLOS) reconstruction by using the time-resolved signal frommultiply scattered light. These works combine ultrafast imaging systems with computation, which back-projects the recorded…

In this paper, we present a method for denoising and reconstruction of low-dimensional manifold in high-dimensional space. We suggest a multidimensional extension of the Locally Optimal Projection algorithm which was introduced by Lipman et…

In this paper, we investigate the almost-periodic solutions for the one-dimensional nonlinear Klein-Gordon equation within the non-relativistic limit under periodic boundary conditions. Specifically, by employing the method introduced in…

Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…

Ghost imaging uses two light beams correlated in the transverse position, time, or frequency to create an image of a spatial, temporal, or spectral object. We propose a scheme of time-to-space ghost imaging for creating a spatial image of a…

We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…

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…