Related papers: A linear time approach to three-dimensional recons…
The reconstruction of an unknown function $f$ from its line sums is the aim of discrete tomography. However, two main aspects prevent reconstruction from being an easy task. In general, many solutions are allowed due to the presence of the…
Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels…
Being able to see beyond the direct line of sight is an intriguing prospective and could benefit a wide variety of important applications. Recent work has demonstrated that time-resolved measurements of indirect diffuse light contain…
We consider the reconstruction of a function on a finite subset of $\mathbb{Z}^2$ if the line sums in certain directions are prescribed. The real solutions form a linear manifold, its integer solutions a grid. First we provide an explicit…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties…
The three-dimensional linear regression problem is a problem of finding a spacial straight line best fitting a group of points in three-dimensional Euclidean space. This problem is considered in the present paper and a solution to it is…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…
The "Auxiliary Extra Dimension" model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free…
Discrete tomography focuses on the reconstruction of functions $f: A \to \mathbb{R}$ from their line sums in a finite number $d$ of directions, where $A$ is a finite subset of $\mathbb{Z}^2$. Consequently, the techniques of discrete…
Recently an algorithm was given in [Garde & Hyv\"onen, SIAM J. Math. Anal., 2024] for exact direct reconstruction of any $L^2$ perturbation from linearised data in the two-dimensional linearised Calder\'on problem. It was a simple forward…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension $N$ on a distributed computing network of $N$ nodes that is connected in a binary communication tree.…
Ghost imaging is a fascinating process, where light interacting with an object is recorded without resolution, but the shape of the object is nevertheless retrieved, thanks to quantum or classical correlations of this interacting light with…