Related papers: PDE-based numerical method for a limited angle X-r…
In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models…
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…
Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic…
We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of…
We consider a PDE approach to numerically solving the reflector antenna problem by solving an Optimal Transport problem on the unit sphere with cost function $c(x,y) = -2\log \left\Vert x - y \right\Vert$. At each point on the sphere, we…
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is…
A new approach is proposed for reconstruction of images from Radon projections. Based on Fourier expansions in orthogonal polynomials of two and three variables, instead of Fourier transforms, the approach provides a new algorithm for the…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…
We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $\Omega$. We show that this problem can be solved…
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative…
Since its formulation by Hamaker et al., the radio interferometer measurement equation (RIME) has provided a rigorous mathematical basis for the development of novel calibration methods and techniques, including various approaches to the…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
Remote sensing of oceanographic data often yields incomplete coverage of the measurement domain. This can limit interpretability of the data and identification of coherent features informative of ocean dynamics. Several methods exist to…
In this work we study weighted Radon transforms in multidimensions. We introduce an analog of Chang approximate inversion formula for such transforms and describe all weights for which this formula is exact. In addition, we indicate…