Related papers: Finite element approximation for quantitative phot…
Idier et al. [IEEE Trans. Comput. Imaging 4(1), 2018] propose a method which achieves superresolution in the microscopy setting by leveraging random speckle illumination and knowledge about statistical second order moments for the…
This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and…
This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
We introduce a variational quantum computing approach for quantum state reconstruction within a discretized logical framework, using experimental measurement data as input. By mapping the reconstruction cost function onto an Ising model,…
Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction problem. The proposed algorithm is based on the…
Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from…
$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…
In this paper we investigate the problem of recovering the source term in an elliptic system from a measurement of the state on a part of the boundary. For the particular interest in reconstructing probably discontinuous sources, we use the…
In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an $H^1(\Omega)$…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…
In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…
Noise is a significant challenge in imaging. Conventional intensity-based techniques mitigate noise through various filtering methods, but they often require prior knowledge of noise characteristics and struggle, especially under low-light…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…