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The theoretical development of quasi-Monte Carlo (QMC) methods for uncertainty quantification of partial differential equations (PDEs) is typically centered around simplified model problems such as elliptic PDEs subject to homogeneous zero…
The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the…
Electrical impedance tomography (EIT) is highly affected by modeling errors regarding electrode positions and the shape of the imaging domain. In this work, we propose a new inclusion detection technique that is completely independent of…
The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the…
Stationary target measurements of the nucleon form factors have been performed with high precision down to $Q^2$ of $\sim$ 0.01 GeV$^2$ for protons ($G_E^p$) and down to $\sim$ 0.1 GeV$^2$ for neutrons ($G_M^n$). Conventional extraction…
Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that has earned significant attention for its potential in real-time monitoring of various physiological parameters. Despite its promise, the sensitivity and…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
Electrical impedance tomography with fully integrated microfluidics and electronics is presented for the first time in a CMOS chip. Chambers and electrodes are fabricated in the interconnect layers of a 65 nm CMOS chip through…
The image reconstruction problem of the tomographic imaging technique magnetic particle imaging (MPI) requires the solution of a linear inverse problem. One prerequisite for this task is that the imaging operator that describes the mapping…
A novel variational method is proposed for calculating the percolation threshold, the real-space structure, and the thermodynamical compressibility of a disordered two-dimensional electron liquid. Its high accuracy is verified against prior…
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth…
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…
Consistency relations of large-scale structure offer a unique and powerful test of the weak equivalence principle (EP) on cosmological scales. If the EP is violated, different tracers will undergo different accelerations in response to a…
This paper explores the use of an entropy-based technique for point cloud reconstruction with the goal of calibrating a lidar to a sensor capable of providing egomotion information. We extend recent work in this area to the problem of…
New techniques for imaging electromagnetic near-fields in nanostructures drive advancements in nanotechnology, optoelectronics, materials science, and biochemistry. Most existing techniques probe near-fields along surfaces, lacking the…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…
In contrast to the standard quantum state tomography, the direct tomography seeks the direct access to the complex values of the wave function at particular positions (i.e., the expansion coefficient in a fixed basis). Originally put…
A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems.…
In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…