Related papers: Inverse conductivity problem with one measurement:…
Transmission matrix measurements of multimode fibers are now routinely performed in numerous labs, enabling control of the electric field at the distal end of the fiber and paving the way for the potential application to ultrathin medical…
The core-EP and BT inverses for rectangular matrices were studied recently in the literature. The main aim of this paper is to unify both concepts by means of a new kind of generalized inverse called $W$-weighted $q$-BT inverse. We analyze…
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction…
We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we study an inverse problem aiming to reconstruct both the…
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…
In laser gravitational waves detectors optical loss restricts sensitivity. We discuss polarization scattering as one more possible mechanism of optical losses. Circulated inside interferometer light is polarized and after reflection its…
In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
We are concerned with the Calder\'on inverse inclusion problem, where one intends to recover the shape of an inhomogeneous conductive inclusion embedded in a homogeneous conductivity by the associated boundary measurements. We consider the…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
The challenge of image-based 3D reconstruction for glossy objects lies in separating diffuse and specular components on glossy surfaces from captured images, a task complicated by the ambiguity in discerning lighting conditions and material…
Accurately modeling how real-world materials reflect light remains a core challenge in inverse rendering, largely due to the scarcity of real measured reflectance data. Existing approaches rely heavily on synthetic datasets with simplified…
A particular instance of the inverse magnetisation problem is considered. It is assumed that the support of a magnetic sample (a source term in the Poisson equation in $\mathbb{R}^3$) is contained in a bounded planar set parallel to the…
A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a…
This short note considerably simplifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant layered conductivities (PCLC) from partial boundary measurements in electrical…
Rotation measure synthesis allows the estimation of Faraday dispersion via a Fourier transform and is the primary tool to probe cosmic magnetic fields. We show this can be considered mathematically equivalent to the one dimensional…
Propagation of light through media with a complex refractive index in which gain and loss are engineered to be $PT$ symmetric has many remarkable features. In particular the usual unitarity relations are not satisfied, so that the…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
We propose the fast semi-analytical method of modelling the polarization curves in the voltammetric experiment. The method is based on usage of the special func- tions and shows a big calculation speed and a high accuracy and stability. Low…
The generalized pseudopotential theory (GPT) is a powerful method for deriving real-space transferable interatomic potentials. Using a coarse-grained electronic structure, one can explicitly calculate the pair ion-ion and multi-ion…