Related papers: Voltammetry: mathematical modelling and Inverse Pr…
In this paper, we consider the intensity-based inversion method (IIM) for quantitative material parameter estimation in quasi-static elastography. In particular, we consider the problem of estimating the material parameters of a given…
We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…
A new method for absolute polarimetric calibration of large telescopes is presented. The proposed method is highly accurate and is based on the calibration of a small sub-aperture, which is then extended to the full system by means of…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a…
We demonstrate a novel experimental technique for quantum-state tomography of the collective density matrix. It is based on measurements of the polarization of light, traversing the atomic vapor. To assess the technique's robustness against…
A simplified model for a collective dynamics in ionic melts is proposed for the description of optic-like excitations. Within a polarization model of ionic melt the analytical expressions for optic and relaxation dipole modes are obtained.…
We present a method based on Mueller calculus to calibrate linear polarimetric observations. The key advantages of the proposed way of calibration are: (1) that it can be implemented in a data reduction pipeline, (2) that it is possible to…
In an attempt to test the possibility of solving the inverse problem for liquid metals i.e. obtaining the effective pair potential from the experimental structure factor, we solve the modified Hypernetted-Chain Integral equation for liquid…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an…
The methods of Nicholson and Shain and Randles-Sevcik are the paradigms of voltammetry of redox species. However, as they were originally developed for aqueous redox couples, they cannot be directly applied to solid redox films such as…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
The backscattering of laser radiation by a relativistic electron beam is a widely used method for measuring the spin polarization of electrons. We consider again the properties of the scattering process paying special attention to recoil…
We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the…