Related papers: On an inverse source problem for the Biot's equati…
This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our case, the inverse problem consists in restoring the…
In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by…
Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…
This paper concerns the quantitative step of the medical imaging modality Thermo-acoustic Tomography (TAT). We model the radiation propagation by a system of Maxwell's equations. We show that the index of refraction of light and the…
Micro-seismic events, naturally occurring within geological formations and quasi-brittle engineered systems, provide a powerful window into the evolving processes of material degradation and failure. Accurate characterization of these…
This letter is focused on the design and analysis of computational wideband time-reversal imaging algorithms, designed to be adaptive with respect to the noise levels pertaining to the frequencies being employed for scene probing. These…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
In this paper, we consider the inverse problem of recovering a time-dependent nonlinearity for a third order nonlinear acoustic equation, which is known as the Jordan-Moore-Gibson-Thompson equation (J-M-G-T equation for short). This third…
This paper studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem to reconstruct Stekloff eigenvalues is investigated using a new integral…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…
This paper introduces a novel numerical method for the inverse problem of electroencephalography(EEG). We pose the inverse EEG problem as an optimal control (OC) problem for Poisson's equation. The optimality conditions lead to a…
In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two spatially variable coefficients in a system of PDEs…
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.…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…
Electrical Impedance Tomography (EIT) systems are becoming popular because they present several advantages over competing systems. However, EIT leads to images with very low resolution. Moreover, the nonuniform sampling characteristic of…
This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…