Related papers: Positive Jacobian constraints for elliptic boundar…
The article deals with electrodynamics in the presence of anisotropic materials having scalar wave impedance. Maxwell's equations written for differential forms over a 3-manifold are analysed. The system is extended to a Dirac type first…
We introduce a framework for performing the inverse imaging of composite elastic materials. Our technique uses surface acoustic wave (SAW) boundary observations within a minimization problem to express the interior composition of the…
The Fourier restriction conjecture is a fundamental problem in harmonic analysis. In this paper, we investigate restriction estimates for degenerate higher codimensional quadratic surfaces and obtain sharp results for some types of…
In this article, we consider the inverse problem of determining spatially heterogeneous absorption and diffusion coefficients from a single measurement of the absorbed energy (in the steady-state diffusion approximation of light transfer).…
Coherent diffractive imaging is a technique that recovers the sample image by numerically inverting its diffraction pattern. We propose a generalization of this method for the inversion of multi-wavelength data. Using this approach, we show…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
The physical situation of the collision and subsequent interaction of plane gravitational waves in a Minkowski background gives rise to a well-posed characteristic initial value problem in which initial data are specified on the two null…
Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…
Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. Especially, Neumann and Robin BVPs are considered. The main obstacle for applying the usual…