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In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
We consider the problem of selective inference after solving a (randomized) convex statistical learning program in the form of a penalized or constrained loss function. Our first main result is a change-of-measure formula that describes…
This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…
In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability…
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
The Alvarez-Macovski method [Alvarez, R. E and Macovski, A., "Energy-selective reconstructions in X-ray computerized tomography", Phys. Med. Biol. (1976), 733--44] requires the inversion of the transformation from the line integrals of the…
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…
This report provides some closed form solutions -- and their inversion -- to a satellite's bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the $J_{2}$ spherical zonal harmonic. The equatorial track of…
We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coefficients from dynamic response operator and answer a…
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models…
We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from 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…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…