Related papers: A globally convergent numerical method for a 1-d i…
We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…
We develop the exact renormalization group approach as a way to evaluate the effective speed of propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight…
We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…
This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion…
A convexification-based numerical method for a Coefficient Inverse Problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman Weight Function in the numerical scheme. Convergence…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves…
Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…
Quantitative susceptibility mapping (QSM) aims to visualize the three dimensional susceptibility distribution by solving the field-to-source inverse problem using the phase data in magnetic resonance signal. However, the inverse problem is…
Full-Waveform Inversion (FWI) has now become a widely accepted tool to obtain high-resolution velocity models from seismic data. Typically, the velocity model in its discrete form is represented on a rectangular grid, and we solve for the…
In this paper we propose a perturbative method for the reconstruction of the covariance matrix of a multinormal distribution, under the assumption that the only available information amounts to the covariance matrix of a spherically…