相关论文: Data-driven basis for reconstructing the contrast …
In this work we propose a theoretical and computational framework for solving the three dimensional inverse medium scattering problem, based on a set of data-driven basis arising from the linearized problem. This set of data-driven basis…
We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using a generalization of the Picard parameter that was…
In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
In this work, we introduce a novel low-rank structure tailored for solving the inverse scattering problem. The particular low-rank structure is given by the generalized prolate spheroidal wave functions, computed stably and accurately via a…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…
The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric…
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and…
Accurate determination of the regularization parameter in inverse problems still represents an analytical challenge, owing mainly to the considerable difficulty to separate the unknown noise from the signal. We present a new approach for…
We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To…
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional…
We introduce two data completion algorithms for the limited-aperture problems in inverse acoustic scattering. Both completion algorithms are independent of the topological and physical properties of the unknown scatterers. The main idea is…
The image reconstruction of chromophore concentrations using Diffuse Optical Tomography (DOT) data can be described mathematically as an ill-posed inverse problem. Recent work has shown that the use of hyperspectral DOT data, as opposed to…
An approach is presented for the inversion of simulated and experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a…
We study an inverse initial-data problem for a nonlinear Schr\"odinger equation in which the initial wave field is reconstructed from lateral measurements. Our approach combines a Legendre-polynomial-exponential-time dimensional reduction…
Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth's surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the…
Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the…