Related papers: Linearized inverse scattering based on seismic Rev…
Recently, the focus of reflection seismologists has shifted to applications where a high-resolution image of the subsurface is required. Least-Squares Reverse-Time Migration (LSRTM) is a common tool used to compute such images. Still, its…
The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.
The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong: in general it cannot be carried…
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…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
We introduce a dispersive point target model based on scattering by a particle in the far-field. The synthetic aperture imaging problem is then expanded to identify these targets and recover their locations and frequency dependent…
The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…
Inverse rendering remains a core challenge in graphics and vision, especially in the snapshot configurations required for lightweight desktop workflows, where the per-frame information budget is highly constrained. Previous inverse…
We propose and investigate efficient numerical methods for inverse problems related to Magnetic Resonance Imaging (MRI). Our goal is to extend the recent convergence results for the Landweber-Kaczmarz method obtained in [Haltmeier, Leitao,…
The scattering transformation developed by Mallat is put into the perspective of field theory. It is shown to be a simultaneous transformation of the field and the "time" parameter explicitly used in the definition of path integrals central…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that…
We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…
Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) method for solving inverse scattering problems based on an…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
The general framework of LSRTM consists of two steps; the first one is generating the RTM image and the second is applying the Least-Squares Migration, however, the convergence of both operations consumes a lot of time to extract the final…