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The presence of a scattering medium in the imaging path between an object and an observer is known to severely limit the visual acuity of the imaging system. We present an approach to circumvent the deleterious effects of scattering, by…

We demonstrate a motion-free intensity diffraction tomography technique that enables direct inversion of 3D phase and absorption from intensity-only measurements for weakly scattering samples. We derive a novel linear forward model,…

Image and Video Processing · Electrical Eng. & Systems 2018-06-26 Ruilong Ling , Waleed Tahir , Hsing-Ying Lin , Hakho Lee , Lei Tian

A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…

Mathematical Physics · Physics 2016-06-21 Subhasis Panda , S. Pratik Khastgir

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…

Analysis of PDEs · Mathematics 2019-05-30 Zhaoxiang Li , Zhiliang Deng , Jiguang Sun

In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a…

Analysis of PDEs · Mathematics 2013-11-19 Manas Kar , Mourad Sini

In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements. The problem is modeled using the…

Analysis of PDEs · Mathematics 2015-09-02 Matias Courdurier , Francois Monard , Axel Osses , Francisco Romero

In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…

Analysis of PDEs · Mathematics 2026-04-07 Rahul Bhardwaj , Mandeep Kumar , Manmohan Vashisth

We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…

Analysis of PDEs · Mathematics 2026-03-30 Adrian Kirkeby

A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…

High Energy Physics - Phenomenology · Physics 2017-03-13 Dmitry Karlovets

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…

Image and Video Processing · Electrical Eng. & Systems 2024-12-23 Matthias M. Saurer , Han Na , Marius Brinkmann , Thomas F. Eibert

Imaging 3D nano-structures at very high resolution is crucial in a variety of scientific fields. However, due to fundamental limitations of light propagation we can only measure the object indirectly via 2D intensity measurements of the 3D…

Image and Video Processing · Electrical Eng. & Systems 2020-02-28 Zalan Fabian , Justin Haldar , Richard Leahy , Mahdi Soltanolkotabi

Reflection phase imaging provides label-free, high-resolution characterization of biological samples, typically using interferometric-based techniques. Here, we investigate reflection phase microscopy from intensity-only measurements under…

Quantitative Methods · Quantitative Biology 2019-12-18 Alex Matlock , Anne Sentenac , Patrick C. Chaumet , Ji Yi , Lei Tian

We study the inverse backscattering problem for the Schr\"odinger equation in two dimensions. We prove that, for a non-smooth potential in 2D the main singularities up to 1/2 of the derivative of the potential are contained in the Born…

Analysis of PDEs · Mathematics 2012-09-14 Juan Manuel Reyes

We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…

Numerical Analysis · Mathematics 2023-07-19 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Adrian Constantin , Vladimir S. Gerdjikov , Rossen I. Ivanov

Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…

We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse problem, originally formulated by Dix, of reconstructing $g$ from boundary measurements…

Analysis of PDEs · Mathematics 2012-12-04 Maarten V. de Hoop , Sean F. Holman , Einar Iversen , Matti Lassas , Bjørn Ursin

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…

Analysis of PDEs · Mathematics 2022-04-11 Isaac Harris

In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…

Information Theory · Computer Science 2023-07-04 Palina Salanevich

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

Numerical Analysis · Mathematics 2025-02-25 Yun Zhang , Xiaoli Feng , Xiongbin Yan