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Traditional imaging systems, such as the eye or cameras, image scenes that lie in the direct line-of-sight (LoS). Most objects are opaque in the optical and infrared regimes and can limit dramatically the field of view (FoV). Current…

Optics · Physics 2022-05-11 Yiran Cui , Georgios C. Trichopoulos

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Computational Engineering, Finance, and Science · Computer Science 2018-12-04 Ivan Dokmanić , Joan Bruna , Stéphane Mallat , Maarten de Hoop

We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\varepsilon$-periodic for large $|x_1|$, allowing…

Numerical Analysis · Mathematics 2017-08-23 Tomáš Dohnal , Ben Schweizer

A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…

Computational Physics · Physics 2018-08-01 Johan Helsing , Anders Karlsson

We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…

Analysis of PDEs · Mathematics 2020-01-08 Hongyu Liu , Xiaodong Liu , Xianchao Wang , Yuliang Wang

Ptychography is a lensless, computational imaging method that utilises diffraction patterns to determine the amplitude and phase of an object. In transmission ptychography, the diffraction patterns are recorded by a detector positioned…

Image and Video Processing · Electrical Eng. & Systems 2023-01-04 Kira A. M. Maathuis , Jacob Seifert , Allard P. Mosk

An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…

Numerical Analysis · Mathematics 2014-04-30 Ying Li

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

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

People have been familiar with the phenomenon of wave refraction for several centuries. Recently, a novel type of refraction, i.e., negative refraction, where both incident and refractory lines locate on the same side of the normal line,…

Other Condensed Matter · Physics 2009-11-13 Zhoujian Cao , Hong Zhang , Gang Hu

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…

Analysis of PDEs · Mathematics 2020-09-14 Fioralba Cakoni , Jingni Xiao

We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…

Numerical Analysis · Mathematics 2022-11-24 Moritz Hauck , Daniel Peterseim

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.

Analysis of PDEs · Mathematics 2026-03-30 Saumyajit Das , Susovan Pramanik

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…

Image and Video Processing · Electrical Eng. & Systems 2025-05-22 Yuanhao Wang , Shirin Shoushtari , Ulugbek S. Kamilov

Lensless imaging is a popular research field for the advantages of small size, wide field-of-view and low aberration in recent years. However, some traditional lensless imaging methods suffer from slow convergence, mechanical errors and…

Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…

Analysis of PDEs · Mathematics 2023-11-29 General Ozochiawaeze

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

Numerical Analysis · Mathematics 2016-10-06 Giovanni S. Alberti , Habib Ammari , Bangti Jin , Jin-Keun Seo , Wenlong Zhang

We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…

Analysis of PDEs · Mathematics 2013-10-15 Guanghui Hu , Jingzhi Li , Hongyu Liu , Hongpeng Sun

Diffusion models are now commonly used to solve inverse problems in computational imaging. However, most diffusion-based inverse solvers require complete knowledge of the forward operator to be used. In this work, we introduce a novel…

Image and Video Processing · Electrical Eng. & Systems 2025-09-22 Yuanyun Hu , Evan Bell , Guijin Wang , Yu Sun