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Metalenses offer a path toward creating ultra-thin optical systems, but they inherently suffer from severe, spatially varying optical aberrations, especially chromatic aberration, which makes image reconstruction a significant challenge.…

Image and Video Processing · Electrical Eng. & Systems 2025-11-27 Harshana Weligampola , Yuanrui Chen , Weiheng Tang , Qi Guo , Stanley H. Chan

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

Numerical Analysis · Mathematics 2024-05-14 Chunlong Sun , Mengmeng Zhang , Zhidong Zhang

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…

Analysis of PDEs · Mathematics 2022-09-20 Florian Faucher , Otmar Scherzer

Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…

Image and Video Processing · Electrical Eng. & Systems 2021-07-09 Tao Hong , Thanh-an Pham , Eran Treister , Michael Unser

Inverse scattering from discrete targets with the single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) measurements is analyzed by compressed sensing theory with and without the…

Mathematical Physics · Physics 2015-05-13 Albert C. Fannjiang

Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors…

Computer Vision and Pattern Recognition · Computer Science 2024-10-28 Yuxin Zhang , Clément Huneau , Jérôme Idier , Diana Mateus

We explore the problem of scattering in a medium modulated by a superluminal rectangular pulse, with the pulse modulation realized through transverse excitations. We solve this problem in the moving frame where the modulation appears purely…

Classical Physics · Physics 2018-03-21 Zoé-Lise Deck-Léger , Alireza Akbarzadeh , Christophe Caloz

Optical focusing through/inside scattering media, like multimode fiber and biological tissues, has significant impact in biomedicine yet considered challenging due to strong scattering nature of light. Previously, promising progress has…

We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…

Analysis of PDEs · Mathematics 2008-03-31 Plamen Stefanov , Gunther Uhlmann

In this paper, the problem of compressive imaging is addressed using natural randomization by means of a multiply scattering medium. To utilize the medium in this way, its corresponding transmission matrix must be estimated. To calibrate…

Computer Vision and Pattern Recognition · Computer Science 2016-08-26 Boshra Rajaei , Eric W. Tramel , Sylvain Gigan , Florent Krzakala , Laurent Daudet

We study an inverse problem for Light Sheet Fluorescence Microscopy (LSFM), where the density of fluorescent molecules needs to be reconstructed. Our first step is to present a mathematical model to describe the measurements obtained by an…

Analysis of PDEs · Mathematics 2020-08-26 Evelyn Cueva , Matias Courdurier , Axel Osses , Victor Castañeda , Benjamin Palacios , Steffen Härtel

In this paper, we propose an approach combining diffusion models and inverse problems for the reconstruction of circumstellar disk images. Our method builds upon the Rhapsodie framework for polarimetric imaging, substituting its classical…

Instrumentation and Methods for Astrophysics · Physics 2025-10-17 Quentin Villegas , Laurence Denneulin , Simon Prunet , André Ferrari , Nelly Pustelnik , Éric Thiébaut , Julian Tachella , Maud Langlois

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy

Deep, high-resolution imaging is essential for unraveling biological complexity and advancing medical diagnostics, yet scattering fundamentally limits optical methods. Among the most promising approaches, photoacoustic imaging achieves…

Inverse rendering, the process of inferring scene properties from images, is a challenging inverse problem. The task is ill-posed, as many different scene configurations can give rise to the same image. Most existing solutions incorporate…

Computer Vision and Pattern Recognition · Computer Science 2023-10-03 Linjie Lyu , Ayush Tewari , Marc Habermann , Shunsuke Saito , Michael Zollhöfer , Thomas Leimkühler , Christian Theobalt

Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…

Computational Physics · Physics 2021-06-02 Philipp M Pelz , Hamish G Brown , Jim Ciston , Scott D Findlay , Yaqian Zhang , Mary Scott , Colin Ophus

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering…

Analysis of PDEs · Mathematics 2020-01-29 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

We deal with the inverse problem of reconstructing acoustic material properties or/and external sources for the time-domain acoustic wave model. The traditional measurements consist of repeated active (or passive) interrogations, as the…

Analysis of PDEs · Mathematics 2025-07-15 Soumen Senapati , Mourad Sini