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This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Masahiro Yamamoto

We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel's principle with the weak vanishing property to…

Numerical Analysis · Mathematics 2026-04-02 Zhiwei Yang , Yikan Liu

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…

Medical Physics · Physics 2022-12-07 Timur E. Gureyev , Hamish G. Brown , Harry M. Quiney , Leslie J. Allen

Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with…

Analysis of PDEs · Mathematics 2021-07-20 Ru-Yu Lai , Kui Ren , Ting Zhou

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…

Analysis of PDEs · Mathematics 2023-05-02 Ravshan Ashurov , Yusuf Fayziev , Muattar Khudoykulova

When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…

Medical Physics · Physics 2021-07-22 Tetsuya Mimura , Yu Jiang , Norikazu Todoroki , Manabu Machida

In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

Analysis of PDEs · Mathematics 2019-11-14 Suman Kumar Sahoo , Manmohan Vashisth

The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-05 Yushan Gao , Thomas Blumensath

This paper studies inverse problems in quantitative photoacoustic tomography with additional optical current data supplemented from diffuse optical tomography. We propose a three-stage image reconstruction method for the simultaneous…

Numerical Analysis · Mathematics 2025-01-27 Yinxi Pan , Kui Ren , Shanyin Tong

Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…

Numerical Analysis · Mathematics 2025-10-29 Oscar P. Bruno , Manuel A. Santana

We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…

Numerical Analysis · Mathematics 2017-06-07 Dinh-Liem Nguyen , Michael V. Klibanov , Loc H. Nguyen , Aleksandr E. Kolesov , Michael A. Fiddy , Hui Liu

Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all…

Optimization and Control · Mathematics 2018-04-25 Michelle Liu , Rajiv Kumar , Eldad Haber , Aleksandr Aravkin

Optical coherence tomography (OCT) and photoacoustic tomography (PAT) are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform PAT and OCT imaging…

Analysis of PDEs · Mathematics 2016-04-19 Peter Elbau , Leonidas Mindrinos , Otmar Scherzer

This article deals with the uniqueness in identifying multiple parameters simultaneously in the one-dimensional time-fractional diffusion-wave equation of fractional time-derivative order $\in (0,2)$ with the zero Robin boundary condition.…

Analysis of PDEs · Mathematics 2021-03-16 Xiaohua Jing , Masahiro Yamamoto

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

Numerical Analysis · Mathematics 2020-08-26 Barbara Kaltenbacher , William Rundell

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…

Analysis of PDEs · Mathematics 2020-03-13 Guanghui Hu , Jingzhi Li

This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

Numerical Analysis · Mathematics 2018-08-29 Bo Zhang , Haiwen Zhang

The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…

Image and Video Processing · Electrical Eng. & Systems 2025-10-29 Andreas Hauptmann , Leonid Kunyansky , Jenni Poimala

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

Analysis of PDEs · Mathematics 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao
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