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The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…

Classical Analysis and ODEs · Mathematics 2020-10-28 Elina Shishkina

Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this…

Numerical Analysis · Mathematics 2018-08-03 Gerhard Zangerl , Markus Haltmeier , Linh V. Nguyen , Robert Nuster

The framework of ultrasound computed tomography (USCT) has recently re-emerged as a powerful, safe and operator-independent way to image the breast. State of the art image reconstruction methods are performed with iterative techniques based…

Medical Physics · Physics 2025-08-13 Luca A. Forte

Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT measurement setup, the used…

Analysis of PDEs · Mathematics 2021-12-07 Linh V. Nguyen , Markus Haltmeier , Richard Kowar , Ngoc Do

Thermoacoustic computed tomography (thermoacoustic CT) has the potential to become a mayor non-invasive medical imaging method. In this paper we derive a general mathematical framework of a novel measuring setup introduced in [P.…

Analysis of PDEs · Mathematics 2008-04-18 M. Haltmeier , T. Fidler

This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach…

Analysis of PDEs · Mathematics 2025-01-22 Xi Chen , Shuai Lu , Ruochong Zhang

The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…

Numerical Analysis · Mathematics 2017-05-31 Rafik Aramyan

In this article, we consider the inverse source problem arising in photoacoustic tomography in elastic media. We show that the time reversal method, proposed by Tittelfitz [Inverse Problems 28.5 (2012): 055004], converges with the sharp…

Analysis of PDEs · Mathematics 2017-07-20 Vitaly Katsnelson , Linh V. Nguyen

Image reconstruction in photoacoustic tomography relies on an accurate knowledge of the speed of sound in the target. However, the speed of sound distribution is not generally known, which may result in artefacts in the reconstructed…

Medical Physics · Physics 2025-11-06 Miika Suhonen , Felix Lucka , Aki Pulkkinen , Simon Arridge , Ben Cox , Tanja Tarvainen

We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…

Analysis of PDEs · Mathematics 2015-09-02 Leonid Kunyansky

In this paper we consider the problem of acoustic inversion in the context of the optoacoustic tomography image reconstruction problem. By leveraging the ability of the recently proposed diffusion models for image generative tasks among…

Image and Video Processing · Electrical Eng. & Systems 2024-04-17 M. G. González , M. Vera , A. Dreszman , L. J. Rey Vega

We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…

Analysis of PDEs · Mathematics 2015-01-20 Markus Haltmeier

The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness theorem is proved and a reconstruction…

Mathematical Physics · Physics 2016-09-07 A. G. Ramm

The paper presents a unified, flexible framework for the tasks of audio inpainting, declipping, and dequantization. The concept is further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the…

Audio and Speech Processing · Electrical Eng. & Systems 2021-01-05 Ondřej Mokrý , Pavel Rajmic , Pavel Záviška

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

A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…

Numerical Analysis · Mathematics 2019-11-26 A. B. Bakushinsky , A. S. Leonov

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…

Analysis of PDEs · Mathematics 2020-01-08 Alexander Beigl , Otmar Scherzer , Jarle Sogn , Walter Zulehner

This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…

Analysis of PDEs · Mathematics 2012-03-07 Guillaume Bal , Gunther Uhlmann

Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and…

Analysis of PDEs · Mathematics 2015-06-04 Jie Chen , Yang Yang

Photoacoustic tomography (PAT) is a novel and promising technology in hybrid medical imaging that involves generating acoustic waves in the object of interest by stimulating electromagnetic energy. The acoustic wave is measured outside the…

Numerical Analysis · Mathematics 2022-08-24 Minam Moon , Injo Hur , Sunghwan Moon
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