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The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…

Numerical Analysis · Mathematics 2024-09-17 Manabu Machida

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

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 develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…

Numerical Analysis · Mathematics 2016-10-25 Lucie Baudouin , Maya de Buhan , Sylvain Ervedoza

We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the…

Instrumentation and Methods for Astrophysics · Physics 2016-03-01 André Ferrari , Jérémy Deguignet , Chiara Ferrari , David Mary , Antony Schutz , Oleg Smirnov

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging modality that has great potential for a wide range of biomedical imaging applications. In this Note, we derive a hybrid reconstruction…

Analysis of PDEs · Mathematics 2015-06-11 Kun Wang , Mark A. Anastasio

We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…

Geophysics · Physics 2009-05-05 R. B. Schlottmann

Sound speed heterogeneities can create aberrations in B-mode ultrasound images by inducing tissue-dependent delays and diffractive effects that conventional beamforming does not incorporate. By using the Fourier split-step method to…

Medical Physics · Physics 2026-05-01 Rehman Ali , Trevor M. Mitcham , Marvin M. Doyley , Nebojsa Duric , Jeremy J. Dahl

This paper investigates photoacoustic tomography with two spatially varying acoustic parameters, the compressibility and the density. We consider the reconstruction of the absorption density parameter (imaging parameter of Photoacoustics)…

Optimization and Control · Mathematics 2016-01-05 Zakaria Belhachmi , Thomas Glatz , Otmar Scherzer

The motivation of this work is the detection of cerebrovascular accidents by microwave tomographic imaging. This requires the solution of an inverse problem relying on a minimization algorithm (for example, gradient-based), where successive…

Computational Engineering, Finance, and Science · Computer Science 2020-03-23 P. -H. Tournier , I. Aliferis , M. Bonazzoli , M. de Buhan , M. Darbas , V. Dolean , F. Hecht , P. Jolivet , I. El Kanfoud , C. Migliaccio , F. Nataf , C. Pichot , S. Semenov

Wavefront-free behavior and the resulting quantification difficulties are intrinsic limitations of vibrothermography due to the diffusive nature of thermal fields. This work proposes a generalized virtual wave reconstruction framework to…

Passive acoustic mapping (PAM) is a key imaging technique for characterizing cavitation activity in therapeutic ultrasound applications. Recent model-based beamforming algorithms offer high reconstruction quality and strong physical…

Image and Video Processing · Electrical Eng. & Systems 2026-01-13 Tatiana Gelvez-Barrera , Barbara Nicolas , Bruno Gilles , Adrian Basarab , Denis Kouamé

We consider the problem of reconstruction of the Cauchy data for the wave equation in $\mathbb{R}^3$ and $\mathbb{R}^2$ by the measurements of its solution on the boundary of the unit ball.

Analysis of PDEs · Mathematics 2025-05-09 M. I. Belishev , D. Langemann , A. S. Mikhaylov , V. S. Mikhaylov

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Numerical Analysis · Mathematics 2021-01-15 Barbara Kaltenbacher , Kha Van Huynh

The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…

Quantum Physics · Physics 2007-05-23 A. S. Gevorkyan , A. A. Udalov

While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this…

Analysis of PDEs · Mathematics 2018-04-18 Alexander Beigl , Peter Elbau , Kamran Sadiq , Otmar Scherzer

The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…

Analysis of PDEs · Mathematics 2014-05-13 Habib Ammari , Loc Hoang Nguyen , Laurent Seppecher

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…

Analysis of PDEs · Mathematics 2015-05-14 Guillaume Bal , Gunther Uhlmann

For photoacoustic image reconstruction, certain parameters such as sensor positions and speed of sound have a major impact in the reconstruction process and must be carefully determined before data acquisition. Uncertainties in these…

Signal Processing · Electrical Eng. & Systems 2021-11-24 L. Hirsch , M. G. Gonzalez , L. Rey Vega

Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…

Computer Vision and Pattern Recognition · Computer Science 2016-05-20 Teodora Szasz , Adrian Basarab , Denis Kouamé