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This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or…

Analysis of PDEs · Mathematics 2021-11-10 Xinchi Huang , Yavar Kian , Eric Soccorsi , Masahiro Yamamoto

How to visually localize multiple sound sources in unconstrained videos is a formidable problem, especially when lack of the pairwise sound-object annotations. To solve this problem, we develop a two-stage audiovisual learning framework…

Computer Vision and Pattern Recognition · Computer Science 2020-07-15 Rui Qian , Di Hu , Heinrich Dinkel , Mengyue Wu , Ning Xu , Weiyao Lin

Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the…

Machine Learning · Computer Science 2022-08-11 Adar Kahana , Symeon Papadimitropoulos , Eli Turkel , Dmitry Batenkov

We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…

Signal Processing · Electrical Eng. & Systems 2024-06-11 Zetao Fei , Hai Zhang

Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this…

Numerical Analysis · Mathematics 2016-11-23 Markus Haltmeier , Thomas Berer , Sunghwan Moon , Peter Burgholzer

A novel approach to improving the performances of confocal scanning imaging is proposed. We experimentally demonstrate its feasibility using acoustic waves. It relies on a new way to encode spatial information using the temporal dimension.…

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang

Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator,…

Data Analysis, Statistics and Probability · Physics 2009-06-16 M. Andrecut

Acoustic metamaterials provide new opportunities for compact and efficient wavefront manipulation, extending beyond conventional bulky and power-intensive phased-arrays. In this work, we exploit the spatial encoding properties of the…

Applied Physics · Physics 2025-12-05 Thomas Macleod , Sebastian Oberst , David A. Powell , Yan Kei Chiang

We consider the inverse problem of determining an unknown vectorial source current distribution associated with the homogeneous Maxwell system. We propose a novel non-iterative reconstruction method for solving the aforementioned inverse…

Analysis of PDEs · Mathematics 2018-01-11 Xianchao Wang , Minghui Song , Yukun Guo , Hongjie Li , Hongyu Liu

We present a method for the recovery of compressively sensed acoustic fields using patterned, instead of point-by-point, detection. From a limited number of such compressed measurements, we propose to reconstruct the field on the sensor…

Numerical Analysis · Mathematics 2016-09-12 Marta M. Betcke , Ben T. Cox , Nam Huynh , Edward Z. Zhang , Paul C. Beard , Simon R. Arridge

We present a simple, frequency domain, preprocessing step to Kirchhoff migration that allows the method to image scatterers when the wave field phase information is lost at the receivers, and only intensities are measured. The resulting…

Numerical Analysis · Mathematics 2016-09-21 Patrick Bardsley , Fernando Guevara Vasquez

This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in 2D. A direct imaging method is proposed to reconstruct the locally rough…

Numerical Analysis · Mathematics 2023-05-11 Long Li , Jiansheng Yang , Bo Zhang , Haiwen Zhang

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

Analysis of PDEs · Mathematics 2026-04-14 Qiling Gu , Wenlong Zhang , Zhidong Zhang

This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way.…

Numerical Analysis · Mathematics 2023-05-09 Isaac Harris , Thu Le , Dinh-Liem Nguyen

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

Mathematical Physics · Physics 2025-10-13 Xinwei Hu , Jingrun Chen , Haijun Yu

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…

Information Theory · Computer Science 2010-03-04 Yuzhe Jin , Young-Han Kim , Bhaskar D. Rao

Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spatial Covariance Analysis (FCA), which is a robust audio source separation method proposed by Duong et al. ["Under-determined reverberant audio source separation using a…

Sound · Computer Science 2018-05-25 Nobutaka Ito , Tomohiro Nakatani