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We propose a multi-frequency algorithm for imaging the trajectory of a moving point source from one and sparse far-field observation directions in the frequency domain. The starting and terminal time points of the moving source are both…

Numerical Analysis · Mathematics 2025-08-25 Hongxia Guo , Guanghui Hu , Guanqiu Ma

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…

Numerical Analysis · Mathematics 2026-04-28 Guanqiu Ma , Hongxia Guo , Guanghui Hu

In this paper, we introduce a novel numerical method for reconstructing the trajectory within three-dimensional space, where both the emission moment and spatial location of the point source are unknown. Our approach relies solely on…

Numerical Analysis · Mathematics 2025-07-29 Guanqiu Ma , Haonan Zhang , Hongxia Guo

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…

Numerical Analysis · Mathematics 2024-01-02 Hongxia Guo , Guanghui Hu

This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…

Numerical Analysis · Mathematics 2022-12-12 Hongxia Guo , Guanghui Hu , Mengjie Zhao

We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some information (size and location) of the source support can be recovered. A non-iterative…

Analysis of PDEs · Mathematics 2017-12-08 Ala Alzaalig , Guanghui Hu , Xiaodong Liu , Jiguang Sun

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…

Analysis of PDEs · Mathematics 2019-06-07 Xia Ji , Xiaodong Liu

Least-squares reverse time migration is well-known for its capability to generate artifact-free true-amplitude subsurface images through fitting observed data in the least-squares sense. However, when applied to realistic imaging problems,…

Geophysics · Physics 2020-03-04 Mengmeng Yang , Zhilong Fang , Philipp Witte , Felix J. Herrmann

We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced…

Numerical Analysis · Mathematics 2021-09-06 Xiaodong Liu , Shixu Meng

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…

Numerical Analysis · Mathematics 2026-03-11 Fenglin Sun , Hongxia Guo

This paper presents a novel frequency-domain approach for path following problem, specifically designed to handle paths described by discrete data. The proposed algorithm utilizes the fast Fourier Transform (FFT) to process the discrete…

Systems and Control · Electrical Eng. & Systems 2023-08-15 Zirui Chen , Zongyu Zuo

This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…

Instrumentation and Methods for Astrophysics · Physics 2016-08-26 Sampsa Pursiainen , Mikko Kaasalainen

Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…

Analysis of PDEs · Mathematics 2016-07-07 Armin Lechleiter

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…

Numerical Analysis · Mathematics 2025-07-22 Minghui Li , Guanghui Hu , Yue Zhao

This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…

Numerical Analysis · Mathematics 2024-01-17 Hongxia Guo , Guanghui Hu , Guanqiu Ma

The upper mid-band (or FR3, spanning 6-24 GHz) is a crucial frequency range for next-generation mobile networks, offering a favorable balance between coverage and spectrum efficiency. From another perspective, the systems operating in the…

Signal Processing · Electrical Eng. & Systems 2024-12-05 Ali Rasteh , Raghavendra Palayam Hari , Hao Guo , Marco Mezzavilla , Sundeep Rangan

In this paper, we consider the 1D wave equation where the spatial domain is a bounded interval. Assuming the initial conditions to be known, we are here interested in identifying an unknown source term, while we take the Neumann derivative…

Optimization and Control · Mathematics 2011-06-30 Marianne Chapouly , Mazyar Mirrahimi

As a sub-field of object detection, moving infrared small target detection presents significant challenges due to tiny target sizes and low contrast against backgrounds. Currently-existing methods primarily rely on the features extracted…

Computer Vision and Pattern Recognition · Computer Science 2024-09-06 Weiwei Duan , Luping Ji , Shengjia Chen , Sicheng Zhu , Mao Ye

The near future of astrophysics involves many large solid-angle, multi-epoch, multi-band imaging surveys. These surveys will, at their faint limits, have data on large numbers of sources that are too faint to be detected at any individual…

Astrophysics · Physics 2014-11-18 Dustin Lang , David W. Hogg , Sebastian Jester , Hans-Walter Rix

We propose a scenario that involves a stationary observer who detects a point like source of light moving with constant velocity at a constant altitude, using a telescope and a frequency-meter. We derive a formula for the angular velocity…

General Physics · Physics 2008-12-04 Bernhard Rothenstein , Ioan Damian
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