9 papers
Quantitative Direct Sampling for Initial Acoustic Sources
Xiaodong Liu, Xianchao Wang
This paper addresses the challenge of quantitatively reconstructing initial acoustic sources from time-dependent wave measurements. We introduce novel indicator functions defined t…
Inverse Obstacle Scattering from Multi-Frequency Near-Field Backscattering Data
Jialei Li, Xiaodong Liu
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscat…
A Radon-transform-based formula for reconstructing acoustic sources from the scattered fields
Xiaodong Liu, Jing Wang
We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating t…
The Radon Transform-Based Sampling Methods for Biharmonic Sources from the Scattered Fields
Xiaodong Liu, Qingxiang Shi, Jing Wang
This paper presents three quantitative sampling methods for reconstructing extended sources of the biharmonic wave equation using scattered field data. The first method employs an…
Identifying convex obstacles from backscattering far field data
Jialei Li, Xiaodong Liu, Qingxiang Shi
The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing th…
A quantitative sampling method for elastic and electromagnetic sources
Xiaodong Liu, Qingxiang Shi
This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicator…
Identifying point sources for biharmonic wave equation from the scattered fields at sparse sensors
Xiaodong Liu, Qingxiang Shi, Jing Wang
This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first s…
The high resolution sampling methods for acoustic sources from multi-frequency far field patterns at sparse observation directions
Xiaodong Liu, Qingxiang Shi
This work is dedicated to novel uniqueness results and high resolution sampling methods for source support from multi-frequency sparse far field patterns. With a single pair of obs…
Uniqueness and modified Newton method for cracks from the far field patterns with a fixed incident direction
Jialei Li, Xiaodong Liu
We consider the inverse cracks scattering problems from the far field patterns with a fixed incident direction. We firstly show that the sound-soft cracks can be uniquely determine…