Related papers: Multifrequency inverse obstacle scattering with un…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
This paper is concerned with the reconstruction of the shape of an acoustic obstacle. Based on the use of the tapered waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…
We propose an inverse scattering scheme of recovering a polyhedral obstacle in $\mathbb{R}^n$, $n=2,3$, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial…
The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown…
This paper is concerned with a nonlinear imaging problem, which aims to reconstruct a locally perturbed, perfectly reflecting, infinite plane from intensity-only (or phaseless) far-field or near-field data. A recursive Newton iteration…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
This paper is concerned with the inverse acoustic scattering problem with phaseless total-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…