Related papers: Reconstruction of the refractive index from experi…
The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time domain, a finite-difference algorithm to compute the frequency-domain…
This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…
We explore the effects of incorporating negative index materials into the physics of time-varying media and find that changing the refractive index from positive to negative creates a perfect time-reversed wave: a perfect time-domain lens.…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the…
We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…
This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…
We examine the refractive index from the viewpoint of modern first-principles materials physics. We first argue that the standard formula, $n^2 = \varepsilon_{\mathrm r} \mu_{\mathrm r}$, is generally in conflict with fundamental principles…
Electron backscatter diffraction (EBSD) has developed over the last few decades into a valuable crystallographic characterisation method for a wide range of sample types. Despite these advances, issues such as the complexity of sample…
A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…
Magnetic resonance imaging (MRI) exam protocols consist of multiple contrast-weighted images of the same anatomy to emphasize different tissue properties. Due to the long acquisition times required to collect fully sampled k-space…
In this paper, we consider simultaneous reconstruction of the diffusion coefficient and initial state for a one-dimensional heat equation through boundary control and measurement. The boundary measurement is known to make the system exactly…
We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is…
To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…
Reflectance bounds the frequency spectrum of illumination in the object appearance. In this paper, we introduce the first stochastic inverse rendering method, which recovers the attenuated frequency spectrum of an illumination jointly with…
The paper presents a globally convergent algorithm for solving coefficient inverse problems. Being rooted in the globally convergent numerical method (SIAM J. Sci. Comput., 31, No.1 (2008), pp. 478-509) for solving multidimensional…