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The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
Optoacoustic tomography (OAT), also known as photoacoustic tomography, is a rapidly emerging hybrid imaging technique that possesses great potential for a wide range of biomedical imaging applications. In OAT, a laser is employed to…
We are concerned with an inverse problem associated with the fractional Helmholtz system that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that…
Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the distribution of optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic…
Optical diffraction tomography (ODT) reconstructs a samples volumetric refractive index (RI) to create high-contrast, quantitative 3D visualizations of biological samples. However, standard implementations of ODT use interferometric…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…
Ultrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human…
For a HOM interferometer with two independent incident pulses, the interference pattern can be affected by adding a dispersion medium on one of the incident directions, but there hasn't been a method to reconstruct the phase constant of the…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
Optical Coherence Tomography(OCT) is a non-invasive technique capturing cross-sectional area of the retina in micro-meter resolutions. It has been widely used as a auxiliary imaging reference to detect eye-related pathology and predict…
Imaging point sources in heterogeneous environments from boundary or far-field measurements has been extensively studied in the past. In most existing results, the environment, represented by the refractive index function in the model…
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…
This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media, particularly for measurements relevant to near-infrared spectroscopy. The three temporal domains,…
We solve the wave equation with periodically time-modulated material parameters in a one-dimensional high-contrast resonator structure in the subwavelength regime exactly, for which we compute the subwavelength quasifrequencies numerically…
In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity…
Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…
The dose of X-ray radiation and the scanning time are crucial factors in computed tomography (CT) for clinical applications. In this work, we introduce a multi-source static CT imaging system designed to rapidly acquire sparse view and…
Material decomposition refers to using the energy dependence of material physical properties to differentiate materials in a sample, which is a very important application in computed tomography(CT). In propagation-based X-ray phase-contrast…