相关论文: A source reconstruction method in two dimensional …
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
We demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in…
We study the reconstruction of the attenuation and absorption coefficients in a stationary linear transport equation from knowledge of albedo operator in dimension $n\geq 3$ on a Riemannian manifold in the presence of a magnetic field. We…
Although travelling faster than the speed of light in vacuum is not physically allowed, the analogous bound in medium can be exceeded by a moving particle. For an electron in dielectric material this leads to emission of photons which is…
We consider the problem of reconstruction of Cauchy data for the wave equation in $\mathbb{R}^1$ by the measurements of its solution on the boundary of the finite interval. This is a one-dimensional model for the multidimensional problem of…
We present two theorems describing analytic left-inverses of partial X-ray transforms. The first theorem concerns X-ray data collected with an arbitrary distribution of parallel projections; it contains a convolution-backprojection formula…
We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…
A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…
Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…
A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation…
The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear…
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…
This work studies the problem of content-based image retrieval, specifically, texture retrieval. It focuses on feature extraction and similarity measure for texture images. Our approach employs a recently developed method, the so-called…