Related papers: On the multi-frequency inverse source problem in h…
We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced…
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…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…
This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
Researchers often have to deal with heterogeneous population with mixed regression relationships, increasingly so in the era of data explosion. In such problems, when there are many candidate predictors, it is not only of interest to…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…
A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual…
Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and…
We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…