Related papers: Uniqueness, Lipschitz stability and reconstruction…
Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…
We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…
We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and…
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…
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…
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 revisit the inverse problem of reconstructing a spatially varying diffusion coefficient in stationary elliptic equations from boundary Cauchy data. From a theoretical perspective, we introduce a gradient-weighted modification of the…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
In this paper we are interested in the inverse problem of recovering a compact supported function from its truncated Fourier transform. We derive new Lipschitz stability estimates for the inversion in terms of the truncation parameter. The…
We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…
In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…
In the paper, we study the problem of recovering the Sturm--Liouville operator with frozen argument from its spectrum and additional data. For this inverse problem, we establish a substantial property of the uniform stability, which…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
This paper concerns the inverse problem of retrieving a stationary potential for the Schr\"odinger evolution equation in a bounded domain of RN with Dirichlet data and discontinuous principal coefficient a(x) from a single time-dependent…
The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…