Related papers: Stability for quantitative photoacoustic tomograph…
While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this…
In this article, we address the absorption properties of a class of stochastic differ- ential equations around singular points where both the drift and diffusion functions vanish. According to the H\"older coefficient alpha of the diffusion…
We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…
In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…
We study the phenomenon of increasing stability in the diffuse optical tomography (DOT). It is well-known that the DOT inverse problem is exponentially ill-posed. In this paper, we show that the ill-posedness decreases when we increase the…
We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…
The resolution of photoacoustic imaging deep inside scattering media is limited by the acoustic diffraction limit. In this work, taking inspiration from super-resolution imaging techniques developed to beat the optical diffraction limit, we…
This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…
We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
In this paper we study the problem of photoacoustic inversion in a weakly attenuating medium. We present explicit reconstruction formulas in such media and show that the inversion based on such formulas is moderately ill--posed. Moreover,…
This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…
Almost all known image reconstruction algorithms for photoacoustic and thermoacoustic tomography assume that the acoustic waves leave the region of interest after a finite time. This assumption is reasonable if the reflections from the…
We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the…
We consider the problem of thermoacoustic tomography (TAT), in which one needs to reconstruct the initial value of a solution of the wave equation from its value on an observation surface. We show that if some geometric rays for the…
This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…
We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or…