相关论文: Increasing stability for optical tomography

A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…

The radiative instability of the relativistic electron beam in a periodic dielectric-filled cylindrical waveguide is considered. The dependence of the beam instability increment on the radiated wave frequency near the region of dispersion…

This work intends to prove that strong instabilities may appear for high order geometric optics expansions of weakly stable quasilinear hyperbolic boundary value problems, when the forcing boundary term is perturbed by a small amplitude…

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 solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…

In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

Recently, it was demonstrated that electrochemical doping fronts in organic semiconductors ex- hibit a new fundamental instability growing from multidimensional perturbations [Phys. Rev. Lett. 107, 016103 (2011)]. In the instability…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusive regime (the Knudsen number $\mathsf{Kn}\ll 1$), the…

As electronic operating frequencies increase toward the terahertz regime, new electrooptic modulators capable of low-voltage high-frequency operation must be developed to provide the necessary optical interconnects. This letter presents a…

We present a study of three-mode parametric instability in large-scale gravitational-wave detectors. Previous work used a linearised model to study the onset of instability. This paper presents a non-linear study of this phenomenon, which…

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…

Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation, coherent manipulation and characterization of free-electron quantum states. The available measurement consists of electron energy…

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…

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence,…

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…

In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…

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…