相关论文: Increasing stability for optical tomography

We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…

This paper describes the mathematical structure of the ill-posed nonlinear inverse problem of low-dose dental cone-beam computed tomography (CBCT) and explains the advantages of a deep learning-based approach to the reconstruction of…

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…

In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the…

In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to…

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 diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable density stratification evolves. In an inclined porous medium,…

We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…

Optical Deflectometric Tomography (ODT) provides an accurate characterization of transparent materials whose complex surfaces present a real challenge for manufacture and control. In ODT, the refractive index map (RIM) of a transparent…

We study increasing stability in the inverse source problems for the Helmholtz equation and the classical Lame system from (minimal) boundary data at multiple wave numbers. By using the Fourier transform with respect to wave numbers,…

Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…

We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure…

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…

Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse…

We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing…

In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid)…

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…

We investigate the stability of an attractive Bose-Einstein condensate in a moving 1D optical lattice in the presence of transverse confinement. By means of a Bogoliubov linear stability analysis we find that the system is dynamically…

In this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e. the solution does not depend continuously on the data. The problem is…