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We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension $n \geq 3$. The stability estimates correspond to a couple of uniqueness results by Dos Santos…
In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and…
We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e…
We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem
Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…
An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…
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…
The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local…
In this paper we consider the inverse scattering problem for high-contrast targets. We mathematically analyze the experimentally-observed phenomenon of super-resolution in imaging the target shape. This is the first time that a mathematical…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…
In this paper we establish mixed norm estimates of interactive Schr\"{o}dinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schr\"{o}dinger equations with mass critical nonlinearity.
We consider the inverse problem of determining the metric-measure structure of collapsing manifolds from local measurements of spectral data. In the part I of the paper, we proved the uniqueness of the inverse problem and a continuity…
A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the…
Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…
We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is…
In this paper the validity of the diffusion approximation for multiple scattering of classical waves in random medium in different regimes is investigated, with emphasize to weak localization effects. Many principle topics are discussed…