Related papers: On geometric inverse problems and microlocal analy…

The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…

We study a class of fractional semilinear elliptic equations and formulate the corresponding Calder\'on problem. We determine the nonlinearity from the exterior partial measurements of the Dirichlet-to-Neumann map by using first order…

We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…

In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however,…

Increasingly in medical imaging has emerged an issue surrounding the reconstruction of noisy images from raw measurement data. Where the forward problem is the generation of raw measurement data from a ground truth image, the inverse…

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

We study the problem of inverting a restricted transverse ray transform to recover a symmetric $m$-tensor field in $\mathbb{R}^3$ using microlocal analysis techniques. More precisely, we prove that a symmetric $m$-tensor field can be…

We consider the inverse problem of determining the highly oscillatory coefficient $a^\epsilon$ in partial differential equations of the form $-\nabla\cdot (a^\epsilon\nabla u^\epsilon)+bu^\epsilon = f$ from given measurements of the…

We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…

We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…

In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a general flow.…

The inverse scattering transform for a special case of the 3-wave resonant interaction equations with non-vanishing boundary conditions is studied. The Jost solutions and the fundamental analytic solutions (FAS) for the associated spectral…

We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calder\'on's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be…

In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…

We prove that uniqueness for the Calder\'on problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $\Delta+V+(\Lambda^{1}_{t}-q)\otimes (\Lambda^{2}_{t}-q)$ defined…