A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
In the recent articles \cite{PSU1,PSU3}, a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central concept is the surjectivity of the adjoint of the geodesic ray transform, or equivalently the exi…
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary r…
We prove a sharp stability estimate for the problem of reconstructing a symmetric 2-tensor from its integrals along all maximal geodesics on a simple manifold.
We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform applied to the pair of tensors is injective modulo the natural obstruction.
Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.
problem Injectivity for tensor fields on negatively curved manifolds with low regularity metrics.
method Pestov energy estimates for transport equation on non-smooth unit sphere bundle, keeping track of regularity, and using functions with more vertical than horizontal regularity.
result Proves solenoidal injectivity for tensor fields on simple Riemannian manifolds with C1,1 metrics and non-positive sectional curvature.
It has been shown in [Pa1] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injective on functions and 1-forms modulo the natural obstruction. Furthermore, the scattering relation determines the connection and Higgs field m…
Consider a compact Riemannian manifold of dimension ≥3 with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-for…
Study geodesic X-ray transforms on hyperbolic surfaces, proposing new reconstruction methods.
problem Inverting geodesic X-ray transforms for symmetric tensor fields on asymptotically hyperbolic surfaces.
method Developed a decomposition theorem for m-tensor fields, used Guillemin-Kazhdan operators and 0-calculus, and provided explicit reconstruction methods.
result Explicit reconstruction methods for even tensor fields from their X-ray transform or normal operator.
Deep network improves electrical tomography across multiple frequencies.
problem Nonlinear multi-frequency electrical impedance tomography (mfEIT) for tissue conductivity estimation.
method Integrates graph neural networks (GNNs) into the iterative Proximal Regularized Gauss Newton (PRGN) framework to reconstruct tissue concentrations accurately.
result Accurate reconstruction of overlapping tissue fraction concentrations across multiple frequencies.
We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introduci…