Related papers: Monodromy of the Radon transform

We study reconstruction of an unknown function from its $d$-plane Radon transform on the flat $n$-torus when $1 \leq d \leq n-1$. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We…

A meromorphic projective structure on a punctured Riemann surface $X\setminus P$ is determined, after fixing a standard projective structure on $X$, by a meromorphic quadratic differential with poles of order three or more at each puncture…

Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…

Consider the family of smooth cubic surfaces which can be realized as threefold-branched covers of $\mathbb{P}^{2}$, with branch locus equal to a smooth cubic curve. This family is parametrized by the space $\mathcal{U}_{3}$ of smooth cubic…

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…

We introduce bi-parametric fractional integrals of the Erdelyi-Kober type that generalize known Garding-Gindikin constructions associated to the cone of positive definite matrices. It is proved that the Radon transform, which maps a zonal…

We describe an algorithm computing the monodromy and the pole order filtration on the top Milnor fiber cohomology of hypersurfaces in $\mathbb{P}^n$ whose pole order spectral sequence degenerates at the second page. In the case of…

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…

The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their…

We study horizontal semistable and horizontal de Rham representations of the absolute Galois group of a certain smooth affinoid over a p-adic field. In particular, we prove that a horizontal de Rham representation becomes horizontal…

We describe algorithmic methods for the Gauss-Manin connection of an isolated hypersurface singularity based on the microlocal structure of the Brieskorn lattice. They lead to algorithms for computing invariants like the monodromy, the…

We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group $G$ to smooth maps into a homogeneous space $M=G/H$, and determine the global monodromy obstruction to reconstructing such maps from…

In this paper we deal with Radon transforms for generalized flag manifolds in the framework of quasi-equivariant D-modules. We shall follow the method employed by Baston-Eastwood and analyze the Radon transform using the…

Let (M,g) be an analytic, compact, Riemannian manifold with boundary, of dimension n >= 2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition [23].…

Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a…

We study horospherical Radon transforms that integrate functions on the $n$-dimensional real hyperbolic space over horospheres of arbitrary fixed dimension $1\le d\le n-1$. Exact existence conditions and new explicit inversion formulas are…

Let S be a K3 surface. In part I of this paper, we constructed a representation of the group Aut D(S), of auto-equivalences of the derived category of S. We interpreted this infinite dimensional representation, as the natural action of Aut…

This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…

For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…

We consider the space of smooth complex projective plane curves of degree d. Defined over this is the tautological family of plane curves, and hence there is a monodromy representation into the mapping class group of the fiber. We show two…