Related papers: Microlocal inversion of a restricted mixed ray tra…

We consider the attenuated geodesic ray transform defined on pairs of symmetric $2$-tensors and $1$-forms on a simple Riemannian manifold. We prove injectivity and stability results for a class of generic simple metrics and attenuations…

Reconstruction and intrinsic decomposition of scenes from captured imagery would enable many applications such as relighting and virtual object insertion. Recent NeRF based methods achieve impressive fidelity of 3D reconstruction, but bake…

We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover we give a stability estimate and develop a reconstruction procedure.

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the…

The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…

A simple example of an $n$-dimensional admissible complex of planes is given for the overdetermined $k$-plane transform in $\mathbb{R}^n$. For the corresponding restricted $k$-plane transform sharp existence conditions are obtained and…

Consider a compact Riemannian manifold of dimension $\geq 3$ 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…

We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are…

We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces and tori. We give proofs of…

This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…

One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…

Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More…

Recovering a function from its integrals over circular cones recently gained significance because of its relevance to novel medical imaging technologies such emission tomography using Compton cameras. In this paper we investigate the case…

We study the light ray transform acting on tensors on a stationary Lorentzian manifold. Our main result is injectivity up to the natural obstruction as long as the associated magnetic vector field satisfies a finite degree property with…

In algebraic geometry, trigonal curves can always be embedded into Hirzebruch surfaces. In tropical geometry, the notion of trigonality does not have a unique translation. We focus on the characterization in terms of the existence of a…

In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D…

We propose TensoIR, a novel inverse rendering approach based on tensor factorization and neural fields. Unlike previous works that use purely MLP-based neural fields, thus suffering from low capacity and high computation costs, we extend…

In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…

This paper is the first in a series of two articles whose aim is to extend a recent result of Guillarmou-Lefeuvre on the local rigidity of the marked length spectrum from the case of compact negatively-curved Riemannian manifolds to the…

In this article, we establish that any symmetric $m$-tensor field can be recovered pointwise from partial data of the $k$-th weighted divergent ray transform for any $k \in \mathbb{Z}^{+} \cup\{0\}$. Using the unique continuation property…