相关论文: Microlocal inversion of a 3-dimensional restricted…

In this paper, a restricted transverse ray transform acting on vector and symmetric $m$-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric $m$-tensor fields in…

In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray…

We study the microlocal inversion of the ray transform on symmetric $m$-tensor fields restricted to all lines passing through a curve in $\mathbb{R}^{n}$. From this incomplete data, we show that the wavefront set of the solenoidal component…

In this article, we study the problem of recovering symmetric $m$-tensor fields (including vector fields) supported in a unit disk $\mathbb{D}$ from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line…

Consider a compact Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of $1+1$ tensors are invertible, up to natural obstructions,…

In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of…

A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation…

The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…

In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal…

In this work, we study a set of generalized Radon transforms over symmetric $m$-tensor fields in $\mathbb{R}^n$. The longitudinal/transversal Radon transform and corresponding weighted integral transforms for symmetric $m$-tensor field are…

The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M,…

We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric $m$-tensor field in $\mathbb{R}^2$. The goal of this article is to recover a symmetric $m$-tensor field…

Consider a Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem…

We show that a vector field in $\mathbb{R}^n$ can be reconstructed uniquely from the knowledge of restricted Doppler and first integral moment transforms. The line complex we consider consists of all lines passing through a fixed curve…

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along…

This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation…

We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…

Let $(M,g)$ be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of $f$ along maximal geodesics vanish on an appropriate open subset of the space of geodesics…

This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…