Related papers: Generalized V-line transforms in 2D vector tomogra…
We consider the Radon transform along lines in an $n$ dimensional vector space over the two element field. It is well known that this transform is injective and highly overdetermined. We classify the minimal collections of lines for which…
We present a novel convolutional neural network architecture for photometric stereo (Woodham, 1980), a problem of recovering 3D object surface normals from multiple images observed under varying illuminations. Despite its long history in…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based…
We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in $\mathbb{R}^n$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
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…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
A certain vector-tensor (VT) theory is revisited. It was proposed and analyzed as a theory of electromagnetism without the standard gauge invariance. Our attention is first focused on a detailed variational formulation of the theory, which…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
We introduce a framework for the reconstruction of the amplitude, phase and polarisation of an optical vector-field using calibration measurements acquired by an imaging device with an unknown linear transformation. By incorporating…
This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…
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…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
We consider the inverse problem of the recovery of the gauge field in R^2 modulo gauge transformations from the non-abelian Radon transform.A global uniqueness theorem is proven for the case when the gauge field has a compact support.
The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the fixed point iterations is…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
In this paper, we present a new compositing approach to obtain stylized reflections and refractions with a simple control. Our approach does not require any mask or separate 3D rendering. Moreover, only one additional image is sufficient to…
We tackle the problem of automatically reconstructing a complete 3D model of a scene from a single RGB image. This challenging task requires inferring the shape of both visible and occluded surfaces. Our approach utilizes viewer-centered,…