Related papers: A series solution and a fast algorithm for the inv…
In this article, we consider the limited data problem for spherical mean transform. We characterize the generation and strength of the artifacts in a reconstruction formula. In contrast to the third's author work [Ngu15b], the observation…
Recovering a 3D surface from its surface normal map, a problem known as normal integration, is a key component for photometric shape reconstruction techniques such as shape-from-shading and photometric stereo. The vast majority of existing…
Despite the increasing prevalence of rotating-style capture (e.g., surveillance cameras), conventional stereo rectification techniques frequently fail due to the rotation-dominant motion and small baseline between views. In this paper, we…
Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
We investigate super-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory. To do this, we constructed a model of the instrument that faithfully reflects the…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
The paper deals with totally geodesic Radon transforms on constant curvature spaces. We study applicability of the historically the first Funk-Radon-Helgason method of mean value operators to reconstruction of continuous and $L^p$ functions…
We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
Depth cameras, typically in RGB-D configurations, are common devices in mobile robotic platforms given their appealing features: high frequency and resolution, low price and power requirements, among others. These sensors may come with…
The aim of this research is to reconstruct the 3D X-ray refractive index gradient maps by the proposed vector Radon transform and its inverse, assuming that the small-angle deviation condition is met. Theoretical analyses show that the…
Very short pulses of x-ray free-electron lasers opened the way to obtain diffraction signal from single particles beyond the radiation dose limit. For 3D structure reconstruction many patterns are recorded in the object's unknown…
In this paper a novel contour integral method is proposed for linear convection-diffusion equations. The method is based on the inversion of the Laplace transform and makes use of a contour given by an elliptic arc joined symmetrically to…
In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general…
The Funk-Radon transform assigns to a function defined on the unit sphere its integrals along all great circles of the sphere. In this paper, we consider a frame decomposition of the Funk-Radon transform, which is a flexible alternative to…
A fast direct inversion scheme for the large sparse systems of linear equations resulting from the discretization of elliptic partial differential equations in two dimensions is given. The scheme is described for the particular case of a…
We prove a novel method for the embedding of a 3-fold rotationally symmetric sphere-type mesh onto a subset of the plane with 3-fold rotational symmetry. The embedding is free-boundary with the only additional constraint on the image set is…
We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…