Related papers: Scale-discretised ridgelet transform on the sphere
We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral…
In this paper we introduce and study a Bargmann-Radon transform on the real monogenic Bargmann module. This transform is defined as the projection of the real Bargmann module on the closed submodule of monogenic functions spanned by the…
In this paper we consider the so-called crystallographic Radon transform (or crystallographic $X$-ray transform) and totally geodesic Radon transform on the group of rotations SO(3). As we show both of these transforms naturally appear in…
We study the interaction of an electromagnetic field with a non-absorbing or absorbing dispersive sphere in the framework of complex angular momentum techniques. We assume that the dielectric function of the sphere presents a Drude-like…
We consider a one-dimensional Radon transform on the group SO(3) which is motivated by texture goniometry. In particular we will derive several inversion formulae and compare them with the inversion of the one-dimensional spherical Radon…
We provide a new algorithm for the treatment of the noisy inversion of the Radon transform using an appropriate thresholding technique adapted to a well-chosen new localized basis. We establish minimax results and prove their optimality. In…
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…
The Hua-Radon and polarized Hua-Radon transform are two orthogonal projections defined on holomorphic functions in the Lie sphere. Both transformations can be written as integral transforms with respect to a suitable reproducing kernel.…
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…
The conical Radon transform is an integral transform that maps a given function $f$ to its integral over a conical surface. In this study, we invesgate the conical Radon transform with a fixed central axis and opening angle, considering the…
Graphite is an example of a layered material that can be bent to form fullerenes which promise important applications in electronic nanodevices. The spheroidal geometry of a slightly elliptically deformed sphere was used as a possible…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…
We theoretically study the scattering of spin waves from a sharp domain wall in an antiferromagnetic spin chain. While the continuum model for an antiferromagnetic material yields the well-known result that spin waves can pass through a…
Recently, the R2D2 paradigm, standing for ''Residual-to-Residual DNN series for high-Dynamic-range imaging'', was introduced for image formation in Radio Interferometry (RI) as a learned version of the traditional algorithm CLEAN. The first…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
We obtain new inversion formulas for the Funk type transforms of two kinds associated to spherical sections by hyperplanes passing through a common point $A$ which lies inside the n-dimensional unit sphere or on the sphere itself.…
We study an inverse acoustic scattering problem in half-space with a probabilistic impedance boundary value condition. The Robin coefficient (surface impedance) is assumed to be a Gaussian random function $\lambda = \lambda(x)$ with a…