Related papers: The conical Radon transform with vertices on tripl…
Expensive computation of the conventional sparse Radon transform limits its use for effective transformation of 3D anisotropic seismic data cubes. We introduce a fast algorithm for azimuthally anisotropic 3D Radon transform with sparsity…
We continue to study the problem of modeling of substitution of production factors motivated by the need for computable mathematical models of economics that could be used as a basis in applied developments. This problem has been studied…
We compare the Radon transform in its standard and symplectic formulations and argue that the inversion of the latter can be performed more efficiently.
We demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…
We consider the X-ray transform in a projective space over a finite field. It is well known (after E. Bolker) that this transform is injective. We formulate an analog of I.M. Gelfand's admissibility problem for the Radon transform, which…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
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…
The formula for analytic torsion of a cone in even dimensions is comprised of three terms. The first two terms are well understood and given by an algebraic combination of the Betti numbers and the analytic torsion of the cone base. The…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
We consider the transformation for the point rotation frames with the angle, spatial coordinate along the axis of rotation and time as variables. The problem arises when light, propagating through 3-fold electrooptical crystal, is modulated…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
The paper is devoted to the range description of the Radon type transform that averages a function over all spheres centered on a given sphere. Such transforms arise naturally in thermoacoustic tomography, a novel method of medical imaging.…
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…
We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a…
Magnetic resonance imaging (MRI) is a potent diagnostic tool, but suffers from long examination times. To accelerate the process, modern MRI machines typically utilize multiple coils that acquire sub-sampled data in parallel. Data-driven…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
The influence of the diffraction limit on the field of view of three-dimensional integral imaging (InI) systems is estimated by calculating the resolution of the InI system along arbitrarily tilted directions. The deteriorating effects of…
The Compton camera is a promising alternative to the Anger camera for imaging gamma radiation, with the potential to significantly increase the sensitivity of SPECT. Two-dimensional Compton camera image reconstruction can be implemented by…
Deep convolutional neural networks accuracy is heavily impacted by rotations of the input data. In this paper, we propose a convolutional predictor that is invariant to rotations in the input. This architecture is capable of predicting the…
We present spherical analysis of electron backscatter diffraction (EBSD) patterns with two new algorithms: (1) band localisation and band profile analysis using the spherical Radon transform; (2) orientation determination using spherical…