Related papers: The Vertical Slice Transform in Spherical Tomograp…
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…
We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the…
Deformations of the canonical spectral triples over the n-dimensional torus are considered. These deformations have a discrete dimension spectrum consisting of non-integer values less than n. The differential algebra corresponding to these…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
We compute, in the large $N$ limit, the topologically twisted index of the 3d $T[SU(N)]$ theory, namely the partition function on $\Sigma_{\mathfrak{g}} \times S^1$, with a topological twist on the Riemann surface $\Sigma_{\mathfrak{g}}$.…
Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and…
A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schredinger equation are elaborated.
The problem of reconstruction a function from spherical means is at the heart of several modern imaging modalities and other applications. In this paper we derive universal back-projection type reconstruction formulas for recovering a…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The model is a solution of the full three-dimensional equations…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of…
The inverse problem for the Euler-Poisson-Darboux equation deals with reconstruction of the Cauchy data for this equation from incomplete information about its solution. In the present article, this problem is studied in connection with the…
The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains \Omega\ of R^4. When \Omega\ is a symmetric slice domain, the twistor transform of such a function is a…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains…
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some…
A study of the partition function of a 3-dimensional scalar-vector model formally related via duality to the Rozansky-Witten topological sigma-model is presented. The partition function is shown to consist of such topological quantities of…
It is known that the Funk transform (the Funk-Radon transform) is invertible in the class of even (symmetric) continuous functions defined on the unit 2-sphere S^2. In this article, for the reconstruction of f from C(S^2) (can be non-even),…
We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…