Related papers: Inversions of the windowed ray transform
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The paper demonstrates the geometric optic properties of the transition radiation (TR) of an ultrarelativistic point-like charged particle crossing the transverse wall of a circular semi-infinite waveguide with ideally conducting walls. It…
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution…
In this article, we study Momentum Light Ray Transform (MLRT) on symmetric tensor fields. MLRT is an integral transform in time-space domain ($(t,x)\in \mathbb{R}^{1+n}$), which integrates a scalar function or a tensor field along the light…
We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional…
In this note, we use the disformal transformation to induce a geometry from the manifold which is originally Riemannian. The new geometry obtained here can be considered as a generalization of Weyl integrable geometry. Based on these…
Radon transform is a type of transform which is used in image processing to transfer the image into intercept-slope coordinate. Its diagonal properties made it appropriate for some applications which need processes in different degrees.…
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…
We propose iterative inversion algorithms for weighted Radon transforms $R_W$ along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x, \theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics in…
This comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT),…
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of…
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…
Generalized Abel equations have been employed in the recent literature to invert Radon transforms which arise in a number of important imaging applications, including Compton Scatter Tomography (CST), Ultrasound Reflection Tomography (URT),…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…
In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a general flow.…
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…