The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Sunghwan Moon - One of the best experts on this subject based on the ideXlab platform.

  • Properties of the fractional (exponential) Radon Transform
    Integral Transforms and Special Functions, 2017
    Co-Authors: Sunghwan Moon
    Abstract:

    ABSTRACTThe fractional Radon Transform defined, based on the Fourier slice theorem and the fractional Fourier Transform, has many potential applications in optics and the pattern-recognition field. Here we study many properties of the fractional Radon Transform using existing theory of the regular Radon Transform: the inversion formulas, stability estimates, uniqueness and reconstruction for a local data problem, and a range description. Also, we define the fractional exponential Radon Transform and present its inversion.

  • inversion of the elliptical Radon Transform arising in migration imaging using the regular Radon Transform
    Journal of Mathematical Analysis and Applications, 2016
    Co-Authors: Sunghwan Moon
    Abstract:

    Abstract In recent years, many types of elliptical Radon Transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography, radio tomography, and migration imaging. In this article, we consider the Transform that integrates a given function in R n over a set of ellipses (when n = 2 ) or ellipsoids of rotation (when n ≥ 3 ) with foci restricted to a hyperplane. We show a relation between this elliptical Radon Transform and the regular Radon Transform, and provide the inversion formula for the elliptical Radon Transform using this relation. Numerical simulations are performed to demonstrate the suggested algorithms in two dimensions, and these simulations are also provided in this article.

  • inversion of the seismic parabolic Radon Transform and the seismic hyperbolic Radon Transform
    Inverse Problems in Science and Engineering, 2016
    Co-Authors: Sunghwan Moon
    Abstract:

    Reflection seismology is a method of exploration of the hidden structure of the earth subsurface by processing received seismograms. For a long time, this processing utilizes the so-called slant stack Transform, or line Radon Transform. More recently, two generalizations of the slant stack Transform have been introduced to extract new features of the seismic data and to improve their treatment. These Transforms are the parabolic and hyperbolic seismic Radon Transforms. The first Transform maps a given function to its integrals over parabolas with a fixed axis direction, whereas the second one maps a function to its integrals over hyperbolas (more generally also over ellipses and circles) of fixed axis directions. We show how they can be converted to a line Radon Transform, and thereby obtain their inversion formulas. Numerical simulations for each Transform were performed and commented to illustrate the suggested algorithms.

  • Inversion of the spherical Radon Transform on spheres through the origin using the regular Radon Transform
    Communications on Pure and Applied Analysis, 2016
    Co-Authors: Sunghwan Moon
    Abstract:

    A spherical Radon Transform whose integral domain is a sphere has many applications in partial differential equations as well as tomography. This paper is devoted to the spherical Radon Transform which assigns to a given function its integrals over the set of spheres passing through the origin. We present a relation between this spherical Radon Transform and the regular Radon Transform, and we provide a new inversion formula for the spherical Radon Transform using this relation. Numerical simulations were performed to demonstrate the suggested algorithm in dimension 2.

  • inversion of the elliptical Radon Transform arising in migration imaging using the regular Radon Transform
    arXiv: Functional Analysis, 2015
    Co-Authors: Sunghwan Moon
    Abstract:

    In recent years, many types of elliptical Radon Transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography, radio tomography, and migration imaging. In this article, we consider the Transform that integrates a given function in $\mathbf R^n$ over a set of ellipses (when $n=2$) or ellipsoids of rotation (when $n\geq 3$) with foci restricted to a hyperplane. We show a relation between this elliptical Radon Transform and the regular Radon Transform, and provide the inversion formula for the elliptical Radon Transform using this relation. Numerical simulations are performed to demonstrate the suggested algorithms in two dimensions, and these simulations are also provided in this article.

Francesca Odone - One of the best experts on this subject based on the ideXlab platform.

  • the Radon Transform intertwines wavelets and shearlets
    Applied and Computational Harmonic Analysis, 2018
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito, Francesca Odone
    Abstract:

    Abstract We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.

Francesca Bartolucci - One of the best experts on this subject based on the ideXlab platform.

  • the Radon Transform intertwines wavelets and shearlets
    Applied and Computational Harmonic Analysis, 2018
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito, Francesca Odone
    Abstract:

    Abstract We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.

  • Radon Transform intertwines shearlets and wavelets
    arXiv: Functional Analysis, 2017
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito
    Abstract:

    We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.

Ernesto De Vito - One of the best experts on this subject based on the ideXlab platform.

  • the Radon Transform intertwines wavelets and shearlets
    Applied and Computational Harmonic Analysis, 2018
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito, Francesca Odone
    Abstract:

    Abstract We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.

  • Radon Transform intertwines shearlets and wavelets
    arXiv: Functional Analysis, 2017
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito
    Abstract:

    We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.

Filippo De Mari - One of the best experts on this subject based on the ideXlab platform.

  • the Radon Transform intertwines wavelets and shearlets
    Applied and Computational Harmonic Analysis, 2018
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito, Francesca Odone
    Abstract:

    Abstract We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.

  • Radon Transform intertwines shearlets and wavelets
    arXiv: Functional Analysis, 2017
    Co-Authors: Francesca Bartolucci, Filippo De Mari, Ernesto De Vito
    Abstract:

    We prove that the unitary affine Radon Transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral Transforms applied to the affine Radon Transform of the signal, thereby opening new perspectives in the inversion of the Radon Transform.