The Experts below are selected from a list of 381 Experts worldwide ranked by ideXlab platform

Christopher Sansing - One of the best experts on this subject based on the ideXlab platform.

  • GABOR FRAMES AND DIRECTIONAL TIME-FREQUENCY ANALYSIS
    2012
    Co-Authors: Loukas Grafakos, Christopher Sansing
    Abstract:

    Abstract. We introduce a directionally sensitive time-frequency decomposition and representation of functions. The coefficients of this representation allow us to measure the “amount ” of frequency a function (signal, image) contains in a certain time interval, and also in a certain direction. This has been previously achieved using a version of wavelets called ridgelets [2, 3] but in this work we discuss an approach based on time-frequency or Gabor elements. For such elements, a Parseval Formula and a continous frame-type representation together with boundedness properties of a semi-discrete frame operator are obtained. Spaces of functions tailored to measure quantitative properties of the time-frequency-direction analysis coefficients are introduced and some of their basic properties are discussed. Applications to image processing and medical imaging are presented. 1

Sansing Christopher - One of the best experts on this subject based on the ideXlab platform.

  • Gabor frames and directional time–frequency analysis
    2008
    Co-Authors: Grafakos Loukas, Sansing Christopher
    Abstract:

    AbstractWe introduce a directionally sensitive time–frequency decomposition and representation of functions. The coefficients of this representation allow us to measure the “amount” of frequency a function (signal, image) contains in a certain time interval, and also in a certain direction. This has been previously achieved using a version of wavelets called ridgelets [E.J. Candès, Harmonic analysis of neural networks, Appl. Comput. Harmon. Anal. 6 (1999) 197–218. [2]; E.J. Candès, D.L. Donoho, New tight frames of curvelets and optimal representations of objects with piesewise-C2 singularities, Comm. Pure Appl. Math. 57 (2004) 219–266. [3]] but in this work we discuss an approach based on time–frequency or Gabor elements. For such elements, a Parseval Formula and a continuous frame-type representation together with boundedness properties of a semi-discrete frame operator are obtained. Spaces of functions tailored to measure quantitative properties of the time–frequency–direction analysis coefficients are introduced and some of their basic properties are discussed. Applications to image processing and medical imaging are presented

Paul L Butzer - One of the best experts on this subject based on the ideXlab platform.

  • the mellin Parseval Formula and its interconnections with the exponential sampling theorem of optical physics
    2016
    Co-Authors: Carlo Bardaro, Paul L Butzer, Ilaria Mantellini
    Abstract:

    ABSTRACTIn this paper, we establish a Mellin version of the classical Parseval Formula of Fourier analysis in the case of Mellin bandlimited functions, and its equivalence with the exponential sampling Formula (ESF) of signal analysis, in which the samples are not equally spaced apart as in the classical Shannon theorem, but exponentially spaced. Two quite different examples are given illustrating the truncation error in the ESF. We employ Mellin transform methods for square-integrable functions.

  • the sampling theorem poisson s summation Formula general Parseval Formula reproducing kernel Formula and the paley wiener theorem for bandlimited signals their interconnections
    2011
    Co-Authors: Paul L Butzer, Gerhard Schmeisser, J R Higgins, Paulo J S G Ferreira, R L Stens
    Abstract:

    It is shown that the Whittaker–Kotel'nikov–Shannon sampling theorem of signal analysis, which plays the central role in this article, as well as (a particular case) of Poisson's summation Formula, the general Parseval Formula and the reproducing kernel Formula, are all equivalent to one another in the case of bandlimited functions. Here equivalent is meant in the sense that each is a corollary of the other. Further, the sampling theorem is equivalent to the Valiron–Tschakaloff sampling Formula as well as to the Paley–Wiener theorem of Fourier analysis. An independent proof of the Valiron Formula is provided. Many of the equivalences mentioned are new results. Although the above theorems are equivalent amongst themselves, it turns out that not only the sampling theorem but also Poisson's Formula are in a certain sense the ‘strongest’ assertions of the six well-known, basic theorems under discussion.

Loukas Grafakos - One of the best experts on this subject based on the ideXlab platform.

  • GABOR FRAMES AND DIRECTIONAL TIME-FREQUENCY ANALYSIS
    2012
    Co-Authors: Loukas Grafakos, Christopher Sansing
    Abstract:

    Abstract. We introduce a directionally sensitive time-frequency decomposition and representation of functions. The coefficients of this representation allow us to measure the “amount ” of frequency a function (signal, image) contains in a certain time interval, and also in a certain direction. This has been previously achieved using a version of wavelets called ridgelets [2, 3] but in this work we discuss an approach based on time-frequency or Gabor elements. For such elements, a Parseval Formula and a continous frame-type representation together with boundedness properties of a semi-discrete frame operator are obtained. Spaces of functions tailored to measure quantitative properties of the time-frequency-direction analysis coefficients are introduced and some of their basic properties are discussed. Applications to image processing and medical imaging are presented. 1

Ilaria Mantellini - One of the best experts on this subject based on the ideXlab platform.