The Experts below are selected from a list of 10005 Experts worldwide ranked by ideXlab platform

Birsen Yazici - One of the best experts on this subject based on the ideXlab platform.

  • radon transform inversion based on harmonic analysis of the euclidean motion group
    International Conference on Acoustics Speech and Signal Processing, 2005
    Co-Authors: Can Evren Yarman, Birsen Yazici
    Abstract:

    We present a new derivation of the spherical harmonic decomposition of the projection slice theorem using harmonic analysis of the Euclidean motion group, M(N). The Radon transform is formulated as a Convolution Integral over M(N). DeConvolution using harmonic analysis of M(N) leads to spherical harmonic decomposition of the projection slice theorem. The proposed method of decomposition leads to new algorithms for the inversion of the Radon transform.

  • radon transform inversion via wiener filtering over the euclidean motion group
    International Conference on Image Processing, 2003
    Co-Authors: Can Evren Yarman, Birsen Yazici
    Abstract:

    In this paper we formulate the Radon transform as a Convolution Integral over the Euclidean motion group (SE(2)) and provide a minimum mean square error (MMSE) stochastic deConvolution method for the Radon transform inversion. Proposed approach provides a fundamentally new formulation that can model nonstationary signal and noise fields. Key components of our development are the Fourier transform over SE(2), stochastic processes indexed by groups and fast implementation of the SE(2) Fourier transform. Numerical studies presented here demonstrate that the method yields image quality that is comparable or better than the filtered backprojection algorithm. Apart from X-ray tomographic image reconstruction, the proposed deConvolution method is directly applicable to inverse radiotherapy, and broad range of science and engineering problems in computer vision, pattern recognition, robotics as well as protein science.

Ji Qiang - One of the best experts on this subject based on the ideXlab platform.

  • a high order fast method for computing Convolution Integral with smooth kernel
    Lawrence Berkeley National Laboratory, 2010
    Co-Authors: Ji Qiang
    Abstract:

    CBP-842 A high-order fast method for computing Convolution Integral with smooth kernel Ji Qiang Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 In this paper we report on a high-order fast method to numerically calculate Convolution Integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the Integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the Integral ap- proximation and a computational cost of O(N log(N )), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h 4 ), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional contin- uous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented. I. INTRODUCTION Convolution has been used in solving some linear differential equations such as the Poisson equation, the Helmoltz equation, and the heat transfer equation based on the Green’s function method under appropriate boundary conditions or initial conditions [1, 2]. For example, the Convolution between the Green’s function of the Poisson equation and the density function has been used to obtain potential field under open boundary conditions in plasma physics, accelerator physics and cosmology simulations [3–5]. The direct numerical calculation of the Convolution for potential field has a computational cost scaling as O(N 2 ), where N is the number of grid points in the domain. Fortunately, the discretized Convolution summation on a uniform grid can be calculated using a cyclic summation on a doubled computational domain using an FFT based method [5–7]. This reduces the computational cost from O(N 2 ) to O(N log(N )). However, the direct numerical Convolution of the density function and the Green’s function on the grid is equivalent to a relatively low-order quadrature rule (trapezoidal rule) approximation to the

  • a high order fast method for computing Convolution Integral with smooth kernel
    Computer Physics Communications, 2010
    Co-Authors: Ji Qiang
    Abstract:

    In this paper we report on a high-order fast method to numerically calculate Convolution Integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the Integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the Integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.

Stig Larsson - One of the best experts on this subject based on the ideXlab platform.

  • adaptive discretization of an integro differential equation with a weakly singular Convolution kernel
    Computer Methods in Applied Mechanics and Engineering, 2003
    Co-Authors: Klas Adolfsson, Mikael Enelund, Stig Larsson
    Abstract:

    An integro-differential equation involving a Convolution Integral with a weakly singular kernel is considered. The kernel can be that of a fractional Integral. The integro-differential equation is discretized using the discontinuous Galerkin method with piecewise constant basis functions. Sparse quadrature is introduced for the Convolution term to overcome the problem with the growing amount of data that has to be stored and used in each time-step. A priori and a posteriori error estimates are proved. An adaptive strategy based on the a posteriori error estimate is developed. Finally, the precision and effectiveness of the algorithm are demonstrated in the case that the Convolution is a fractional Integral. This is done by comparing the numerical solutions with analytical solutions.

Mikael Enelund - One of the best experts on this subject based on the ideXlab platform.

  • adaptive discretization of an integro differential equation with a weakly singular Convolution kernel
    Computer Methods in Applied Mechanics and Engineering, 2003
    Co-Authors: Klas Adolfsson, Mikael Enelund, Stig Larsson
    Abstract:

    An integro-differential equation involving a Convolution Integral with a weakly singular kernel is considered. The kernel can be that of a fractional Integral. The integro-differential equation is discretized using the discontinuous Galerkin method with piecewise constant basis functions. Sparse quadrature is introduced for the Convolution term to overcome the problem with the growing amount of data that has to be stored and used in each time-step. A priori and a posteriori error estimates are proved. An adaptive strategy based on the a posteriori error estimate is developed. Finally, the precision and effectiveness of the algorithm are demonstrated in the case that the Convolution is a fractional Integral. This is done by comparing the numerical solutions with analytical solutions.

  • damping described by fading memory analysis and application to fractional derivative models
    International Journal of Solids and Structures, 1999
    Co-Authors: Mikael Enelund, Peter Olsson
    Abstract:

    Abstract Some damping models where the actual stress does not depend on the actual strain but also on the entire strain history are studied. Basic requirements in the frequency and time domain significant for the choice of damping model are outlined. A one-dimensional linear constitutive viscoelastic equation is considered. Three different equivalent constitutive equations describing the viscoelastic model are presented. The constitutive relation on the Convolution Integral form is studied in particular. A closed form expression for the memory kernel corresponding to the fractional derivative model of viscoelasticity is given. The memory kernel is examined with respect to its regularity and asymptotic behavior. The memory kernels relation to the fractional derivative operator is discussed in particular and the fractional derivative of the Convolution term is derived. The fractional derivative model is also given by two coupled equations using an internal variable. The inclusion of the fractional derivative constitutive equation in the equations of motion for a viscoelastic structure is discussed. We suggest a formulation of the structural equations that involves the Convolution Integral description of the fractional derivative model of viscoelasticity. This form is shown to possess several mathematical advantages compared to an often used formulation that involves a fractional derivative operator form of constitutive relation. An efficient time discretization algorithm, based on Newmarks method, for solving the structural equations is presented and some numerical examples are given. A simplification of the fractional derivative of the memory kernel, derived in the present study, is then employed, which avoids the actual evaluation of the memory kernel.

Can Evren Yarman - One of the best experts on this subject based on the ideXlab platform.

  • radon transform inversion based on harmonic analysis of the euclidean motion group
    International Conference on Acoustics Speech and Signal Processing, 2005
    Co-Authors: Can Evren Yarman, Birsen Yazici
    Abstract:

    We present a new derivation of the spherical harmonic decomposition of the projection slice theorem using harmonic analysis of the Euclidean motion group, M(N). The Radon transform is formulated as a Convolution Integral over M(N). DeConvolution using harmonic analysis of M(N) leads to spherical harmonic decomposition of the projection slice theorem. The proposed method of decomposition leads to new algorithms for the inversion of the Radon transform.

  • radon transform inversion via wiener filtering over the euclidean motion group
    International Conference on Image Processing, 2003
    Co-Authors: Can Evren Yarman, Birsen Yazici
    Abstract:

    In this paper we formulate the Radon transform as a Convolution Integral over the Euclidean motion group (SE(2)) and provide a minimum mean square error (MMSE) stochastic deConvolution method for the Radon transform inversion. Proposed approach provides a fundamentally new formulation that can model nonstationary signal and noise fields. Key components of our development are the Fourier transform over SE(2), stochastic processes indexed by groups and fast implementation of the SE(2) Fourier transform. Numerical studies presented here demonstrate that the method yields image quality that is comparable or better than the filtered backprojection algorithm. Apart from X-ray tomographic image reconstruction, the proposed deConvolution method is directly applicable to inverse radiotherapy, and broad range of science and engineering problems in computer vision, pattern recognition, robotics as well as protein science.