scholarly journals Two-dimensional local Fourier image reconstruction via domain decomposition Fourier continuation method

PLoS ONE ◽  
2019 ◽  
Vol 14 (1) ◽  
pp. e0197963
Author(s):  
Ruonan Shi ◽  
Jae-Hun Jung ◽  
Ferdinand Schweser
Keyword(s):  
Image Reconstruction ◽  
Domain Decomposition ◽  
Continuation Method ◽  
Two Dimensional ◽  
Fourier Image ◽  
Fourier Continuation

scholarly journals Two-dimensional local Fourier image reconstruction via domain decomposition Fourier continuation method

2018 ◽  
Author(s):  
Ruonan Shi ◽  
Jae-Hun Jung ◽  
Ferdinand Schweser
Keyword(s):  
Domain Decomposition ◽  
Continuation Method ◽  
Image Data ◽  
Spatial Domain ◽  
Numerical Results ◽  
Reconstruction Method ◽  
Local Reconstruction ◽  
Fourier Data ◽  
Fourier Continuation ◽  
Mri Image

AbstractThe MRI image is obtained in the spatial domain from the given Fourier coefficients in the frequency domain. It is costly to obtain the high resolution image because it requires higher frequency Fourier data while the lower frequency Fourier data is less costly and effective if the image is smooth. However, the Gibbs ringing, if existent, prevails with the lower frequency Fourier data. We propose an efficient and accurate local reconstruction method with the lower frequency Fourier data that yields sharp image profile near the local edge. The proposed method utilizes only the small number of image data in the local area. Thus the method is efficient. Furthermore the method is accurate because it minimizes the global effects on the reconstruction near the weak edges shown in many other global methods for which all the image data is used for the reconstruction. To utilize the Fourier method locally based on the local non-periodic data, the proposed method is based on the Fourier continuation method. This work is an extension of our previous 1D Fourier domain decomposition method to 2D Fourier data. The proposed method first divides the MRI image in the spatial domain into many subdomains and applies the Fourier continuation method for the smooth periodic extension of the subdomain of interest. Then the proposed method reconstructs the local image based on L2 minimization regularized by the L1 norm of edge sparsity to sharpen the image near edges. Our numerical results suggest that the proposed method should be utilized in dimension-by-dimension manner instead of in a global manner for both the quality of the reconstruction and computational efficiency. The numerical results show that the proposed method is effective when the local reconstruction is sought and that the solution is free of Gibbs oscillations.

scholarly journals A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Oscar P. Bruno ◽  
Timothy Elling ◽  
Ayon Sen
Keyword(s):  
Eigenvalue Problems ◽  
Continuation Method ◽  
Gibbs Phenomenon ◽  
Variable Coefficients ◽  
Computational Method ◽  
The Novel ◽  
Two Dimensional ◽  
Fourier Approximation ◽  
Fourier Continuation ◽  
Elliptic Eigenvalue Problems

We present a new computational method for the solution of elliptic eigenvalue problems with variable coefficients in general two-dimensional domains. The proposed approach is based on use of the novel Fourier continuation method (which enables fast and highly accurate Fourier approximation of nonperiodic functions in equispaced grids without the limitations arising from the Gibbs phenomenon) in conjunction with an overlapping patch domain decomposition strategy and Arnoldi iteration. A variety of examples demonstrate the versatility, accuracy, and generality of the proposed methodology.

scholarly journals Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves

2018 ◽  
Vol 52 (4) ◽  
pp. 1569-1596 ◽  
Author(s):  
Xavier Antoine ◽  
Fengji Hou ◽  
Emmanuel Lorin
Keyword(s):  
Domain Decomposition ◽  
Decomposition Methods ◽  
Nonlinear Schrödinger Equations ◽  
Waveform Relaxation ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Domain Decomposition Methods ◽  
Schwarz Waveform Relaxation ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear

This paper is devoted to the analysis of convergence of Schwarz Waveform Relaxation (SWR) domain decomposition methods (DDM) for solving the stationary linear and nonlinear Schrödinger equations by the imaginary-time method. Although SWR are extensively used for numerically solving high-dimensional quantum and classical wave equations, the analysis of convergence and of the rate of convergence is still largely open for linear equations with variable coefficients and nonlinear equations. The aim of this paper is to tackle this problem for both the linear and nonlinear Schrödinger equations in the two-dimensional setting. By extending ideas and concepts presented earlier [X. Antoine and E. Lorin, Numer. Math. 137 (2017) 923–958] and by using pseudodifferential calculus, we prove the convergence and determine some approximate rates of convergence of the two-dimensional Classical SWR method for two subdomains with smooth boundary. Some numerical experiments are also proposed to validate the analysis.

The award of medals by the President, Sir Andrew Huxley, O.M., at the Anniversary Meeting, 30 November 1985

1986 ◽  
Vol 405 (1829) ◽  
pp. 181-184
Keyword(s):  
Electron Microscopy ◽  
Image Reconstruction ◽  
Coat Protein ◽  
Tobacco Mosaic Virus ◽  
Mosaic Virus ◽  
Deep Insight ◽  
Living Matter ◽  
Fourier Image ◽  
Reconstruction Methods ◽  
Insight Into

The Copley Medal is awarded to Dr A. Klug, F. R. S., in recognition of his outstanding contributions to our understanding of complex biological structures and the methods used for determining them. Together with D. Kaspar, Klug developed a theory that predicted the arrangement of sub-units in the protein shells of spherical viruses. This theory brought order and understanding into a confused field ; nearly all the observed structures of small spherical viruses, many of them elucidated by Klug and his collaborators, are consistent with it. After more than 20 years’ work on tobacco mosaic virus Klug and his colleagues solved the structure of its coat protein in atomic detail. They also elucidated the mechanisms by which the helical virus particle assembles itself from its RNA and its 2130 protein sub-units. Recently his group succeeded in crystallizing chromatin, and solved its structure at a resolution sufficient to see the double-helical DNA coiled around the spool of histone. Many of Klug’s successes were made possible by his introduction of Fourier image reconstruction methods into electron microscopy. Klug’s work is characterized by deep insight into the physics of diffraction and image formation and the intricate geometry of living matter.

scholarly journals Analytic time-of-flight positron emission tomography reconstruction: two-dimensional case

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Gengsheng L. Zeng ◽  
Ya Li ◽  
Qiu Huang
Keyword(s):  
Positron Emission Tomography ◽  
Image Reconstruction ◽  
Iterative Algorithm ◽  
Emission Tomography ◽  
Two Dimensional ◽  
Profile Function ◽  
Positron Emission ◽  
Pet Image Reconstruction ◽  
2D Filter ◽  
Tof Pet

AbstractIn a positron emission tomography (PET) scanner, the time-of-flight (TOF) information gives us rough event position along the line-of-response (LOR). Using the TOF information for PET image reconstruction is able to reduce image noise. The state-of-the-art TOF PET image reconstruction uses iterative algorithms. Analytical image reconstruction algorithm exits for TOF PET which emulates the iterative Landweber algorithm. This paper introduces such an algorithm, focusing on two-dimensional (2D) reconstruction. The proposed algorithm is in the form of backprojection filtering, in which the backprojection is performed first, and then a 2D filter is applied to the backprojected image. For the list-mode data, the backprojection is carried out in the event-by-event fashion, and a profile function may be used along the projection LOR. The 2D filter depends on the TOF timing resolution as well as the backprojection profile function. In order to emulate the iterative algorithm effects, a Fourier-domain window function is suggested. This window function has a parameter, k, which corresponds to the iteration number in an iterative algorithm.

Sign in / Sign up

Export Citation Format

Share Document