Proceedings ArticleDOI
Novel Properties Of The Fourier Decomposition Of The Sinogram
Paul R. Edholm,Robert M. Lewitt,Bernt Lindholm +2 more
- Vol. 0671, pp 8-18
TLDR
The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections as discussed by the authors.Abstract:
The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency w (continuous) and angular harmonic number n (discrete). For |w| large, the Fourier coefficients on the line n=kw of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed.read more
Citations
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Journal ArticleDOI
Exact and approximate rebinning algorithms for 3-D PET data
TL;DR: This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data that are approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data.
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Iterative reconstruction techniques in emission computed tomography.
Jinyi Qi,Richard M. Leahy +1 more
TL;DR: A review of recent progress in developing statistically based iterative techniques for emission computed tomography describes the different formulations of the emission image reconstruction problem and their properties and describes the numerical algorithms used for optimizing these functions.
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Joel S. Karp,Gerd Muehllehner,David A. Mankoff,C.E. Ordonez,John M. Ollinger,Margaret E. Daube-Witherspoon,Arthur T. Haigh,Daniel J. Beerbohm +7 more
TL;DR: The PENN-PET scanner consists of six hexagonally arranged position-sensitive Nal(TI) detectors, which offers high spatial resolution in all three dimensions, high sampling density along all three axes without scanner motion, a large axial acceptance angle, good energy resolution, and good timing resolution.
Cone-Beam Reconstruction Using Filtered Backprojection
TL;DR: The art of medical computed tomography is constantly evolving and the last years have seen new ground breaking systems with multi-row detectors, which are able to increase both scanning and resolution.
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Overview of methods for image reconstruction from projections in emission computed tomography
Robert M. Lewitt,Samuel Matej +1 more
TL;DR: The paper presents a broad overview of algorithms for PET and SPECT, giving references to the literature where these algorithms and their applications are described in more detail.
References
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Journal ArticleDOI
The Reconstruction of a Three-Dimensional Structure from Projections and its Application to Electron Microscopy
TL;DR: In this paper, the Fourier transform is used to combine data from a number of different views of a transmission electron micrograph to reconstruct a 3D image of a given particle to a given degree of resolution.
Journal ArticleDOI
Image reconstruction from finite numbers of projections
TL;DR: In this paper, a trigonometrical Fourier series is used for angular interpolation and a consistency condition is established whereby a posteriori estimates can be made of the errors in the given data, and a basic image which contains only that information common to all physically permissible interpolation schemes.
Book ChapterDOI
The Inverse Discrete Radon Transform with Applications to Tomographic Imaging Using Projection Data
Allen G. Lindgren,Paul A. Rattey +1 more
TL;DR: The ultimate purpose of this chapter is to establish a firm theoretical foundation for tomographic imaging systems where the measurements are regularly spaced.
Journal ArticleDOI
Tomogram reconstruction using an opticophotographic method.
TL;DR: The new principle of tomography that first gained practical application with the design of the EMI scanner constitutes one of the most important advances in the field of diagnostic radiology and has a number of disadvantages, including high cost, the need for digitalizing data and images, and low resolution.