Journal ArticleDOI
A Hankel transform approach to tomographic image reconstruction
William E. Higgins,D.C. Munson +1 more
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TLDR
The HTR algorithm is outlined, and it is shown that its performance compares favorably to the popular convolution-backprojection algorithm.Abstract:
A relatively unexplored algorithm is developed for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, referred to as the Hankel-transform-reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r, theta ) of an image into a Fourier series in theta ; calculates the appropriately ordered Hankel transform of the coefficients of this series, giving the coefficients for the Fourier series of the polar-form image f(p, phi ); resolves this series, giving a polar-form reconstruction; and interpolates this reconstruction to a rectilinear grid. The HTR algorithm is outlined, and it is shown that its performance compares favorably to the popular convolution-backprojection algorithm. >read more
Citations
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Journal ArticleDOI
Wavelet localization of the Radon transform
T. Olson,J. DeStefano +1 more
TL;DR: An algorithm which significantly reduces radiation exposure in X-ray tomography, when a local region of the body is to be imaged, is developed, which uses the properties of wavelets to essentially localize the Radon transform.
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An algorithm for the rapid evaluation of special function transforms
TL;DR: A new class of fast algorithms for the application to arbitrary vectors of certain special function transforms, including the Fourier–Bessel transform, the non-equispaced Fourier transform, transforms associated with all classical orthogonal polynomials, etc.
Journal ArticleDOI
Algorithms to numerically evaluate the Hankel transform
Michael J. Cree,Philip J. Bones +1 more
TL;DR: It is found that the performance of all algorithms depends on the type of function to be transformed, and the projection based methods provide acceptable accuracy with better efficiency than numerical quadrature.
Journal ArticleDOI
Fast Hankel transform by fast sine and cosine transforms: the Mellin connection
TL;DR: A novel modified Hankel transform procedure that does not require exponential sampling is presented, which can be implemented by means of fast sine and cosine transforms.
Journal ArticleDOI
Region-of-interest tomography using exponential radial sampling
Berkman Sahiner,Andrew E. Yagle +1 more
TL;DR: The authors combine several ideas, including nonuniform sampling and circular harmonic expansions, into a new procedure for reconstructing a small region of interest (ROI) of an image from a set of its projections that are densely sampled in the ROI and coarsely sampled outside theROI.
References
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L. A. Shepp,B. F. Logan +1 more
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TL;DR: General principles are formulated for the objective reconstruction of a three dimensional object from a set of electron microscope images and applied to the calculation of aThree dimensional density map of the tail of bacteriophage T4.
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Three-dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolutions instead of Fourier Transforms
TL;DR: Tests of the convolution method with computer-simulated shadowgraphs show that it is also more accurate than the Fourier transform method, and has good potentialities for application in electron microscopy and x-radiography.
Journal ArticleDOI
A tomographic formulation of spotlight-mode synthetic aperture radar
TL;DR: In this article, a projection-slice theorem from computer-aided tomograpy (CAT) is used to analyze the signal recorded at each SAR transmission point, which is modeled as a portion of the Fourier transform of a central projection of the imaged ground area.
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Strip Integration in Radio Astronomy
TL;DR: In this paper, it is shown that the resolution obtained by the cross-sectional profile of the strip beam in the narrow dimension is set by the resolution of the original spectrum, and that when the strip reduces to a line, the resolution is complete and full reconstruction of the true distribution is possible but scans must be made in all directions.