A convolution backprojection formula for three-dimensional vector tomography

J. L. Prince

doi:10.1109/ICIP.1994.413685

A convolution backprojection formula for three-dimensional vector tomography

J. L. Prince

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

Three-dimensional (3-D) tomographic measurements of vector flow fields are possible using acoustical, optical, and magnetic resonance imaging. A general mathematical framework for this type of data acquisition called the probe transform has been studied by the author in previous work. It has been shown that the irrotational field component can be reconstructed using only one probe direction, and that the solenoidal field component can be reconstructed using only two probe directions. Previously, the reconstruction formulas were of the backprojection-convolution type; that is, first backproject then convolve in 3-D. In this paper a convolution-backprojection formula, which has significant computational savings, is developed. Numerical simulations are also given to demonstrate the performance of this new approach.

Original language	English (US)
Article number	413685
Pages (from-to)	820-824
Number of pages	5
Journal	Proceedings - International Conference on Image Processing, ICIP
Volume	2
DOIs	https://doi.org/10.1109/ICIP.1994.413685
State	Published - 1994
Externally published	Yes
Event	The 1994 1st IEEE International Conference on Image Processing - Austin, TX, USA Duration: Nov 13 1994 → Nov 16 1994

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Signal Processing

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10.1109/ICIP.1994.413685

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title = "A convolution backprojection formula for three-dimensional vector tomography",

abstract = "Three-dimensional (3-D) tomographic measurements of vector flow fields are possible using acoustical, optical, and magnetic resonance imaging. A general mathematical framework for this type of data acquisition called the probe transform has been studied by the author in previous work. It has been shown that the irrotational field component can be reconstructed using only one probe direction, and that the solenoidal field component can be reconstructed using only two probe directions. Previously, the reconstruction formulas were of the backprojection-convolution type; that is, first backproject then convolve in 3-D. In this paper a convolution-backprojection formula, which has significant computational savings, is developed. Numerical simulations are also given to demonstrate the performance of this new approach.",

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note = "Publisher Copyright: {\textcopyright} 1994 IEEE.; The 1994 1st IEEE International Conference on Image Processing ; Conference date: 13-11-1994 Through 16-11-1994",

year = "1994",

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AU - Prince, J. L.

PY - 1994

Y1 - 1994

N2 - Three-dimensional (3-D) tomographic measurements of vector flow fields are possible using acoustical, optical, and magnetic resonance imaging. A general mathematical framework for this type of data acquisition called the probe transform has been studied by the author in previous work. It has been shown that the irrotational field component can be reconstructed using only one probe direction, and that the solenoidal field component can be reconstructed using only two probe directions. Previously, the reconstruction formulas were of the backprojection-convolution type; that is, first backproject then convolve in 3-D. In this paper a convolution-backprojection formula, which has significant computational savings, is developed. Numerical simulations are also given to demonstrate the performance of this new approach.

AB - Three-dimensional (3-D) tomographic measurements of vector flow fields are possible using acoustical, optical, and magnetic resonance imaging. A general mathematical framework for this type of data acquisition called the probe transform has been studied by the author in previous work. It has been shown that the irrotational field component can be reconstructed using only one probe direction, and that the solenoidal field component can be reconstructed using only two probe directions. Previously, the reconstruction formulas were of the backprojection-convolution type; that is, first backproject then convolve in 3-D. In this paper a convolution-backprojection formula, which has significant computational savings, is developed. Numerical simulations are also given to demonstrate the performance of this new approach.

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DO - 10.1109/ICIP.1994.413685

M3 - Conference article

AN - SCOPUS:84997831808

SN - 1522-4880

VL - 2

SP - 820

EP - 824

JO - Proceedings - International Conference on Image Processing, ICIP

JF - Proceedings - International Conference on Image Processing, ICIP

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T2 - The 1994 1st IEEE International Conference on Image Processing

Y2 - 13 November 1994 through 16 November 1994

ER -

A convolution backprojection formula for three-dimensional vector tomography

Abstract

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