Convolution backprojection formulas for 3-D vector tomography with application to MRI

Research output: Contribution to journalArticle

Abstract

Vector tomography is the reconstruction of vector fields from measurements of their projections. In previous work, it has been shown that reconstruction of a general three-dimensional (3-D) vector field is possible from the so-called inner product measurements. It has also been shown how reconstruction of either the irrotational or solenoidal component of a vector field can be accomplished with fewer measurements than that required for the full field. The present paper makes three contributions. First, in analogy to the two-dimensional (2-D) approach of Norton, several 3-D projection theorems are developed. These lead directly to new vector field reconstruction formulas that are convolution backprojection formulas. It is shown how the local reconstruction property of these 3-D reconstruction formulas permits reconstruction of point flow or of regional flow from a limited data set. Second, simulations demonstrating 3-D reconstructions, both local and nonlocal, are presented. Using the formulas derived herein and those derived in previous work, these results demonstrate reconstruction of the irrotational and solenoidal components, their potential functions, and the field itself from simulated inner product measurement data. Finally, it is shown how 3-D inner product measurements can be acquired using a magnetic resonance scanner.

Original languageEnglish (US)
Pages (from-to)1462-1472
Number of pages11
JournalIEEE Transactions on Image Processing
Volume5
Issue number10
DOIs
StatePublished - 1996

Fingerprint

Tomography
Convolution
Magnetic resonance imaging
3D
Vector Field
Scalar, inner or dot product
3D Reconstruction
Magnetic resonance
Projection
Magnetic Resonance
Potential Function
Scanner
Analogy
Three-dimensional
Theorem
Demonstrate
Simulation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Convolution backprojection formulas for 3-D vector tomography with application to MRI. / Prince, Jerry Ladd.

In: IEEE Transactions on Image Processing, Vol. 5, No. 10, 1996, p. 1462-1472.

Research output: Contribution to journalArticle

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