A Hankel Transform Approach to Tomographic Image Reconstruction

William Evan Higgins, David C. Munson

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We develop a relatively unexplored algorithm for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, which we refer to as the Hankel-transform reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r, θ) of an image into a Fourier series in θ; 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, Φ); resolves this series, giving a polar-form reconstruction; and finally, if desired, interpolates this reconstruction to a rectilinear grid. We outline the HTR algorithm and show that its performance can compare favorably to the popular convolution-backprojection algorithm.

Original languageEnglish (US)
Pages (from-to)59-72
Number of pages14
JournalIEEE Transactions on Medical Imaging
Volume7
Issue number1
DOIs
StatePublished - Jan 1 1988

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Computer-Assisted Image Processing
Image reconstruction
Mathematical transformations
Fourier Analysis
Fourier series
Convolution
Fourier transforms

All Science Journal Classification (ASJC) codes

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

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A Hankel Transform Approach to Tomographic Image Reconstruction. / Higgins, William Evan; Munson, David C.

In: IEEE Transactions on Medical Imaging, Vol. 7, No. 1, 01.01.1988, p. 59-72.

Research output: Contribution to journalArticle

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