Efficient convolution kernels for computerized tomography

Surender K. Kenue, James F Greenleaf

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Three concepts are presented: 1) Extended kernels: The Ramachandran-Lakshminarayanan convolution kernel has one zero between each non-zero value in the spatial domain. By extending the kernel in Fourier space, it is shown that each extension leads to two additional zeros in the spatial domain of the convolution kernel, thus decreasing the required number of multiplications necessary for convolution. Any known kernel can be extended and in the limit of extension a simple backprojection reconstruction is obtained. 2) Binary kernels: A technique for generating binary approximations to any convolution kernel is described. Excluding the central element, all other elements of the kernel are approximated by an even power of two; thus, multiplications are replaced by shift operations in the convolution procedure. 3) Recursive convolution: It is shown how additions can be saved by using a recursive formulation which generates new elements in the convolution procedure utilizing only a few summation steps. Results from both extended kernels and their binary approximations are described for simulated phantoms and ultrasound data obtained from breast scans of patients.

Original languageEnglish (US)
Pages (from-to)232-244
Number of pages13
JournalUltrasonic Imaging
Volume1
Issue number3
DOIs
StatePublished - 1979

Fingerprint

convolution integrals
tomography
Tomography
Breast
multiplication
approximation
breast
formulations
shift

Keywords

  • Computerized tomography
  • convolution kernels
  • hardware
  • image reconstruction
  • ultrasound
  • x-ray

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging
  • Acoustics and Ultrasonics

Cite this

Efficient convolution kernels for computerized tomography. / Kenue, Surender K.; Greenleaf, James F.

In: Ultrasonic Imaging, Vol. 1, No. 3, 1979, p. 232-244.

Research output: Contribution to journalArticle

Kenue, Surender K. ; Greenleaf, James F. / Efficient convolution kernels for computerized tomography. In: Ultrasonic Imaging. 1979 ; Vol. 1, No. 3. pp. 232-244.
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