A method of iterative data refinement and its applications

Y. Censor, T. Elfving, G. T. Herman, B. Brosowski

Research output: Contribution to journalArticlepeer-review

Abstract

Iterative data refinement (IDR) is a general procedure for producing a sequence of estimates of the data that would be collected by a measuring device which is idealized to a certain extent, starting from the data that are collected by an actual measuring device. Following a discussion of the fundamentals of IDR, we present a number of previously published procedures which are special cases of it. We concentrate on examples from medical imaging. In particular, we discuss beam hardening correction in x‐ray computerized tomography, attenuation correction in emission computerized tomography, and compensation for missing data in reconstruction from projections. We also show that a standard method of numerical mathematics (the parallel chord method) as well as a whole family of constrained iterative restoration algorithms are special cases of IDR. Thus IDR provides a common framework within which a number of originally different looking procedures are presented and discussed. We also present a result of theoretical nature concerning the initial behavior of IDR.

Original languageEnglish
Pages (from-to)108-123
Number of pages16
JournalMathematical Methods in the Applied Sciences
Volume7
Issue number1
DOIs
StatePublished - 1985
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)
  • Engineering (all)

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