Cross-reference weighted least square estimates for positron emission tomography

Henry Horng Shing Lu*, Chung Ming Chen, I. Hsin Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


An efficient new method, termed as the crossreference weighted least square estimate (WLSE) [CRWLSE], is proposed to integrate the incomplete local smoothness information to improve the reconstruction of positron emission tomography (PET) images in the presence of accidental coincidence events and attenuation. The algebraic reconstruction technique (ART) is applied to this new estimate and the convergence is proved. This numerical technique is based on row operations. The computational complexity is only linear in the sizes of pixels and detector tubes. Hence, it is efficient in storage and computation for a large and sparse system. Moreover, the easy incorporation of range limits and spatially variant penalty will not deprive the efficiency. All this makes the new method practically applicable. An automatically data-driven selection method for this new estimate based on the generalized cross validation is also studied. The Monte Carlo studies demonstrate the advantages of this new method.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalIEEE Transactions on Medical Imaging
Issue number1
StatePublished - 1 Jan 1998


  • Algebraic reconstruction technique
  • Generalized cross-validation
  • Regularization
  • Weighted least square estimate

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