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smoothness information should be incorporated in order to get better reconstructed
PET images (Ouyang et al.,
). his was accomplished by combining the prior
boundary information with Gibbs sampling in the Bayesian reconstruction. How-
ever, the choices of the neighborhood system, the parameters in the Gibbs prior, and
the weighting factors in the weighted line sites are di
cult to determine, and their
computational costs are considerable.
herefore, this author and his colleagues proposed a more e
cient method that
used ART to combine the local smoothness information, to get better PET recon-
struction in the presence of AC events and attenuation (termed the cross-reference
weighted least square estimate, CRWLSE), with the algebraic reconstruction tech-
nique (ART) (Lu et al.,
). First, the WLSE with ART algorithm is applied to get
an initial reconstruction. Second, the boundaries and the WLSE are used to retrieve
a mean estimate. Finally, a penalized WLSE incorporates the boundary information
using the ART algorithm. he computational complexity is only linear with respect
to the sizes of the pixels and detector tubes. he range limits and spatially variant
penalty are easily incorporated without compromising computational e
ciency. he
reconstructionwasquitesuccessfulatreducingthenoiseandedgeeffects,asreported
in Lu et al. (
).
he author and colleagues also proposed a cross-reference MLE (CRMLE) with
amodifiedEMalgorithm forPETwith orwithout ACevents (LuandTseng,
;Tu
et al.,
). hese e
cient methods equip the MLE with the related but incomplete
boundary information and only one penalty parameter. hese forms of penalized
MLE have penalty terms that are derived from the boundary information of related
medical modalities. Several speedy approaches can be used that apply the bound-
ary information during reconstruction. hesolution, the accelerated cross-reference
maximum likelihood estimate (ACRMLE), is unique. New algorithms adap-
ted from the expectation/conditional maximization (ECM) algorithm in Meng and
Rubin (
) as well as the space-alternating generalized expectation maximization
(SAGE) algorithms in Fessler and Hero (
,
) allow the computational com-
plexity to remain linear and the range limits to be preserved. hese algorithms are
convergent, and even faster convergence speeds are achieved by using the modified
SAGE algorithm first,followed bythe modified ECM algorithm. hepenalty param-
eter can be selected by users or data-driven methods. he penalty parameter can
bequickly determinedautomatically using generalized approximatecross-validation
(GACV) (Xiang and Wahba,
).
Currently, the high spatial resolution andsensitivity of microPETmake it an ideal
modality for in vivo molecular and genetic imaging in functional genomic studies.
Atthis stage,it can beusedtodetect the effects of gene therapy inside animals. High-
quality image reconstruction is important for establishing a solid basis for the quan-
titative studyofmicroPETimages(Chatziioannou etal.,
).Maximumlikelihood
estimation with the expectation maximum algorithm (MLE-EM)permits the recon-
struction of microPET images with random correction using joint prompt and delay
sinograms(PDEM)(Chenetal.,
).hejointPoissonmodelhastheadvantagesof
preservingPoissonpropertieswithoutincreasingthevariancecausedbyrandomcor-
rection. he stopping criterion for PDEM is determined by K-fold cross-validation.
