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resonance imaging, and others (Lu et al.,
; Lu and Tseng,
; Tu et al.,
).
he reconstruction problems are even more challenging for the types of molecular
imaging associated with genomic and medical studies in the post-genomic era, such
as microPET, which requires further research to provide more accurate images at
molecular levels of resolution.
Image synthesis and segmentation by spatial-frequential analysis were developed
to model human vision; see Malik and Perona (
); Jain and Farrokhnia (
);
Dunn etal.(
);Tan (
);Zhu etal.(
).hesestudies reveal that the descrip-
tors of texture images can be represented by the outputs from multichannel Gabor
filters,whichareconstructed todetecttheresponsesat differentorientations andfre-
quencies.hisvisionmodelcanbeappliedtosegmentmedicalimagesusingthetech-
niques of image processing and computational statistics. In particular, ultrasound
images are noisy due to inherent speckle noise. Vision model-based segmentation
methods for ultrasound images were developed fromactive contour models (i.e.,the
snake-balloon model), region competition, and related methods (Chen et al.,
;
Chen and Lu,
; Chen et al.,
a,b,
,
). In addition, the technique of
sliced inverse regression (Li,
)wasextended tosegment dynamic images, includ-
ing magnetic resonance images (Wuand Lu,
). Further developments and chal-
lenges associated with the visualization and analysis of dynamic images in
-D are
also discussed in this chapter.
PET Images
2.2
he scanning, acquisition and reconstruction process of a PET system is displayed
in Fig.
.
. An object with a radioactive chemical tracer is injected into the body in
order to detect the biochemical activity inside it; detectors outside the body monitor
the radiation emitted by the tracer. his type of imaging is described in more depth
in various topics on medical imaging (Suetens,
; Prince and Links,
).
An ideal model for PET images was introduced in Shepp and Vardi (
); Vardi
et al. (
). Initially, positrons resulting from biochemical activity are emitted from
inside the body. hese positrons hit nearby electrons and annihilate themselves.
When a positron hits an electron, a pair of photons are generated and they travel
inopposite directions. hisphoton pair is detectedbya pairof scintillation detectors
outside the body. Before these pairs of photons arrive at the detectors, their energy
is attenuated by Compton scattering as they pass through tissue. herefore, some of
these photon pairs do not retain a detectable level of energy, and remain undetected.
he other attenuated photon pairs are recorded, and can be described by a survival
probability (Politte and Snyder,
). he detectors may also receive stray photon
pairsthatarenotgeneratedbytheannihilationsthatoccuratthetargetimageinaspe-
cific slice of the body. hat is, there are accidental (or random) coincidence (AC or
RC) events. he observations made by a pair of detectors are the sum of the photon
pairs that occur at the target image and the AC events. herefore, to recover the true
