Biomedical Engineering Reference
In-Depth Information
where
λ
k
+
1
are the image estimates obtained from iterations
k
and
k
+
1,
respectively. The ML-EM algorithm has some special properties:
k
and
λ
The objective function increases monotonically at each iteration, i.e.
k
+
1
)
≥
L
(
p
|
λ
k
)
.
L
(
p
|
λ
The estimate
λ
k
converges to an image
˜
λ
that maximizes the log-likelihood
function for
k
→∞
and
All successive estimates
λ
k
are nonnegative if the initial estimate is non-
negative.
The major drawback of iterative reconstruction methods, however, has been
their excessive computational burden, which has been the main reason that
these methods are less practical to implement than FBP. Considerable effort has
been directed toward the development of accelerated reconstruction schemes
that converge much rapidly. The ordered subsets EM (OS-EM) algorithm pro-
posed by Hudson and Larkin [40] which subdivides the projection data into
“ordered subsets” has shown accelerated convergence of at least an order of
magnitude as compared to the standard EM algorithm. Practical application of
the OS-EM algorithm has demonstrated marked improvement in tumor detec-
tion in whole-body PET [41].
A problem with iterative reconstruction algorithms is that they all produce
images with larger variance when the number of iterations is increased. Some
forms of regularization are required to control the visual quality of the recon-
structed image. Regularization can be accomplished by many different ways,
including post-reconstruction smoothing, stopping the algorithm after an ef-
fective number of reconstruction parameters (number of iterations and sub-
sets for OS-EM), and incorporation of constraints and
a priori
information
as described earlier. However, caution should be taken when using regular-
ization because too much regularization can have an adverse effect on the
bias of the physiologic parameter estimates obtained from kinetic modeling,
which will be described later in this chapter. Nevertheless, with the develop-
ment of fast algorithm and the improvement in computational hardware, ap-
plication of iterative reconstruction techniques on a routine basis has become
practical.
