Medical Image Processing - Signal Processing Systems - page 353

When the matrix element values converge to steady state values, usually after
hundreds of iterations, the algorithm terminates. The iterative nature of the al-
gorithm makes this algorithm computationally inefficient and less favorable for
practical implementation. However, unlike previously described algorithms, this
algorithm is capable of reconstructing an image from a limited number of projec-
tions. This feature is helpful in emission imaging and in (nonmedical) earth resource
imaging, either of which may gather projections distributed over less than 180 ◦ or
360 ◦ needed for filtered backprojection algorithm.

4.2 PET/SPECT Reconstruction

PET and SPECT systems also collect CT-like projections and, therefore, filtered
backprojection reconstruction is applicable to these imaging modalities, provided
projections are properly corrected for attenuation as gamma rays travel through the
tissues. In CT, the source of the radiation is outside the body and its characteristics
are known. The only unknown is the attenuation characteristics of the body, and
the goal of CT is to generate a map of attenuation coefficients. The goal in nuclear
medicine, however, is to create a distribution of unknown emission sources located
within the body when the attenuation coefficients themselves are unknown. For this
reason, in PET always and in SPECT often, a CT-like transmission scan with a
known external source is created. This scan, a map of attenuation coefficients,
serves to correct for tissue attenuation. While this so-called attenuation correction
is straightforward in PET because of coincident detection (two photons travel
in opposite directions from the point of their origin), the step remains difficult in
SPECT because the distance a photon travels before hitting a detector is unknown.
Several practical solutions exist to overcome this problem. All in all, filtered
backprojection following attenuation correction remains a common reconstruction
approach in PET and SPECT.
The photon emission intensity in PET and SPECT are very small and the
resulting projections that represent detected photon counts are generally noisy.
The photon detection process in nuclear medicine is often modeled as Poisson
process and therefore statistically-based iterative reconstruction techniques specif-
ically for PET and SPECT also exist. The most common of these methods is the
maximum likelihood expectation maximization (ML-EM) technique [ 34 ] . If Q is
the ensemble of detector measurements and R represents the reconstructed image,
the ML approach maximizes the likelihood p . This likelihood function is

further expanded in terms of individual detectors readings and pixel intensities while
incorporating the Poisson model. The practical implementation maximizes log-
likelihood iteratively using the EM algorithm. The ML-EM algorithm usually better
accounts for the noise in the projection data and yields better-quality reconstructed
SPECT and PET images. The price paid is the high computation cost of ML-EM.
Two common variants of the algorithm, one using ordered subsets [ 12 ] and another

( Q | R )