A Generalization of the Maximum Likelihood Expectation Maximization
(MLEM) Method: Masked-MLEM
Abstract
In our previous work on image reconstruction for single-layer
collimatorless scintigraphy, we introduced the min-min weighted robust
least squares (WRLS) optimization algorithm to address the challenge of
reconstructing images when both the system matrix and the projection
data are uncertain. Whereas the WRLS algorithm has been successful in
two-dimensional (2D) reconstruction, expanding it to three-dimensional
(3D) reconstruction is difficult since the WRLS optimization problem is
neither smooth nor strongly-convex. To overcome these difficulties and
achieve robust image reconstruction in the presence of system
uncertainties and projection noise, we propose a generalized iterative
method based on the maximum likelihood expectation maximization (MLEM)
algorithm, hereinafter referred to as the Masked-MLEM algorithm. In the
Masked-MLEM algorithm, only selected subsets (“masks”) in the system
matrix and the projection contribute to the image update to satisfy the
constraints imposed by the system uncertainties. We validate the
Masked-MLEM algorithm and compare it to the standard MLEM algorithm
using data from both collimated and uncollimated imaging instruments,
including parallel-hole collimated SPECT, 2D collimatorless
scintigraphy, and 3D collimatorless tomography. The results show that
the Masked-MLEM and standard MLEM reconstructions are similar in SPECT
imaging, while the Masked-MLEM algorithm outperforms the standard MLEM
algorithm in collimatorless imaging. A good choice of system uncertainty
can make the Masked-MLEM reconstruction more robust than the standard
MLEM reconstruction, effectively reducing the likelihood of
reconstructing higher activities in regions without radioactive sources.