A Generalization of the Maximum Likelihood Expectation Maximization (MLEM) Method: Masked-MLEM

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.