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

Abstract

<p>In our previous work on image reconstruction for single-layer collimatorless scintigraphy, the min-min weighted robust least squares (WRLS) optimization algorithm was proposed to address a general reconstruction problem in which both the system matrix and the projection data are uncertain. Whereas the WRLS algorithm has been successful in two-dimensional (2D) reconstruction, expanding this algorithm to three-dimensional (3D) reconstruction is difficult. To solve the WRLS optimization problem for more robust image reconstruction, 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 will contribute to the image update in order to satisfy the constraints on 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 in SPECT imaging the Masked-MLEM and standard MLEM reconstructions are similar, and in collimatorless imaging, the Masked-MLEM algorithm outperforms the standard MLEM algorithm. A good choice of system uncertainty can make the Masked-MLEM reconstruction more robust than the standard MLEM reconstruction in both collimated and uncollimated imaging. Furthermore, the computation time of each Masked-MLEM iteration is comparable to that in the standard MLEM algorithm. Although, the memory consumption of the Masked-MLEM algorithm is higher due to the storage of the system matrix uncertainties.</p>