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A Generalization of the Maximum Likelihood Expectation Maximization (MLEM) Method: Masked-MLEM
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  • Yifan Zheng ,
  • Emily Frame ,
  • Javier Caravaca ,
  • Grant Gullberg ,
  • Kai Vetter ,
  • Youngho Seo
Yifan Zheng
University of California, University of California

Corresponding Author:[email protected]

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Emily Frame
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Javier Caravaca
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Grant Gullberg
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Kai Vetter
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Youngho Seo
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Abstract

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.