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Zheng Y, Frame E, Caravaca J, Gullberg GT, Vetter K, Seo Y. A generalization of the maximum likelihood expectation maximization (MLEM) method: Masked-MLEM. Phys Med Biol 2023; 68:10.1088/1361-6560/ad0900. [PMID: 37918026 PMCID: PMC10819675 DOI: 10.1088/1361-6560/ad0900] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 11/02/2023] [Indexed: 11/04/2023]
Abstract
Objective.In our previous work on image reconstruction for single-layer collimatorless scintigraphy, we developed 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.Approach.In the Masked-MLEM algorithm, only selected subsets ('masks') from 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 experimental data obtained from both collimated and uncollimated imaging instruments, including parallel-hole collimated SPECT, 2D collimatorless scintigraphy, and 3D collimatorless tomography. Additionally, we conduct comprehensive Monte Carlo simulations for 3D collimatorless tomography to further validate the effectiveness of the Masked-MLEM algorithm in handling different levels of system uncertainties.Main results.The Masked-MLEM and standard MLEM reconstructions are similar in cases with negligible system uncertainties, whereas the Masked-MLEM algorithm outperforms the standard MLEM algorithm when the system matrix is an approximation. Importantly, the Masked-MLEM algorithm ensures reliable image reconstruction across varying levels of system uncertainties.Significance.With a good choice of system uncertainty and without requiring accurate knowledge of the actual system matrix, the Masked-MLEM algorithm yields more robust image reconstruction than the standard MLEM algorithm, effectively reducing the likelihood of erroneously reconstructing higher activities in regions without radioactive sources.
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Affiliation(s)
- Yifan Zheng
- Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA 94143, USA
- Department of Nuclear Engineering, University of California, Berkeley, CA 94720, USA
| | - Emily Frame
- Department of Nuclear Engineering, University of California, Berkeley, CA 94720, USA
| | - Javier Caravaca
- Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA 94143, USA
| | - Grant T. Gullberg
- Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA 94143, USA
| | - Kai Vetter
- Department of Nuclear Engineering, University of California, Berkeley, CA 94720, USA
- Applied Nuclear Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94502, USA
| | - Youngho Seo
- Department of Radiology and Biomedical Imaging, University of California, San Francisco, CA 94143, USA
- Department of Nuclear Engineering, University of California, Berkeley, CA 94720, USA
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