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Among all tomographic imaging devices, X-ray cone-beam computed tomography (CBCT) and positron emission tomography are two important tools used widely in numerous medical imaging applications, and both have enjoyed tremendous progress in both hardware and reconstruction algorithm development in the past few decades. Advanced optimization-based algorithms, which have gained fast development recently in CBCT imaging, have demonstrated the capability of accommodating a variety of CBCT imaging configurations, improving image quality, and exploiting image-sparsity properties with the intention of reducing data sampling. In this work, we continue investigating optimization-based reconstructions in CBCT for solving existing, practical issues. Meanwhile, we leverage the experience in CBCT image reconstruction from sparse data, and develop advanced algorithms for enabling the design of innovative PET systems with sparsely populated detectors, while not significantly compromising the PET capability and image quality. In this dissertation, we investigate numerous optimization programs and solve them by using advanced iterative algorithms. Results of the work suggest that, with appropriately designed optimization programs, optimization-based reconstruction tools can be obtained for 1 ) reducing the artifacts existing in the off-middle planes of FDK reconstruction from short-scan CBCT data, 2 ) enabling a sparse-PET configuration with reduced crystal while not significantly compromising the image quality, and 3 ) allowing iterative reconstruction based on an image with variable resolution. In addition, results indicate that the selection of program/algorithm parameters may have significant impact on the outcome.


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