Post-reconstruction MRI-guided Enhancement of PET Images using Parallel Level Set Method with Bregman Iteration

179 Objectives: We propose and investigate a parallel level set (PLS) method with Bregman iteration, utilizing MRI anatomical information, to guide post-reconstruction enhancement of PET images. We evaluate the proposed method against conventional PLS with Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Methods: PLS is a promising method which can improve quality of PET images with anatomical prior from MRI[1]. By enforcing alignment of gradients between PET and MR images, it incorporates anatomical information into PET images without requiring segmentation. The PLS framework has been successfully implemented with the quasi-Newton L-BFGS algorithm [2]. The Bregman iteration method was originally proposed to solve total variation models [3]. In Bregman iteration, data residual is added back to the original data after every iteration. In our task, after every Bregman iteration, we compute the difference between the reconstructed image and a blurred image acquired by convoluting the post processed image with system PSF. This difference, which contains both noise and fine structure information, is then added back to the reconstructed noisy and blurry image for next iteration. With this procedure, we expect the algorithm could provide more detail and improved quantitative performance compared with the PLS method implemented by the L-BFGS algorithm. For assessment, simulation experiments were conducted using the BrainWeb phantom [4], incorporating realistic resolution blurring as well as 10 noise realizations to generate PET sinograms. For reconstruction, the OSEM algorithm was implemented with 10 subsets and 24 iterations. Reconstructed images were smoothed by a Gaussian filter with FWHM=2.5mm and then fed into the L-BFGS PLS and Bregman iteration PLS methods. We performed 3 Bregman iterations. In each Bregman iteration, the PLS regularized subproblem was solved by L-BFGS with no more than 300 iterations. For the purely L-BFGS PLS method, the number of iterations was set to 900. Mean percentage bias as well as standard deviation were computed in gray matter and white matter. Subsequently, by varying regularization parameters, we obtained bias vs. noise trade-off curves for the two methods. Results: For visual inspection, both methods generated PET images with enhanced quality compared to OSEM reconstructed images. To compare images from L-BFGS PLS and Bregman iteration PLS, we choose images with regularization parameter that generates matched noise level. We noticed Bregman iteration PLS is able to provide more structure details. For quantitative results, PLS with Bregman iteration outperformed L-BFGS PLS by reducing bias by about 12% for gray matter and 13% for white matter at matched noise level with statistical significance (p<0.01 for paired t test). For Bregman iteration PLS, we also observed as regularization parameter decreases, noise increases quickly while bias stops from further decreasing. This is caused by the fact that small regularization parameters fail to penalize noise sufficiently when we add back the residual term. For larger regularization parameters, while images appear blurry after first Bregman iteration, more structure details are extracted from the residual term in later iterations. In addition, larger regularization parameters help suppress noise from the residual term. This results in a relative clean image with important edges preserved. Conclusions: A Bregman iteration PLS method was studied in this work. The method provides more structure details and enhances quantitative performance of PET images compared with the use of conventional L-BFGS PLS method.Acknowledgments: This work was supported by NIH R21 grant AG056142 and the Natural Science Foundation of Guangdong Province, grant 2018A030313366.