Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning
This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden- Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGSB), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGSB and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGSB- PC shows promise for clinical application.
Tsai, Y., Bousse, A., Ehrhardt, M. J., Stearns, C. W., Ahn, S., Hutton, B. F., Arridge, S. & Thielemans, K. (2018). Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning. IEEE Transactions on Medical Imaging, 37 (4), 1000-1010.