Landweber scheme for compact operator equation in Hilbert space and its applications

Abstract

SUMMARYWe study the Landweber scheme for linear compact operator equation in infinite Hilbert spaces. Using the singular value decomposition for compact operators, we obtain a formula for the Landweber scheme after n iterations and iterative truncated error and consequently establish its convergence conditions. Our results extend known results on convergence conditions. As applications, we apply the Landweber scheme to the X-ray tomography and extrapolation of band-limited functions, and establish accelerated strategies for each application.

Special issue on recent advances in computational techniques for biomedical imaging

“…Lu and Chatziioannou [11] simulate the photon migration with a parallel adaptive finite element method. Finally, Qu and Jiang [12] examine the Landweber scheme for solving compact operator equations and their biomedical applications.…”