Abstract
In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency.
Acknowledgments
M Hegland is partially supported under Australian Research Council’s Discovery Projects funding scheme (DP130101738) and the Technische Universität München Institute for Advanced Study, funded by the German Excellence Initiative. Q Jin is partially supported by the grant DE120101707 of Australian Research Council. W Wang is partially supported by Zhejiang Provincial Natural Science Foundation of China (No. LQ14A010013).
Notes
Dedicated to Bernd Hofmann on the occasion of his 60th birthday.