Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

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.

Keywords:

• linear inverse problems in Banach spaces
• accelerated Landweber iteration
• convex penalty function

AMS Subject Classifications:

• 65J10
• 65J20

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.