Acceleration of multiplicative iterative algorithms for image deblurring by duality maps in Banach spaces

Abstract

An acceleration technique for multiplicative iterative methods, such as Lucy–Richardson and Image Space Reconstruction Algorithm, is presented. The technique is inspired by the Landweber method in Banach spaces and is based on the application of duality maps, which allow to compute the iterations in the dual space. We show the link between the proposed acceleration and the previously known Meinel acceleration, which consists in the introduction of an exponent in the basic iterative formulas. We prove that the new acceleration technique is more stable than the Meinel acceleration. This implies that, in the restoration process, the former is able to get better accuracy and higher speeding-up than the latter. In addition to the main focus of the paper, we propose a generalization of the Landweber method in Banach space, in order to overcome some drawbacks of this recent strategy when compared with classical (Hilbertian) Landweber method. Numerical results show the behavior and the features of the several techniques considered, highlighting the goodness of our proposals.