Framelet based deconvolution

Abstract

In this paper, two framelet based disconsolation algorithms are proposed. The basic idea of frame let based approach is to convert the disconsolation problem to the problem of in painting in a frame domain by constructing a frame let system with one of the masks being the given (discrete) convolution kernel via the unitary extension principle of [26], as introduced in [6-9]. The first algorithm unifies our previous works in high resolution image reconstruction and infra-red chopped and nodded image restoration, and the second one is a combination of our previous frame-based disconsolation algorithm and the iterative shareholding algorithm given by [14,16]. The strong convergence of the algorithms in infinite dimensional settings is given by employing proximal forward-backward splitting (PFBS) method. Consequently, it unifies iterative algorithms of infinite and finite dimensional setting and simplifies the proof of the convergence of the algorithms of [6]. © 2010 by AMSS, Chinese Academy of Sciences.