Please use this identifier to cite or link to this item: https://doi.org/10.4208/jcm.1001-m1002
Title: Framelet based deconvolution
Authors: Cai, J.-F.
Shen, Z. 
Keywords: Deconvolution
Framelet
Soft-thresholding
Tight frame
Wavelet
Issue Date: May-2010
Citation: Cai, J.-F., Shen, Z. (2010-05). Framelet based deconvolution. Journal of Computational Mathematics 28 (3) : 289-308. ScholarBank@NUS Repository. https://doi.org/10.4208/jcm.1001-m1002
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.
Source Title: Journal of Computational Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103296
ISSN: 02549409
DOI: 10.4208/jcm.1001-m1002
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