@Article{JCM-28-289,
author = {Jian-Feng Cai and Zuowei Shen},
title = {Framelet Based Deconvolution},
journal = {Journal of Computational Mathematics},
year = {2010},
volume = {28},
number = {3},
pages = {289--308},
abstract = {<p style="text-align: justify;">In this paper, two framelet based deconvolution algorithms are proposed. The basic idea of framelet based approach is to convert the deconvolution problem to the problem of inpainting in a frame domain by constructing a framelet 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 deconvolution algorithm and the iterative thresholding 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].</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1001-m1002},
url = {http://global-sci.org/intro/article_detail/jcm/8521.html}
}