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Volume 28, Issue 3
Framelet Based Deconvolution

Jian-Feng Cai & Zuowei Shen

J. Comp. Math., 28 (2010), pp. 289-308.

Published online: 2010-06

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  • Abstract

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].

  • AMS Subject Headings

65T60, 90C90, 94A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-289, author = {}, title = {Framelet Based Deconvolution}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {3}, pages = {289--308}, abstract = {

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].

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1001-m1002}, url = {http://global-sci.org/intro/article_detail/jcm/8521.html} }
TY - JOUR T1 - Framelet Based Deconvolution JO - Journal of Computational Mathematics VL - 3 SP - 289 EP - 308 PY - 2010 DA - 2010/06 SN - 28 DO - http://doi.org/10.4208/jcm.1001-m1002 UR - https://global-sci.org/intro/article_detail/jcm/8521.html KW - Framelet, deconvolution, wavelet, tight frame, soft-thresholding. AB -

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].

Jian-Feng Cai & Zuowei Shen. (2019). Framelet Based Deconvolution. Journal of Computational Mathematics. 28 (3). 289-308. doi:10.4208/jcm.1001-m1002
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