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Two-Level method for the total fractional-order variation model in image deblurring problem

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Abstract

Image deblurring with total fractional-order variation model is used to improve the quality of the deblurred images. This model is very efficient in preserving edges and removing staircase effect. However, the regularization matrix associated with the total fractional-order model is dense which complicate developing an efficient numerical algorithm. In this research work, we present an efficient and robust Two-Level method to overcome the dense problem. The Two-Level method started by reducing the problem to one small non-linear system with dense regularization matrix (Level-I) and one less expensive large linear system with sparse regularization matrix (Level-II). The derivation of the optimal regularization parameter of Level-II is studied and formula is presented. Numerical experiments on several images are also provided to demonstrate the efficiency of the Two-Level method.

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Funding

This work received funding support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals (KFUPM) through project no. SR161018.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia

    Faisal Fairag & Shahbaz Ahmad

  2. PYP-Math, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    Adel Al-Mahdi

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  1. Faisal Fairag
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  2. Adel Al-Mahdi
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  3. Shahbaz Ahmad
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Correspondence to Adel Al-Mahdi.

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Fairag, F., Al-Mahdi, A. & Ahmad, S. Two-Level method for the total fractional-order variation model in image deblurring problem. Numer Algor 85, 931–950 (2020). https://doi.org/10.1007/s11075-019-00845-0

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