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Combining Compact Finite Difference Schemes with Filters for Image Restoration

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In this study, the Rudin, Osher, and Fatemi (ROF) model is considered to restore images. To this end, the compact finite difference (CFD) method is introduced to approximate the spatial derivatives in the ROF model. Moreover, two filters are presented to improve the performance of the first- and second-order derivative approximation. The third-order total variation diminishing Runge-Kutta (TVD-RK3) method is applied to solve the obtained system along the time axis. Two examples are given to show the efficiency and accuracy of the method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    N. Aghazadeh & F. Akbarifard

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  1. N. Aghazadeh
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  2. F. Akbarifard
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Correspondence to N. Aghazadeh.

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Aghazadeh, N., Akbarifard, F. Combining Compact Finite Difference Schemes with Filters for Image Restoration. Comput Math Model 27, 206–216 (2016). https://doi.org/10.1007/s10598-016-9315-4

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