Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal

Abdelgader Siddig; Zhichang Guo; Zhenyu Zhou; Boying Wu; Abdelgader Siddig; Zhichang Guo; Zhenyu Zhou; Boying Wu

doi:10.3934/math.2021236

AIMS Mathematics

2021, Volume 6, Issue 4: 3974-3995. doi: 10.3934/math.2021236

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Research article

Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
2.
Department of Mathematics, University of Albutana, Ruffa'a, 420, Sudan

Received: 13 October 2020 Accepted: 26 January 2021 Published: 03 February 2021
MSC : 94A08, 65J15

Noise is regarded as an unavoidable component of digital image acquisition. Hence, noise removal has been considered as one of the fundamental tasks in the field of image processing. Accordingly, excellent results have been achieved by using second-order models. However, these outcomes are affected by the staircase effect. To eliminate this anomaly and maintaining the balance of removing noise and preserving edges, a fourth-order model is proposed. The existence and uniqueness of the entropy solution for this model are established. Besides, to to verify the effectiveness of the model in noise removal, we carried out numerical experiment and presented our results. Indeed, the experimental results show that our model is superior to PM model and ROF model in terms of removing noise and preserving edges.
- entropy solution,
- fourth-order PDE,
- noise removal,
- adaptive $ BV^2 $ space
Citation: Abdelgader Siddig, Zhichang Guo, Zhenyu Zhou, Boying Wu. Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal[J]. AIMS Mathematics, 2021, 6(4): 3974-3995. doi: 10.3934/math.2021236

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Abstract

Noise is regarded as an unavoidable component of digital image acquisition. Hence, noise removal has been considered as one of the fundamental tasks in the field of image processing. Accordingly, excellent results have been achieved by using second-order models. However, these outcomes are affected by the staircase effect. To eliminate this anomaly and maintaining the balance of removing noise and preserving edges, a fourth-order model is proposed. The existence and uniqueness of the entropy solution for this model are established. Besides, to to verify the effectiveness of the model in noise removal, we carried out numerical experiment and presented our results. Indeed, the experimental results show that our model is superior to PM model and ROF model in terms of removing noise and preserving edges.

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