### AIMS Mathematics

2021, Issue 4: 3974-3995. doi: 10.3934/math.2021236
Research article

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

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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