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Recent Advances in Electrical & Electronic Engineering

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ISSN (Print): 2352-0965
ISSN (Online): 2352-0973

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Research Article

Local Adaptiveness of Mixed Higher Order Partial Differential Equations and Its Application in Image Denoising

Author(s): Zengqiang Ma, Hang Yang, Dandan Xu, Weiming Wang* and Sasa Ma

Volume 16, Issue 1, 2023

Published on: 13 October, 2022

Page: [45 - 55] Pages: 11

DOI: 10.2174/2352096515666220829140841

Price: $65

Abstract

Background: Image denoising methods based on partial differential equations have attracted much attention due to their "infinite" local adaptation capabilities, high flexibility, and strong mathematical theoretical support.

Methods: This paper proposes a mixed higher order partial differential equation denoising model for the step effect caused by the second-order denoising model and the edge blur caused by the fourth-order denoising model. The model combines the second-order and fourth-order terms based on the relationship between the variational energy minimization and the partial differential equations. The fourth-order term is used to remove noise in the uniform area of the image to avoid the step effect, and the second-order term is used at the edge to avoid boundary blur.

Results: Theoretical analysis and numerical experiment results show that the proposed model has weak solutions and can effectively avoid the step effect and maintain the edge.

Conclusion: The image denoising results of the model are better than those of other improved denoising models in subjective effect, and objective evaluation indicators, such as SNR, PSNR, and MSSIM.

Keywords: Image, denoising, anisotropic, diffusion, gradient modulus, mixed higher order, partial differential equations

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[1]
Y.A. Üncü, G. Sevim, and M. Canpolat, "Approaches to preclinical studies with heterogeneous breast phantom using reconstruction and three dimensional image processing algorithms for diffuse optical imaging", Int. J. Imaging Syst. Technol., vol. 32, no. 1, pp. 343-353, 2022.
[http://dx.doi.org/10.1002/ima.22648]
[2]
E. Baranwal, and S. Ahmad, "Retrieving spatial pattern of urban using spectral ratios for major features of an urban ecosystem with satellite image processing", IOP Conf. Ser. Earth Environ. Sci., vol. 795, no. 1, p. 012034, 2021.
[http://dx.doi.org/10.1088/1755-1315/795/1/012034]
[3]
M. Kang, "Approximate versions of proximal iteratively reweighted algorithms including an extended IP-ICMM for signal and image processing problems", J. Comput. Appl. Math., vol. 376, p. 112837, 2020.
[http://dx.doi.org/10.1016/j.cam.2020.112837]
[4]
A. Rajput, J. Li, F. Akhtar, Z. Hussain Khand, J.C. Hung, Y. Pei, and A. Börner, "A content awareness module for predictive lossless image compression to achieve high throughput data sharing over the network storage", Int. J. Distrib. Sens. Netw., vol. 18, no. 3, 2022.
[http://dx.doi.org/10.1177/15501329221083168]
[5]
G. Ghimpeteanu, T. Batard, M. Bertalmio, and S. Levine, "A decomposition framework for image denoising algorithms", IEEE Trans. Image Process., vol. 25, no. 1, pp. 388-399, 2016.
[http://dx.doi.org/10.1109/TIP.2015.2498413] [PMID: 26561436]
[6]
Y. Yu, J. Qian, and Q. Wu, "Visual saliency via multiscale analysis in frequency domain and its applications to ship detection in optical satellite images", Front. Neurorobot., vol. 15, p. 767299, 2022.
[http://dx.doi.org/10.3389/fnbot.2021.767299] [PMID: 35095455]
[7]
L. Shao, R. Yan, X. Li, and Y. Liu, "From heuristic optimization to dictionary learning: A review and comprehensive comparison of image denoising algorithms", IEEE Trans. Cybern., vol. 44, no. 7, pp. 1001-1013, 2014.
[http://dx.doi.org/10.1109/TCYB.2013.2278548] [PMID: 24002014]
[8]
Loeza C.B., and Chen K., "On high order denoising models and fast algorithms for vector-valued images", IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society, vol. 19, no. 6, p. 1518-27, 2010.
[http://dx.doi.org/10.1109/TIP.2010.2042655]
[9]
C. Bowd, A. Belghith, L.M. Zangwill, M. Christopher, M.H. Goldbaum, R. Fan, J. Rezapour, S. Moghimi, A. Kamalipour, H. Hou, and R.N. Weinreb, "Deep learning image analysis of optical coherence tomography angiography measured vessel density improves classification of healthy and glaucoma eyes", Am. J. Ophthalmol., vol. 236, pp. 298-308, 2022.
[http://dx.doi.org/10.1016/j.ajo.2021.11.008] [PMID: 34780803]
[10]
D. Jain, P. Singh, and P.K. Bharti, "RETRACTED: Deep learning based clinical image segmentation methods with different modalities", J. Phys. Conf. Ser., vol. 2236, no. 1, p. 012002, 2022.
[http://dx.doi.org/10.1088/1742-6596/2236/1/012002]
[11]
P. Perona, and J. Malik, "Scale space and edge detection using anisotropic diffusion", IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 7, pp. 629-639, 1990.
[http://dx.doi.org/10.1109/34.56205]
[12]
X. Zhang, M. Hao, H. Xing, and X. Zeng, "Research on speckle suppression of SAR image based on 3D matching block", J. Elect. Measure. Instr., vol. 31, no. 10, pp. 1621-1626, 2017.
[13]
O. Niang, A. Thioune, É. Deléchelle, and J. Lemoine, "Spectral intrinsic decomposition method for adaptive signal representation", ISRN Signal Process., vol. 2012, pp. 1-10, 2012.
[http://dx.doi.org/10.5402/2012/457152]
[14]
M. Heydari, M.R. Karami, and A. Babakhani, "A new adaptive coupled diffusion PDE for MRI Rician noise", Signal Image Video Process., vol. 10, no. 7, pp. 1211-1218, 2016.
[http://dx.doi.org/10.1007/s11760-016-0878-5]
[15]
V.B.S. Prasath, and P. Kalavathi, Mixed Noise Removal Using Hybrid Fourth Order Mean Curvature Motion., vol. 425, pp. 625-632, 2016.
[16]
X. Zhang, and X. Yu, "Anisotropic denoising model based on adaptive gradient threshold", J. Qufu Norm. Uni., vol. 45, no. 173, pp. 27-34, 2019.
[17]
You Y.L., and Kaveh M., "Fourth order partial differential equations for noise removal", In: IEEE Transactions on image processing:a publication of the IEEE Signal Processing Society, vol. 9. 2000, no. 10, p. 1723-1730.
[18]
Gilboa G., Sochen N., and Zeevi Y.Y., "Forward and backward diffusion processes for adaptive image enhancement and denoising", In: IEEE transactions on image processing : A publication of the IEEE Signal Processing Society, vol. 11. 2002, no. 7, pp. 689-703.
[19]
A.L. Bertozzi, and J.B. Greer, "Low curvature image simplifiers: Global regularity of smooth solutions and Laplacian limiting schemes", Commun. Pure Appl. Math., vol. 57, no. 6, pp. 764-790, 2004.
[http://dx.doi.org/10.1002/cpa.20019]
[20]
L. Min, X. Yang, and D. Ye, "Well-posedness for a fourth order nonlinear equation related to image processing", Nonlinear Anal. Real World Appl., vol. 17, no. 6, pp. 192-202, 2014.
[http://dx.doi.org/10.1016/j.nonrwa.2013.11.005]
[21]
A. Chambolle, and P.L. Lions, "Image recovery via total variation minimization and related problems", Numer. Math., vol. 76, no. 2, pp. 167-188, 1997.
[http://dx.doi.org/10.1007/s002110050258]
[22]
Q. Ma, F. Dong, and D. Kong, "A fractional differential fidelity based PDE model for image denoising", Mach. Vis. Appl., vol. 28, no. 5-6, pp. 635-647, 2017.
[http://dx.doi.org/10.1007/s00138-017-0857-z]
[23]
Z. Mbarki, H. Seddik, S. Tebini, and E.B. Braiek, "A new rapid auto adapting diffusion function for adaptive anisotropic image de noising and sharply conserved edges", Comput. Math. Appl., vol. 74, no. 8, pp. 1751-1768, 2017.
[http://dx.doi.org/10.1016/j.camwa.2017.06.026]
[24]
J. Bai, and X.C. Feng, "Image denoising using generalized anisotropic diffusion", J. Math. Imaging Vis., vol. 60, no. 7, pp. 994-1007, 2018.
[http://dx.doi.org/10.1007/s10851-018-0790-4]
[25]
L. Min, Z. Li, C. Feng, and M. Zhu, "New image denoising model based on partial Differential equation", J. Nanjing Uni. Posts Telecommun., vol. 39, no. 181, pp. 13-19, 2019.
[26]
F. Li, C. Shen, J. Fan, and C. Shen, "Image restoration combining a total variational filter and a fourth order filter", J. Vis. Commun. Image Represent., vol. 18, no. 4, pp. 322-330, 2007.
[http://dx.doi.org/10.1016/j.jvcir.2007.04.005]
[27]
F. Dong, and Y. Chen, "A fractional order derivative based variational framework for image denoising", Inverse Probl. Imaging (Springfield), vol. 10, no. 1, pp. 27-50, 2016.
[http://dx.doi.org/10.3934/ipi.2016.10.27]
[28]
J.M. Yu, X.T. Zhang, and S.B. Zhou, "Hybrid image restoration model with adaptive weight parameter", J. Electron. Imaging, vol. 26, no. 5, p. 1, 2017.
[http://dx.doi.org/10.1117/1.JEI.26.5.053026]
[29]
R. Gao, and D. Cheng, "Multiplicative noise removal model based on non-local regularization and split-bregman algorithm", J. Zhongyuan Institute Technol., vol. 27, no. 135, pp. 18-22, 2016.
[30]
S.J. Jemila, A.B. Therese, and S.J. Jemila, "Selection of suitable segmentation technique based on image quality metrics", Imaging Sci. J., vol. 67, no. 8, pp. 475-480, 2019.
[http://dx.doi.org/10.1080/13682199.2020.1718298]
[31]
S. Jeevakala, and T.A. Brintha, "Sharpening enhancement technique for MR images to enhance the segmentation", Biomed. Signal Process. Control, vol. 41, pp. 21-30, 2017.
[32]
Y.F. Yang, "Research on image quality evaluation algorithm based on human vision system", China Uni. Mining Technol, 2016.

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