Abstract
In this paper, a novel denoising algorithm based on the denoising methods of partial differential equations is presented. The proposed algorithm is obtained by using a stochastic algorithm for combining two denoising methods based on partial differential equations. The model provides a new approach for solving the contradiction in the image restoration. The new hybrid model has more ability to restore the image in terms of peak signal to noise ratio, blind/referenceless image spatial quality evaluator and visual quality, compared with each of denoising methods separately used. Experimental results show that our approach is more efficient in image denoising than the used denoising methods.
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References
Aharon M, Elad M, Bruckstein A (2006) The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Trans Image Process 54(11):4311–4322
Andreu F, Mazόn JM, Moll JS (2005) The total variation flow with nonlinear boundary conditions. Asymptot Anal 43(1–2):9–46
Aubert G, Kornprobst P (2006) Mathematical problems in image processing PDEs and the calculus of variations, 2nd edn. Springer, New York
Barbu T, Barbu V, Biga V, Coca D (2009) A PDE variational approach to image denoising and restorations. Nonlinear Anal RWA 10:1351–1361
Barcelos CAZ, Boaventura M, Silva EC Jr (2003) A well-balanced flow equation for noise removal and edge detection. IEEE Trans Image Process 12(7):751–763
Beck A, Teboulle M (2009) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans Image Process 18(11):2419–2434
Black MJ, Sapiro G, Marimont DH, Heeger D (1998) Robust anisotropic diffusion. IEEE Trans Image Process 7(3):421–432
Chambolle A (2004) An algorithm for total variation minimization and applications. J Math Imaging Vision 20(1–2):89–97
Chan T, Zhou H (1999) Adaptive ENO-wavelet Transforms for Discontinuous Functions. Computational and Applied Mathematics Technical Report, Department of Mathematics, UCLA. Tech. Rep. 99–21, Jun. 1999
Chan T, Shen J, Vese L (2003) Variational PDE models in image processing. Notices of the AMS 50(1):14–26
Chaux C, Duval L, Benazza-Benyahia A, Pesquet JC (2008) A nonlinear stein-based estimator for multichannel image denoising. IEEE Trans Signal Process 56(8):3855–3870
Chen B, Li Y, Cai JL (2012) Noisy image segmentation based on nonlinear diffusion equation model. Appl Math Model 36(3):1197–1208
Dong W, Li X, Zhang L, Shi G (2011) Sparsity-based image denoising via dictionary learning and structural clustering. CVPR 2011 (oral)
Drapaca C (2009) A nonlinear total variation-based denoising method with two regularization parameters. IEEE Trans Biomed Eng 56(3):582–586
Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745
Fouskakis D, Draper D (2002) Stochastic optimization: a review. Int Stat Rev 70(3):315–349
Gai S, Luo L (2015) Image denoising using normal inverse Gaussian model in quaternion wavelet domain. Multimedia Tools and Applications 74(3):1107–1124
Gonzalez RC, Woods RE (2006) Digital Image Processing. Prentice-Hall, Inc., Upper Saddle River
Isgrὸ F, Tegolo D (2008) A distributed genetic algorithm for restoration of vertical line scratches. Parallel Comput 34(12):727–734
Jain AK (1989) Fundamentals of digital image processing. Prentice Hall, NJ
Jain P, Tyagi V (2017) An adaptive edge-perserving image denoising technique using patch-based weighted_ SVD filtering in wavelet domain. Multimedia Tools and Applications 76(2):1659–1679
Jin JS, Wang Y, Hiller J (2000) An adaptive nonlinear diffusion algorithm for filtering medical images. IEEE Trans Inf Technol Biomed 4(4):298–305
Kaisar S, Rijwan S, Al Mahmud J, Rahman MM (2008) Salt and pepper noise detection and removal by tolerance based selective arithmetic Mean filtering technique for image restoration. International Journal of Computer Science and Network Security 8(6):271–278
Katkovnik V, Egiazarian AJ (2006) Local approximation techniques in signal and image processing. SPIE Press. Monograph, vol PM157
Korürek M, Yüksel A, Iscan Z, Dokur Z, Ölmez T (2010) Retr-ospective correction of near field effect of X-ray source in radiographic images by using genetic algorithms. Expert Syst Appl 37(3):1946–1954
Kumar M, Dass S (2009) A total variation-based algorithm for pixel-level image function. IEEE Trans Image Process 18(9):2137–2143
Lysaker M, Lundervold A, Tai X-C (2003) Noise removal using fourth-order partial differential equation with application to medical magnetic resonance images in space and time. IEEE Trans Image Process 12(12):1579–1590
Lysaker M, Osher S, Tai X-C (2004) Noise removal using smoothed normal and surface fitting. IEEE Trans Image Process 13(10):1345–1357
Mairal J, Elad M, Sapiro G (2008) Sparse representation for color image restoration. IEEE Trans Image Process 17(1):53–69
Mittal A, Moorthy AK, Bovik AC (2012) No-reference image quality assessment in the spatial domain. IEEE Trans Image Process 21(12):4695–4708
Monteil J, Beghdadi A (1998) A new adaptive nonlinear anisotropic diffusion for noise smoothing. In: IEEE International conference on image processing, vol. 3. Chicago Oct 1998, pp 254–258
Pargas RP, Jain R (1993) A parallel algorithm for solving 2D bin packing problems. In: ICNN, pp 18–25
Perona P, Malik J (1987) Scale space and edge detection using anisotropic diffusion. In: Proc. of IEEE Computer society workshop on Computer Vision, pp. 16–22 (November 1987)
Portilla J, Strela V, Wainwright MJ, Simoncelli EP (2013) Image denoising using scale mixtures of gaussians in the wavelet domain. IEEE Trans Image Process 12(11):1338–1351
Prasath VBS, Vorotnikov D (2014) Weighted and well-balanced anisotropic diffusion scheme for image denoising and restoration. Nonlinear Anal Real World Appl 17:33–46
Ram I, Elad M, Cohen I (2011) Generalized tree-based wavelet transform. IEEE Trans Signal Process 59(9):4199–4209
Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phisica D: Nonlinear Phenomena 60(1):259–268
Russo F (2003) A method for estimation and filtering of Gaussian noise in images. IEEE Trans Instrum Meas 52(4):1148–1154
Russo F (2004) Image filtering based on piecewise linear models. In: IEEE International Workshop IST, Stresa, Italy, May 2004, pp 7–12
Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in Computational geometry, fluid mechanics, Computer Vision and Materials Sciences. Cambridge University Press
Toledo CFM, de Oliveira L, da Silva RD, Pedrini H (2013) Image denoising based on genetic algorithm. In IEEE Congress on Evolutionary Computation, pp. 1294–1301
Tukey JW (1974) Nonlinear methods for smoothing data. In: Conf. Rec. EASCON`74, 1974, pp 673
Weickert J (1998) Anisotropic diffusion in image processing. European consortium for mathematics in industry. B. G. Teubner, Stuttgart
Windyga PS (2001) Fast impulsive noise removal. IEEE Trans Image Process 10(1):173–178
Xu P, Miao Q, Tang X, Zhang J (2014) A denoising algorithm via wiener filtering in the shearlet domain. Multimedia Tools and Applications 71(3):1529–1558
Yahya AA, Tan JQ, Hu M (2014) A blending method based on partial differential equations for image denoising. Multimedia Tools and Applications 73(3):1843–1862
Yin X, Zhou S, Abubakar M (2016) Fractional nonlinear anisotropic diffusion with P-Laplace variation method for image restoration. Multimedia Tools and Applications 75(8):4505–4526
Zeng W, Lu X, Tan X (2015) A local structural adaptive partial differential equation for image denoising. Multimedia Tools and Applications 74(3):743–757
Zhang X, Feng X (2015) Image denoising using local adaptive wiener filter in the gradient domain. Multimedia Tools and Applications 74(23):10495–10514
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The authors are grateful to three anonymous referees for their valuable comments which substantially improved the quality of this paper.
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Mohamadi, N., Soheili, A.R. & Toutounian, F. A new hybrid denoising model based on PDEs. Multimed Tools Appl 77, 12057–12072 (2018). https://doi.org/10.1007/s11042-017-4858-8
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DOI: https://doi.org/10.1007/s11042-017-4858-8