Total curvature (TC) model and its alternating direction method of multipliers algorithm for noise removal

Abstract

This paper develops a variational model for image noise removal using total curvature (TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation (TV) and total Laplace (TL) model.

References

[1] ZhuS M, SongQ H, XiangZ G, PingT S, GuangJ. Optoelectronics Letters, 2018, 14: 226

[2] ZhiyuanZ, XinL, ZihengZ, XiaohuaH, JingangS, ZhenhongS, LanT, YechaoB, QiongW, XingganZ. Image Denoising via group Sparsity Residual Constraint, 2017,

[3] Zhang K., Zuo W., Chen Y., Meng D. and Zhang L., IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society PP, 1 (2017).

[4] AntoniB. Coll Bartomeu and Morel Jean Michel. Siam Journal on Multiscale Modeling & Simulation, 2006, 4: 490

[5] LingS, RuomeiY, XuelongL, LiuY. IEEE Transactions on Cybernetics, 2014, 44: 1001

[6] VegaM, MateosJ, MolinaR, Katsaggelos AggelosK. Statistical Methodology, 2016, 9: 19

[7] Jordan MichaelI, GhahramaniZ, Jaakkola TommiS, Saul LawrenceK. Machine Learning, 1999, 37: 183

[8] PardoE, KapolkaM. Journal of Computational Physics, 2017, 344: 339

[9] XiangliN, HongQ, BoZ, XiayuanH. IEEE Transactions on Image Processing, 2016, 25: 2620

[10] GillesA, PierreK. Applied Intelligence, 2006, 40: 291

[11] Bardeji SomayehGh, Figueiredo IsabelN, ErciliaS. Applied Numerical Mathematics, 2017, 114: 188

[12] YangL, ChuanjiangH, YongfeiW. Digital Signal Processing, 2018, 78: 42

[13] Rudin LeonidI, OsherS, FatemiE, PhysicaD. Nonlinear Phenomena, 1992, 60: 259

[14] AntoninC, ThomasP. Mathematical Programming, 2016, 159: 253

[15] Raymond HC, HaixiaL, SuhuaW, MilaN, ChengT X. Inverse Problems & Imaging, 2015, 9: 55

[16] JunL, ZhuH T, GuangL X, SiW. Applied Mathematical Modelling, 2017, 45: 516

[17] JinmingD, Ward WilO C, LukeS, ZhenkuanP, LiB. Digital Signal Processing, 2017, 69: 323

[18] YouY L, KavehM. IEEE Transactions on Image Processing: A Publication of the IEEE Signal Processing Society, 2000, 9: 1723

[19] De ReyesJ C L, SchönliebC B, ValkonenT. Journal of Mathematical Imaging & Vision, 2017, 57: 1

[20] HinterbergerW, ScherzerO. Computing, 2006, 76: 109

[21] JinmingD, ZhaowenQ, WenqiL, GuodongW, ZhenkuanP, LiB. Digital Signal Processing, 2016, 49: 162

[22] Prasath V. BS, KalavathiP. Mixed Noise Removal Using Hybrid Fourth Order Mean Curvature Motion, Springer International Publishing, 2016,

[23] WeiZ, ChengT X, TonyC. Inverse Problems & Imaging, 2017, 7: 1409

[24] MarkN, DavidM. The 2.1-D Sketch, International Conference on Computer Vision, 1990,

[25] WenqiL, JinmingD, ZhaowenQ, ZhenkuanP, WenL R, LiB. Mathematical Methods in the Applied Sciences, 2016, 39: 4208

[26] AlainH, DjemelZ. Image Quality Metrics: PSNR vs. SSIM, International Conference on Pattern Recognition, 2010,