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紧框架域混合正则化模型在图像恢复中的应用

DOI: 10.11834/jig.20151202

Keywords: 紧框架域,混合正则化模型,交替方向迭代算法,图像恢复

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Abstract:

目的有界变差函数容易造成恢复图像纹理信息丢失,并产生虚假边缘,为克服此缺点,在紧框架域,提出一种保护图像纹理信息,抑制虚假边缘产生的混合正则化模型,并推导出交替方向迭代乘子算法。方法首先,在紧框架域,对系统和泊松噪声模糊的图像,用Kullback-Leibler函数作为拟合项,用有界变差函数半范数和L1范数组成混合正则项,二者加权组成能量泛函正则化模型。其次,分析混合正则化模型解的存在性和唯一性。再次,通过引入辅助变量,利用交替方向迭代乘子算法,将混合正则化模型最小化问题分解为4个容易处理的子问题。最后,子问题交替迭代形成有效的优化算法。结果紧框架域混合正则化模型有效地克服有界变差函数容易导致纹理信息丢失、产生虚假边缘的不足。相对经典算法,本文算法提高峰值信噪比大约0.10.7dB。结论与其他图像恢复正则化模型相比,本文算法有利于保护图像的纹理,抑制虚假边缘,取得较高的峰值信噪比和结构相似测度,适用于恢复系统和泊松噪声模糊的图像。

References

[1]  Landi G, Piccolomini E L. NPTool:a matlab software for nonnegative image restoration with Newton projection methods[J]. Numerical Algorithm, 2013, 62(3):487-504.
[2]  Li X C. Expectation maximization method for parameter estimation of image statistical model[J]. Journal of Image and Graphics, 2012, 17(6):619-629.[李旭超.图像统计模型参数估计中的期望最大值算法[J].中国图象图形学报, 2012, 17(6):619-629.] [DOI:10.11834/jig.20120602]
[3]  Alex S, Christoph B, Thomas K, et al. EM-TV methods for iverse problems with Poisson noise[J]. Level Set and PDE based reconstruction methods in imaging, 2013, 2090(8):71-142.
[4]  Beck A, Teboulle M. A fast dual proximal gradient algorithm for convex minimization and applications[J]. Operations Research Letters, 2014, 42(1):1-6.
[5]  Bonettini S, Ruggiero V. An alternating extragradient method for total variation based image restoration from Poisson data[J]. Inverse Problems, 2011, 27(9):1-28.
[6]  Hao Y, Xu J L. An effective dual method for multiplicative noise removal[J]. Journal of Visual Communication & Image Representation, 2014, 25(2):306-312.
[7]  Liu X W,Huang L H,Guo Z Y. Adaptive fourth order partial differential equation filter for image denoising[J]. Applied Mathematics Letters,2011,24(8):1282-1288.
[8]  Cai J F, Ji H, Liu C Q. Framelet-based blind motion deblurring from a single image[J]. IEEE Transactions on Image Processing, 2012, 21(2):562-572.
[9]  Chen X M, Wang H C, Wang R R. A null space analysis of the l1-synthesis method in dictionary-based compressed sensing[J]. Applied and Computational Harmonic Analysis, 2014, 37(3):492-515.
[10]  Cai J F, Dong B, Osher Stanley, et al. Image restoration:total variation, wavelet frames, and beyond[J]. Journal of the American Mathematical Society, 2012, 25(4):1033-1089.
[11]  Guo Z C, Liu Q, Sun J B, et al. Reaction-diffusion systems with p(x)-growth for image denoising[J]. Nonlinear Analysis:Real World Applications, 2011, 12(5):2904-2918.
[12]  Aubert G, Kornprobst P. Mathematical Problems in Image Processing, Partial Differential Equations and the Calculus of Variations[M]. New York, USA:Springer Verlag, 2006:1-371.
[13]  Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms[J]. Physical D:Nonlinear Phenomena, 1992, 60(1):259-268.
[14]  Boyd S,Vandenberghe L. Convex Optimization[M]. Cambridge, United Kingdom:Cambridge University Press, 2004:1-727.
[15]  Dinh Q T, Cevher V. A primal-dual algorithmic framework for constrained convex minimization[EB/OL].[2015-4-30]. http://arXiv. org/abs/1406.5403.
[16]  Bonettini S, Ruggiero V. On the convergence of primal-dual hybrid gradient algorithms for total variation image restoration[J]. Journal of Mathematical Imaging and Vision, 2012, 44(3):236-253.
[17]  Chambolle A. An algorithm for total variation minimization and applications[J]. Journal of Mathematical Imaging and Vision, 2004, 20(1):89-97.
[18]  Wang Z, Bovik A, Sheikh H, et al. Image quality assessment:from error visibility to structural similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4):1-14.

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