基于噪声与图像同步迭代来确定时间步进法的规整化参数

刘鹏; 刘定生; 李国庆

doi:10.3724/SP.J.1146.2008.00582

基于噪声与图像同步迭代来确定时间步进法的规整化参数

doi: 10.3724/SP.J.1146.2008.00582

基金项目:

国家863计划项目资助课题

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出版历程
- 收稿日期: 2008-05-14
- 修回日期: 2009-01-15
- 刊出日期: 2009-07-19

Selecting Regularization Parameter in Time Marching Method Based on the Synchronous Iteration of Noise and Image

摘要

摘要: 为了在反卷积过程中正确地估计噪声的方差，该文构造一幅纯噪声图像跟实际的观测图像同步进行反卷积计算，并把纯噪声图像的方差作为观测图像中噪声方差的估计值来辅助计算规整化参数。针对规整化的各项异性，该文提出了能够保持两种噪声同步变化的特殊的规整化项。新的规整化项在迭代纯粹噪声图像时使用，这样确保每次迭代都可以保持人工噪声与实际图像噪声的统计特性相一致。在能够准确知道迭代过程中图像包含噪声的方差的时候，该文建立了规整化参数与图像噪声方差之间的关系式并转化成简单的解一元二次方程问题。实验证明新的算法不但更好地抑制了噪声而且避免了过平滑，基于时间步进法计算变分图像恢复的适应性被明显的提高了。
- 图像恢复;规整化参数;变分法
Abstract: In order to correctly estimate the variance of noise in iteration, a pure synthesis noise as an image is synchronously iterated with the observation image in de-convolution, and it takes variance of pure noise image as the estimation of the variance of noise in observation image and computes the regularization parameter by the variance. A novel regularization term that can ensure the synchronous changing of the variance of the two noises is proposed in this article. The new regularization term is put into use only in iteration of pure noise image. Under the condition of knowing the variance of noise of image in iteration, this paper established the relationship between the variance of synthetic noise and the regularization parameter, and the relationship was converted to a simple quadratic equation. Experiments confirm that the new algorithm not only better restrains the noise but also avoids the over smoothing. The adaptability of total variation based image restoration is improved.

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Rudin L, Osher S, and Fatemi E. Nonlinear total variationbased noise removal algorithms[J].Physica D.1992, 60(1-4):259-268[2]Vogel C R and Oman M E. Fast, robust total variation-basedreconstruction of noisy, blurred images[J].IEEE Transactionson Image Processing.1998, 7(6):813-824[3]Chan Tony F, Golub Gene H, and Mulet Pep. A nonlinearprimal-dual method for total variation-based imagerestoration[R]. UCLA Math Department CAM Report, 1995.[4]Bouman C and Sauer K. A generalized Gaussian image modelfor edge-preserving MAP estimation[J].IEEE Transactionson Image Processing.1993, 2(3):296-310[5]Charbonnier P, Blanc-Fraud L, Aubert G, and Barlaud M.Deterministic edge-preserving regularization in computerimaging[J].IEEE Transactions on Image Process.1997, 6(2):298-311[6]Perona P and Malik J. Scale space and edge detection usinganisotropic diffusion[J].IEEE Transactions on PatternAnalysis and Machine Intelligence.1990, 12(7):629-639[7]Teboul S, Blanc-Feraud L, Aubert G, and Barlaud M.Variational approach for edge-preserving regularization usingcoupled PDE's[J].IEEE Transactions on Image Processing.1998, 7(3):387-397[8]Chan T F and Wong C K. Total variation blinddeconvolution[J].IEEE Transactions on Image Processing.1998, 7(3):370-375[9]Gilboa G, Sochen N, and Zeevi Y Y. Estimation of optimalPDE-based denoising in the SNR sense[J].IEEETransactions on Image Processing.2006, 15(8):2269-2280[10]Gilboa G, Sochen N, and Zeevi Y Y. Variational denoising ofpartly-textured images by spatially varying constraints[J].IEEE Transactions on Image Processing.2006, 15(8):2281-2289[11]Mrazek P. Selection of optimal stopping time for nonlineardiffusion filtering[J]. International Journal of ComputerVision, 2003, 52(2/3): 189-203.[12]Golub G H, Heath M, and Wahba G. Generalizedcross-validation as a method for choosing a good ridgeparameter [J].Technometrics.1979, 21(2):215-223[13]Craven P and Wahba G. Smoothing noisy data with splinefunctions-estimating the correct degree of smoothing by themethod of generalized cross validation[J]. NumerischeMathematik, 1979, 31(4): 377-403.[14]Hansen P C and O'Leary D P. The use of the L-curve in theregularization of discrete ill posed problems[J].SIAM Journalof Science Computing.1993, 14(6):1487-1503[15]Hansen P C. Analysis of discrete ill-posed problems by meansof the L-curve[J].SIAM Review archive.1992, 34(4):561-580[16]Archer G and Titterington D. On some bayesianregularization methods for image restoration[J].IEEETransactions on on Image Processing.1995, 4(7):989-995[17]Galatsanos N and Katsaggelos A. Methods for choosing theregularization parameter and estimating the noise variance inimage restoration and their relation[J].IEEE Transactions onon Image Processing.1992, 1(3):322-336[18]Galatsanos N, Mesarovic V, Molina R, Mateos J, andKatsaggelos A. Hyper-parameter estimation using gammahyper-priors in image restoration from partially-knownblurs[J].Optical Engineering.2002, 41(8):1845-1854[19]Molina R, Katsaggelos A, and Mateos J. Bayesian andregularization methods for hyperparameter estimation inimage restoration[J].IEEE Transactions on Image Processing.1999, 8(2):231-246[20]Deng G. Iterative learning algorithms for linear Gaussianobservation models[J].IEEE Transactions on on SignalProcessing.2004, 52(8):2286-2297[21]Morozov V A. On the solution of functional equations by themethod of regularization[J]. Soviet Math. Dokl, 1966, 7(1):414-417.

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