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Wavelet inverse scale space for image restoration

Journal of Systems Engineering and Electronics 2012年第6期23卷 929-935页

作者： Binbin Hao Jianguang Zhu School of Science China University of Petroleum Qingdao 266580 E R. China School of Science Shandong University of Science and Technology Qingdao 266590 R R. China

This paper proposes a model for image restoration.by combining the wavelet shrinkage and inverse scale space （ISS） method. The ISS is applied to the wavelet representation to modify the retained wavelet coefficients, and the coefficients smaller than the threshold are set to zero. The curvature term of the ISS can remove the edge artifacts and preserve sharp edges. For the multiscale interpretation of the ISS and the multiscale property of the wavelet representation, small details are preserved. This paper illustrates that the wavelet ISS model can be deduced from the wavelet based on a total variation minimization problem. A stopping criterion is obtained from this minimization in the sense of the Bregman distance in the wavelet domain. Numerical examples show the improvement for the image denoising with the proposed method in the sense of the signal to noise ratio and with fewer details remained in the residue.

关键词： wavelet shrinkage inverse scale space (ISS) curva-ture term total variation minimization image restoration.

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Iterative Lavrentiev regularization for symmetric kernel-driven operator equations: with application to digital image restoration.problems

引用

Science in China(Series F) 2005年第4期48卷 467-483页

作者： WANGYanfei GUXingfa YUTao FANShufang InstituteofRemoteSensingApplications ChineseAcademyofSciencesBeijing100101China//DepartmentofMathematicsUniversityofCenterFloridaFL32816USA InstituteofRemoteSensingApplications ChineseAcademyofSciencesBeijing100101China//INRA-UnitèdeBioclimatologie84914AvignonFrance InstituteofRemoteSensingApplications ChineseAcademyofSciencesBeijing100101China DepartmentofMathematics BeijingNormalUniversityBeijing100875China

The symmetric kernel-driven operator equations play an important role in mathematical physics, engineering, atmospheric image processing and remote sensing sciences. Such problems are usually ill-posed in the sense that even if a unique solution exists, the solution need not depend continuously on the input data. One common technique to overcome the difficulty is applying the Tikhonov regularization to the symmetric kernel operator equations, which is more generally called the Lavrentiev regularization. It has been shown that the iterative implementation of the Tikhonov regularization can improve the rate of convergence. Therefore in this paper, we study the iterative Lavrentiev regularization method in a similar way when applying it to symmetric kernel problems which appears frequently in applications, say digital image restoration.problems. We first prove the convergence property, and then under the widely used Morozov discrepancy principle(MDP), we prove the regularity of the method. Numerical performance for digital image restoration.is included to confirm the theory. It seems that the iterated Lavrentiev regularization with the MDP strategy is appropriate for solving symmetric kernel problems.

关键词： Lavrentiev regularization iterative implementation discrepancy principle image restoration.

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