LI Min, XU Chen. Variational Image Restoration and Decomposition in Shearlet Smoothness Spaces[J]. Chinese Journal of Electronics, 2017, 26(5): 1017-1021. doi: 10.1049/cje.2017.08.021
Citation: LI Min, XU Chen. Variational Image Restoration and Decomposition in Shearlet Smoothness Spaces[J]. Chinese Journal of Electronics, 2017, 26(5): 1017-1021. doi: 10.1049/cje.2017.08.021

Variational Image Restoration and Decomposition in Shearlet Smoothness Spaces

doi: 10.1049/cje.2017.08.021
Funds:  This work is supported by the National Natural Science Foundation of China (No.61472257, No.61402290) and Shenzhen Basis Research Project (No.JCYJ20160520161847267).
More Information
  • Corresponding author: XU Chen (corresponding author) was born in Zhejiang Province. He received the B.S. and M.S. degrees in mathematics from Xidian University in 1986 and 1989, the Ph.D. degree in mathematics from Xi'an Jiaotong University in 1992 respectively. He is now a professor at Shenzhen University. His research interests include information and computational science, analysis and application of wavelet. (Email:xuchen
  • Received Date: 2015-09-17
  • Rev Recd Date: 2016-08-11
  • Publish Date: 2017-09-10
  • We present the shearlet-based variational model for image restoration and decomposition. The new model can be seen as generalizations of DaubechiesTeschke's model. By using regularization term in shearlets smoothness spaces, and writing the problem in a shearlet framework, we obtain elegant shearlet shrinkage schemes. Furthermore, the model allows us to incorporate general bounded linear blur operators into the problem. The experiments on denoising, deblurring and decomposition of images show that our algorithm is very efficient.
  • loading
  • L. Rudin, S. Osher and E. Fatemi, "Nonlinear total variation based noise removal algorithms", Phys. D, Vol.60, No.1-4, pp.259-268, 1992.
    Y. Meyer, "Oscillating patterns in image processing and nonlinear evolution equations", University Lecture Series, American Mathematical Society, 2002.
    L.A. Vese and S.J. Osher, "Modeling textures with total variation minimization and oscillating patterns in image processing", J. Sci. Comput., Vol.19, No.1-3, pp.553-572, 2003.
    S. Osher, A. Sole and L. Vese, "AImage decomposition and restoration using total variation minimization and the H-1 norm", Multiscal Model. Simul., Vol.1, No.3, pp.349-370, 2003.
    I. Daubechies and G. Teschke, "Variational image restoration by means of wavelets:Simultaneous decomposition, deblurring and denoising", Appl. Comput. Harmon. Anal., Vol.19, No.391, pp.1-16, 2005.
    L. Lieu and L. Vese,"Image restoration and decompostion via bounded total variation and negative Hilbert-Sobolev spaces", Appl. Math. Optim., Vol.58, pp.167-193, 2008.
    Lingling Jiang, Xiangchu Feng and Haiqing Yin, "Variational image restoration and decomposition with curvelet shrinkage", J. Math. Imaging Vis., Vol.30, No.2, pp.125-132, 2008.
    J. Gilles and Y. Meyer, "Properties of BV -G structures + textures decomposition models. Application to road detection in satellite images", IEEE Trans. Image Process., Vol.19, No.11, pp.2793-2800, 2010.
    M.K. Ng, X. Yuan and W. Zhang, "Coupled variational image decomposition and restoration model for blurred cartoon-plustexture images with missing pixels", IEEE Trans. Image Process., Vol.22, No.6, pp. 2233-2246, 2013.
    Han Yu, Xu Chen, Baciu George, et al., "Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer", International Journal of Computer Mathematics, Vol.91, No.10, pp.2243-2259, 2014.
    D. Labate, L. Mantovani and P. Negi, "Shearlet smoothness spaces", J. Fourier Anal. Appl., Vol.19, pp.577-611, 2013.
    I. Daubechies, M. Defrise and C. De mol, "An iterative thresholding algorithm for linear inverse problem with a sparsity constraint", Communications on Pure and Applied Mathematics, Vol.57, No.11, pp.1413-1457, 2004.
    Li Min, Xu Chen and Sun Xiaoli, "Iterative regularization and nonlinear inverse scale space in curvelet-type decomposition spaces", Chinese Journal of Electronics, Vol.22, No.4, pp.702-706, 2013.
    Jean-Francois Aujol, Gilles Aubert, Laure Blanc-Feraud and Antonin Chambolle, "Image decomposition into a bounded variation component and an oscillating component", Journal of Mathematical Imaging and Vision, Vol.22, No.1, pp.71-88, 2005.
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (148) PDF downloads(370) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint