An image denoising algorithm via wiener filtering in the shearlet domain is proposed in this paper, it makes full use of the advantages of them. Shearlets have the features of directionality, localization, anisotropy and multiscale, the image can be decomposed more accurately, and the noise information locates at the high frequency contents in the frequency spectrum, which can help the removal of noise. The wiener filtering is based on minimizing the mean square error criteria; and it has a good performance on removing the Gaussian white noise. So the combination between them can remove noise more effectively. The noisy image is decomposed by the shearlet transform at any scales and in any directions firstly, the high and low frequency coefficients are thus acquired. And then, in the shearlet domain, the high frequency parts are filtered by wiener filtering. Finally, the inverse shearlet transform is adopted to obtain the denoised image. At the end of paper, the experiments show that the proposed algorithm could get better results than others.
Image denoising Shearlets Shearlet domain Wiener filtering Minimizing the mean square error criteria Shrinkage factor
This is a preview of subscription content, log in to check access
The authors would like to thank the anonymous reviewers for their helpful comments and advices which contributed much to the improvement of this paper. The work was jointly supported by the National Natural Science Foundations of China under grant No. 61072109, 61272280, 41271447, the Fundamental Research Funds for the Central Universities under grant No. K5051203020 and K5051203001, the Creative Project of the Science and Technology State of xi’an under grant No. CXY1133(1) and CXY1119(6).
Aboshosha A, Hassan M, Ashour M, El Mashade M (2009) Image denoising based on spatial filters, an analytical study. Computer Engineering & Systems, 2009. ICCES 2009. International Conference on. 245–250Google Scholar
Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE transactions on image processing 9(9):1532–1546CrossRefMATHMathSciNetGoogle Scholar
Do MN, Vetterli M (2005) The contourlet transform: An efficient directional multiresolution image representation. IEEE Transaction on Image Processing 14(12):2091–2106CrossRefMathSciNetGoogle Scholar
Lee YW (1960) Statistical Theory of Communication. John Wiley and Sons, Inc., New YorkMATHGoogle Scholar
Liu S-p, Fang Y (2008) Image Denosing Based on Contourlet Transform and Wiener Filter. Comput Eng 34(5):210–212, in ChineseMathSciNetGoogle Scholar
Liu YX, Peng YH, Qu HJ, Yin Y (2007) Energy-based adaptive orthogonal FRIT and its application in image denoising. Science in China Series F: Information Sciences 50(2):212–226CrossRefMATHMathSciNetGoogle Scholar
Liu G, Zeng X, Liu Y (2012) Image denoising by random walk with restart Kernel and non-subsampled contourlet transform. IET Signal Process 6(2):148–158CrossRefMathSciNetGoogle Scholar
Miao Q-g, Shi C, Xu P-f, Yang M, Shi Y-b (2011) A Novel Algorithm of Image Fusion Using Shearlets. Opt Commun 284(6):1540–1547CrossRefGoogle Scholar
Na Deng, Chang-sen Jiang. Selection of Optimal Wavelet Basis for Signal Denoising. 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012). 2012.Google Scholar
Ramin Eslami, Hayder Radha. Translation-Invariant Contourlet Transform and Its Application to Image Denoising. IEEE Transaction on image processing, 15(11), NOV. 2006Google Scholar
Shao-Wei D, Yan-Kui S, Xiao-Lin T, Ze-Sheng T (2007) Image denoising based on complex contourlet transform. Wavelet Analysis and Pattern Recognition, 2007. ICWAPR’07 International Conference on 4:1742–1747Google Scholar