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A denoising algorithm via wiener filtering in the shearlet domain

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Abstract

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.

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Acknowledgments

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).

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Authors and Affiliations

  1. School of Computer, Xidian University, Xi’an, 710071, Shaanxi, China

    Pengfei Xu, Qiguang Miao, Xing Tang & Junying Zhang

Authors
  1. Pengfei Xu
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  2. Qiguang Miao
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  3. Xing Tang
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Corresponding author

Correspondence to Qiguang Miao.

Appendix

Appendix

The additional test images:

Fig. 11
figure 11

The additional test images and their corresponding noisy images with σ = 50

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Fig. 12
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The PSNR performance analysis of different methods

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The results and the local enlarged images acquired by different methods

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Fig. 14
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The results and the local enlarged images acquired by STWN and STTD

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Fig. 15
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The PSNR performance analysis of STWN and STTD

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Table 4 The comparison of performances between the proposed algorithm and the denoising methods in other domains
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Table 5 The comparison of performances between STWN and STTD
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Xu, P., Miao, Q., Tang, X. et al. A denoising algorithm via wiener filtering in the shearlet domain. Multimed Tools Appl 71, 1529–1558 (2014). https://doi.org/10.1007/s11042-012-1290-y

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  • DOI: https://doi.org/10.1007/s11042-012-1290-y

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