Skip to main content
SpringerLink
Log in

Adaptive sparse coding on PCA dictionary for image denoising

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Sparse coding is a popular technique in image denoising. However, owing to the ill-posedness of denoising problems, it is difficult to obtain an accurate estimation of the true code. To improve denoising performance, we collect the sparse coding errors of a dataset on a principal component analysis dictionary, make an assumption on the probability of errors and derive an energy optimization model for image denoising, called adaptive sparse coding on a principal component analysis dictionary (ASC-PCA). The new method considers two aspects. First, with a PCA dictionary-related observation of the probability distributions of sparse coding errors on different dimensions, the regularization parameter balancing the fidelity term and the nonlocal constraint can be adaptively determined, which is critical for obtaining satisfying results. Furthermore, an intuitive interpretation of the constructed model is discussed. Second, to solve the new model effectively, a filter-based iterative shrinkage algorithm containing the filter-based back-projection and shrinkage stages is proposed. The filter in the back-projection stage plays an important role in solving the model. As demonstrated by extensive experiments, the proposed method performs optimally in terms of both quantitative and visual measurements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. Available at https://users.soe.ucsc.edu/~priyam/PLOW and http://www.pentaxforums.com/reviews/pentax-645z-review/low-light-high-iso.html. We use their grayscale versions.

References

  1. Amer, A., Dubois, E.: Fast and reliable structure-oriented video noise estimation. Circ. Syst. Video Technol. IEEE Trans. 15(1), 113–118 (2005)

    Article  Google Scholar 

  2. Bini, A.A., Bhat, M.S.: A nonlinear level set model for image deblurring and denoising. Vis. Comput. 30(3), 311–325 (2014)

    Article  Google Scholar 

  3. Buades, A., Coll, B., Morel, J.M.: A non-local algorithm for image denoising. In: Computer Vision and Pattern Recognition, vol. 2, pp. 60–65. IEEE (2005)

  4. Chan, T., Esedoglu, S., Park, F., Yip, A.: Recent developments in total variation image restoration. In: Mathematical Models of Computer Vision. Springer (2005)

  5. Chang, S.G., Yu, B., Vetterli, M.: Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Process. 9(9), 1532–1546 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)

    Article  MathSciNet  Google Scholar 

  7. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Bm3d image denoising with shape-adaptive principal component analysis. In: Workshop on signal processing with adaptive sparse structured representations (2009)

  8. Daubechies, I., Defrise, M., DeMol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dong, W., Zhang, L., Shi, G., Li, X.: Nonlocally centralized sparse representation for image restoration. IEEE Trans. Image Process. 22(4), 1620–1630 (2013)

    Article  MathSciNet  Google Scholar 

  10. Dong, W., Zhang, L., Shi, G., Wu, X.: Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans. Image Process. 20(7), 1838–1857 (2011)

    Article  MathSciNet  Google Scholar 

  11. Donoho, D.L., Elad, M.: Optimally sparse representation in general (nonorthogonal) dictionaries via l 1 minimization. Proc. Natl. Acad. Sci. 100(5), 2197–2202 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Donoho, D.L., Johnstone, J.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425–455 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  14. Ignácio, U.A., Jung, C.R.: Block-based image inpainting in the wavelet domain. Vis. Comput. 23(9–11), 733–741 (2007)

    Article  Google Scholar 

  15. Liang, M., Du, J., Liu, H.: Self-adaptive spatial image denoising model based on scale correlation and sure-let in the nonsubsampled contourlet transform domain. Sci. China-Ser. F: Inf. Sci. 57(9), 1–15 (2014)

    Google Scholar 

  16. Liu, W., Lin, W.: Additive white gaussian noise level estimation in svd domain for images. Image Process. IEEE Trans. 22(3), 872–883 (2013)

    Article  MathSciNet  Google Scholar 

  17. Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: International conference on computer vision, pp. 2272–2279. IEEE (2009)

  18. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: International Conference on Computer Vision, vol. 2, pp. 416–423. IEEE (2001)

  19. Muresan, D.D., Parks, T.W.: Adaptive principal components and image denoising. In: International conference on image processing, vol. 1, pp. I-101-4. IEEE (2003)

  20. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)

    Article  Google Scholar 

  21. Rajwade, A., Rangarajan, A., Banerjee, A.: Image denoising using the higher order singular value decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 849–862 (2013)

    Article  Google Scholar 

  22. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenom. 60(1), 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  23. Shi, J., Liu, Z., Tian, J.: Bilateral signal variance estimation for wavelet-domain image denoising. Sci. China-Ser. F: Inf. Sci. 56(6), 1–6 (2013)

    MathSciNet  Google Scholar 

  24. Shin, D.H., Park, R.H., Yang, S., Jung, J.H.: Block-based noise estimation using adaptive gaussian filtering. Consumer Electron. IEEE Trans. 51(1), 218–226 (2005)

    Article  Google Scholar 

  25. Starck, J.L., Candès, E.J., Donoho, D.L.: The curvelet transform for image denoising. IEEE Trans. Image Process. 11(6), 670–684 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Tan, S., Jiao, L.: Multivariate statistical models for image denoising in the wavelet domain. Int. J. Comput. Vis. 75(2), 209–230 (2007)

    Article  Google Scholar 

  27. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: International conference on vomputer vision, pp. 839–846. IEEE (1998)

  28. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  29. Zhang, L., Dong, W., Zhang, D., Shi, G.: Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recognit. 43(4), 1531–1549 (2010)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

We thank all the anonymous reviewers for their helpful suggestions. This work was supported by the National Natural Science Foundation of China (61332015, 61373078, 61272245, 61472220, 61202148) and the NSFC-Guangdong Joint Fund (U1201258).

Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Jinan, 250101, China

    Qian Liu, Caiming Zhang, Qiang Guo, Hui Xu & Yuanfeng Zhou

  2. Shandong Provincial Key Laboratory of Digital Media Technology, Shandong University of Finance and Economics, Jinan, 250014, China

    Caiming Zhang & Qiang Guo

Authors
  1. Qian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Caiming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiang Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuanfeng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Caiming Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Q., Zhang, C., Guo, Q. et al. Adaptive sparse coding on PCA dictionary for image denoising. Vis Comput 32, 535–549 (2016). https://doi.org/10.1007/s00371-015-1087-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-015-1087-x

Keywords

Search

Navigation