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Bayesian Anchored Neighborhood Regression for Single-Image Super-Resolution

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Abstract

Anchored neighborhood regression (ANR) single-image super-resolution (SISR) method demonstrates great superiority in speed and performance. However, ridge regression adopted by ANR didn’t take the prior knowledge of regression parameters into account, which easily leads to over-fitting and is not robust to noise. To mitigate this problem, a Bayesian ANR method is proposed for SISR, called B-ANR. B-ANR uses sparse Bayesian regression model to build the mapping relationship between the low resolution (LR) image patch and its neighbors. The parameters of Bayesian regression model as well as its variance are estimated using maximum a posterior. Since our proposed B-ANR is deduced in the probabilistic framework, it has stronger generalization performance and robustness to noise. Experimental results verify that our method is superior to ANR in performance.

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Data Availibility

Both training and test datasets used in research study are openly accessible.

References

  1. H. Chang, D. Y. Yeung, Y. Xiong, Super-resolution through neighbor embedding, in Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR) (2004), pp. 275–282

  2. X. Chen, C. Qi, Nonlinear neighbor embedding for single image super-resolution via kernel mapping. Signal Process. 94, 6–22 (2014)

    Article  Google Scholar 

  3. Y. Chen, Y. Xie, Z. Zhou, F. Shi, A. G. Christodoulou, D. Li, Brain MRI super resolution using 3D deep densely connected neural networks, in 2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI) (2018), pp. 739–742. https://doi.org/10.1109/ISBI.2018.8363679

  4. C. Dong, C.C. Loy, K. He, X.O. Tang, Image super-resolution using deep convolutional networks. IEEE Trans. Pattern Anal. Mach. Intell. 38(2), 295–307 (2016). https://doi.org/10.1109/TPAMI.2015.2439281

    Article  Google Scholar 

  5. C. Dong, C. C. Loy, X. O. Tang, Accelerating the super-resolution convolutional neural network, in Computer Vision–ECCV 2016: 14th European Conference (Amsterdam, The Netherlands, 2016b), pp. 391–407

  6. W.S. Dong, L. Zhang, G.M. Shi, X. Li, Nonlocally centralized sparse representation for image restoration. IEEE Trans. Image Process. 22(4), 1620–1630 (2013). https://doi.org/10.1109/TIP.2012.2235847

    Article  MathSciNet  Google Scholar 

  7. A. Esmaeilzehi, M.O. Ahmad, M. Swamy, Compnet: a new scheme for single image super resolution based on deep convolutional neural network. IEEE Access 6, 59963–59974 (2018). https://doi.org/10.1109/ACCESS.2018.2874442

    Article  Google Scholar 

  8. A. Esmaeilzehi, M. O. Ahmad, M. Swamy, DSEGAN: a deep light-weight segmentation-based attention network for image restoration, in 2022 IEEE International Symposium on Circuits and Systems (ISCAS) (2022), pp. 1284–1288. https://doi.org/10.1109/ISCAS48785.2022.9937894

  9. A. Esmaeilzehi, M.O. Ahmad, M. Swamy, Ultralight-weight three-prior convolutional neural network for single image super resolution. IEEE Trans. Artif. Intell. 4(6), 1724–1738 (2023). https://doi.org/10.1109/TAI.2022.3224417

    Article  Google Scholar 

  10. A. Faul, M. Tipping, Analysis of sparse Bayesian learning, in Advances in Neural Information Processing Systems (2001), pp. 383–389

  11. W. Freeman, T. Jones, E. Pasztor, Example-based super-resolution. IEEE Comput. Graph. Appl. 22(2), 56–65 (2002). https://doi.org/10.1109/38.988747

    Article  Google Scholar 

  12. X.B. Gao, K.B. Zhang, D.C. Tao, X.L. Li, Image super-resolution with sparse neighbor embedding. IEEE Trans. Image Process. 21(7), 3194–3205 (2012). https://doi.org/10.1109/TIP.2012.2190080

    Article  MathSciNet  Google Scholar 

  13. H. He, W. C. Siu, Single image super-resolution using Gaussian process regression, in CVPR 2011 (2011), pp. 449–456. https://doi.org/10.1109/CVPR.2011.5995713

  14. L. He, H. Qi, R. Zaretzki, Non-parametric Bayesian dictionary learning for image super resolution, in 2011 Future of Instrumentation International Workshop (FIIW) Proceedings (2011), pp. 122–125. https://doi.org/10.1109/FIIW.2011.6476831

  15. H.S. Hou, H.C. Andrews, Cubic splines for image interpolation and digital filtering. IEEE Trans. Acoust. Speech Signal Process. 26(6), 508–517 (1978)

    Article  Google Scholar 

  16. Z. L. Hu, T. Li, Y. F. Yang, X. Liu, H. R. Zhang, D. Liang, Super-resolution pet image reconstruction with sparse representation, in 2017 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (2017), pp. 1–3. https://doi.org/10.1109/NSSMIC.2017.8532893

  17. J.J. Jiang, X. Ma, C. Chen, T. Lu, Z.Y. Wang, J.Y. Ma, Single image super-resolution via locally regularized anchored neighborhood regression and nonlocal means. IEEE Trans. Multimed. 19(1), 15–26 (2017)

    Article  Google Scholar 

  18. K.I. Kim, Y. Kwon, Single-image super-resolution using sparse regression and natural image prior. IEEE Trans. Pattern Anal. Mach. Intell. 32(6), 1127–1133 (2010). https://doi.org/10.1109/TPAMI.2010.25

    Article  Google Scholar 

  19. F. Kong, M. X. Li, S. W. Liu, D. Liu, J. W. He, Y. Bai, F. G. Chen, L. Fu, Residual local feature network for efficient super-resolution, in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2022), pp. 765–775

  20. Z. Lei, X. Wu, An edge-guided image interpolation algorithm via directional filtering and data fusion. IEEE Trans. Image Process. 15(8), 2226–2238 (2006)

    Article  Google Scholar 

  21. B. Li, H. Chang, S. G. Shan, X. L. Chen, Locality preserving constraints for super-resolution with neighbor embedding, in 2009 16th IEEE International Conference on Image Processing (ICIP) (2009), pp. 1189–1192. https://doi.org/10.1109/ICIP.2009.5413691

  22. J. M. Li, Y. Y. Qu, Y. Gu, T. Z. Fang, C. H. Li, Super-resolution based on fast linear kernel regression, in 2013 International Conference on Machine Learning and Cybernetics (2013), pp. 333–339. https://doi.org/10.1109/ICMLC.2013.6890490

  23. M. Li, T.Q. Nguyen, Markov random field model-based edge-directed image interpolation. IEEE Trans. Image Process. 17(7), 1121–1128 (2008). https://doi.org/10.1109/TIP.2008.924289

    Article  MathSciNet  Google Scholar 

  24. Z. Li, W.J. Leong, M. Durand, I. Howat, K. Wadkowski, B. Yadav, J. Moortgat, Super-resolution deep neural networks for water classification from free multispectral satellite imagery. J. Hydrol. 626, 130248 (2023)

    Article  Google Scholar 

  25. Y. Ogawa, T. Hori, T. Takiguchi, Y. Ariki, Super-resolution using GMM and PLS regression, in 2012 IEEE International Symposium on Multimedia (2012), pp. 298–301. https://doi.org/10.1109/ISM.2012.62

  26. M. E. Philip, G. S. Kumar, An improved color video super-resolution using kernel regression and fuzzy enhancement, in 2012 International Conference on Advances in Computing and Communications (2012), pp. 114–117. https://doi.org/10.1109/ICACC.2012.25

  27. H.P. Song, H. Ma, Y.X. Si, J.Y. Gong, H.Y. Meng, Y.P. Lai, Back projection deep unrolling network for handwritten text image super resolution. Comput. Electr. Eng. 111, 108965 (2023)

    Article  Google Scholar 

  28. Y. Tang, Z. Jiang, J. H. Chen, Single-image super-resolution via multiple matrix-valued kernel regression, in 2019 International Conference on Machine Learning and Cybernetics (ICMLC) (2019), pp. 1–7. https://doi.org/10.1109/ICMLC48188.2019.8949261

  29. Y. Tang, T. Wang, D. Liu, MFFAGAN: generative adversarial network with multilevel feature fusion attention mechanism for remote sensing image super-resolution. IEEE J-STARS. 17, 6860–6874 (2024)

    Google Scholar 

  30. C.W. Tian, R.B. Zhuge, Z.H. Wu, Y. Xu, W.M. Zuo, C. Chen, C.W. Lin, Lightweight image super-resolution with enhanced CNN. Know-Based Syst. 205, 106235 (2020)

    Article  Google Scholar 

  31. R. Timofte, V. De Smet, L. Van Gool, Anchored neighborhood regression for fast example-based super-resolution, in Proceedings of the IEEE International Conference on Computer Vision (2013), pp. 1920–1927

  32. M.E. Tipping, Sparse Bayesian learning and the relevance vector machine. J. Mach. Learn. Res. 1, 211–244 (2001)

    MathSciNet  Google Scholar 

  33. M. E. Tipping, A. C. Faul, Fast marginal likelihood maximisation for sparse Bayesian models, in International Workshop on Artificial Intelligence and Statistics (2003), pp. 276–283

  34. Y.F. Wang, L.J. Wang, H.Y. Wang, P.H. Li, End-to-end image super-resolution via deep and shallow convolutional networks. IEEE Access 7, 31959–31970 (2019). https://doi.org/10.1109/ACCESS.2019.2903582

    Article  Google Scholar 

  35. L. Xin, M.T. Orchard, New edge-directed interpolation. IEEE Trans. Image Process. 10(10), 1521–1527 (2001)

    Article  Google Scholar 

  36. J.C. Yang, J. Wright, T.S. Huang, Y. Ma, Image super-resolution via sparse representation. IEEE Trans. Image Process. 19(11), 2861–2873 (2010)

    Article  MathSciNet  Google Scholar 

  37. J. Yang, Z. Wang, Z. Lin, S. Cohen, T. Huang, Coupled dictionary training for image super-resolution. IEEE Trans. Image Process. 21(8), 3467–3478 (2012). https://doi.org/10.1109/TIP.2012.2192127

    Article  MathSciNet  Google Scholar 

  38. W.S. Yu, S.Q. Chen, An improved neighbor embedding method to super-resolution reconstruction of a single image. Proc. Eng. 15, 2418–2422 (2011)

    Article  Google Scholar 

  39. R. Zeyde, M. Elad, M. Protter, On single image scale-up using sparse-representations, in Curves and Surfaces (Springer, 2012), pp. 711–730

  40. Y. Zhang, K. Gu, Zhang, J. Zhang, Q. Dai, Image super-resolution based on dictionary learning and anchored neighborhood regression with mutual incoherence, in 2015 IEEE International Conference on Image Processing (ICIP) (2015), pp. 591–595. https://doi.org/10.1109/ICIP.2015.7350867

  41. Y. Zhang, Y. Zhang, J. Zhang, Q. Dai, Ccr: clustering and collaborative representation for fast single image super-resolution. IEEE Trans. Multimed. 18(3), 405–417 (2016). https://doi.org/10.1109/TMM.2015.2512046

    Article  Google Scholar 

  42. Y. Zhang, Y. Zhang, J. Zhang, X. Dong, F. Yun, Y. Wang, X. Ji, Q. Dai, Collaborative representation cascade for single-image super-resolution. IEEE Trans. Syst. Man Cybern. 49(5), 845–860 (2019). https://doi.org/10.1109/TSMC.2017.2705480

    Article  Google Scholar 

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Acknowledgements

This work was partly supported by the Provincial Key Laboratory Performance Subsidy Project (22567612H) and Medicine-Engineering Interdisciplinary Special Cultivation Project (UH202208).

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Authors and Affiliations

  1. School of Electrical Engineering, Yanshan University, The Westward Direction of Hebei Street, Qinhuangdao, 438, Hebei Province, China

    Yinggan Tang & Ailian Fan

  2. Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, The Westward Direction of Hebei Street, Qinhuangdao, 438, Hebei Province, China

    Yinggan Tang

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Tang, Y., Fan, A. Bayesian Anchored Neighborhood Regression for Single-Image Super-Resolution. Circuits Syst Signal Process (2024). https://doi.org/10.1007/s00034-024-02720-3

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