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Image super-resolution by learning weighted convolutional sparse coding

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Abstract

Single image super-resolution (SISR) has witnessed substantial progress recently by deep learning-based methods, due to the data-driven end-to-end training. However, most existing DL-based models are built intuitively, with little thought on priors. And the lack of interpretability limits their further improvements. To avoid this, this paper presents an end-to-end trainable unfolding network which leverages both DL- and prior-based methods. Specifically, we introduce the reweighted algorithm into CSC model and solve it by learning weighted iterative soft thresholding algorithm in a convolutional manner. Based on this, we present a SISR model by learning weighted convolutional sparse coding, in which the channel attention is resorted to learn the weight. Extensive experiments demonstrate the superiority of our method to recent state-of-the-art SISR methods, in terms of both quantitative and qualitative results.

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References

  1. Agustsson, E., Timofte, R.: NTIRE 2017 challenge on single image super-resolution: Dataset and study. In: CVPRW, pp. 126–135 (2017)

  2. Bevilacqua, M., Roumy, A., Guillemot, C., Alberi-Morel, M.L.: Low-complexity single-image super-resolution based on nonnegative neighbor embedding. In: BMVC (2012)

  3. Cai, J., Gu, S., Timofte, R., Zhang, L.: Ntire 2019 challenge on real image super-resolution: methods and results. In: CVPRW (2019)

  4. Cai, J., Zeng, H., Yong, H., Cao, Z., Zhang, L.: Toward real-world single image super-resolution: a new benchmark and a new model. In: ICCV (2019)

  5. Candes, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted \(\ell _{1}\) minimization. J. Fourier Anal. Appl. 14(5–6), 877–905 (2008)

    Article  MathSciNet  Google Scholar 

  6. Chartrand, R.: Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process. Lett. 14(10), 707–710 (2007)

    Article  Google Scholar 

  7. Dai, S., Han, M., Xu, W., Wu, Y., Gong, Y.: Soft edge smoothness prior for alpha channel super resolution. CVPR 7, 1–8 (2007)

    Google Scholar 

  8. Dai, T., Cai, J., Zhang, Y.B., Xia, S., Zhang, L.: Second-order attention network for single image super-resolution. In: CVPR, pp. 11057–11066 (2019)

  9. Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. A J. Issued Courant Inst. Math. Sci. 57(11), 1413–1457 (2004)

    Article  MathSciNet  Google Scholar 

  10. Dong, C., Loy, C.C., He, K., Tang, X.: Image super-resolution using deep convolutional networks. TPAMI 38, 295–307 (2016)

    Article  Google Scholar 

  11. Dong, W., Wang, P., Yin, W., Shi, G., Wu, F., Lu, X.: Denoising prior driven deep neural network for image restoration. TPAMI 41, 2305–2318 (2019)

    Article  Google Scholar 

  12. Donoho, D.L., et al.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  13. Foucart, S., Lai, M.J.: Sparsest solutions of underdetermined linear systems via \(\ell _{q}\)-minimization for 0\(<\)q\(\le \)1. Appl. Comput. Harmon. Anal. 26(3), 395–407 (2009)

    Article  MathSciNet  Google Scholar 

  14. Fu, X., Zha, Z., Wu, F., Ding, X., Paisley, J.W.: Jpeg artifacts reduction via deep convolutional sparse coding. In: ICCV, pp. 2501–2510 (2019)

  15. Gregor, K., LeCun, Y.: Learning fast approximations of sparse coding. In: ICML (2010)

  16. Guo, Z., Chen, Z., Yu, T., Chen, J., Liu, S.: Progressive image inpainting with full-resolution residual network. In: ACM multimedia, pp. 2496–2504 (2019)

  17. Haris, M., Shakhnarovich, G., Ukita, N.: Deep back-projection networks for super-resolution. In: CVPR (2018)

  18. He, K., Zhang, X., Ren, S., Sun, J.: Delving deep into rectifiers: surpassing human-level performance on ImageNet classification. In: ICCV, pp. 1026–1034 (2015)

  19. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: CVPR, pp. 770–778 (2016)

  20. Hu, J., Shen, L., Sun, G.: Squeeze-and-excitation networks. In: CVPR, pp. 7132–7141 (2018)

  21. Huang, J.B., Singh, A., Ahuja, N.: Single image super-resolution from transformed self-exemplars. In: CVPR, pp. 5197–5206 (2015)

  22. Kim, J., Lee, J.K., Lee, K.M.: Accurate image super-resolution using very deep convolutional networks. In: CVPR, pp. 1646–1654 (2016)

  23. Kim, J., Lee, J.K., Lee, K.M.: Deeply-recursive convolutional network for image super-resolution. In: CVPR, pp. 1637–1645 (2016)

  24. Ledig, C., Theis, L., et al.: Photo-realistic single image super-resolution using a generative adversarial network. In: CVPR (2016)

  25. Lim, B., Son, S., Kim, H., Nah, S., Lee, K.M.: Enhanced deep residual networks for single image super-resolution. In: CVPRW, pp. 1132–1140 (2017)

  26. Liu, R., Cheng, S., He, Y., Fan, X., Lin, Z., Luo, Z.: On the convergence of learning-based iterative methods for nonconvex inverse problems. In: TPAMI (2019)

  27. Liu, Z., Yu, L., Sun, H.: Image denoising via nonlocal low rank approximation with local structure preserving. IEEE Access 7, 7117–7132 (2019)

    Article  Google Scholar 

  28. Lyu, Q., Lin, Z., She, Y., Zhang, C.: A comparison of typical \(\ell _{p}\) minimization algorithms. Neurocomputing 119, 413–424 (2013)

    Article  Google Scholar 

  29. Mairal, J., Bach, F.R., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: ICCV, pp. 2272–2279 (2009)

  30. Martin, D.R., Fowlkes, C.C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: ICCV (2001)

  31. Papyan, V., Romano, Y., Elad, M.: Convolutional neural networks analyzed via convolutional sparse coding. J. Mach. Learn. Res. 18, 83:1–83:52 (2017)

    MathSciNet  MATH  Google Scholar 

  32. Pérez-Pellitero, E., Salvador, J., Hidalgo, J.R., Rosenhahn, B.: PSyCo: manifold span reduction for super resolution. In: CVPR, pp. 1837–1845 (2016)

  33. Peyré, G., Bougleux, S., Cohen, L.: Non-local regularization of inverse problems. In: ECCV (2008)

  34. Rabaud, V., Belongie, S.: Big little icons. In: CVPRW, p. 24 (2005)

  35. Simon, D., Elad, M.: Rethinking the csc model for natural images. In: NeurIPS (2019)

  36. Sreter, H., Giryes, R.: Learned convolutional sparse coding. In: ICASSP, pp. 2191–2195 (2018)

  37. Tai, Y., Yang, J., Liu, X.: Image super-resolution via deep recursive residual network. In: CVPR, pp. 2790–2798 (2017)

  38. Tai, Y., Yang, J.X., Liu, X., Xu, C.: MemNet: a persistent memory network for image restoration. In: ICCV, pp. 4549–4557 (2017)

  39. Wang, F., Jiang, M., Qian, C., Yang, S., Li, C.C., Zhang, H., Wang, X., Tang, X.: Residual attention network for image classification. In: CVPR, pp. 6450–6458 (2017)

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

    Google Scholar 

  41. Wang, Z., Liu, D., Yang, J., Han, W., Huang, T.: Deep networks for image super-resolution with sparse prior. In: ICCV, pp. 370–378 (2015)

  42. Xie, C., Liu, Y., Zeng, W., Lu, X.: An improved method for single image super-resolution based on deep learning. SIVP 13(3), 557–565 (2019)

    Google Scholar 

  43. Xie, Z., Hu, J.: Rewighted \(\ell _{1}\)-minimization for sparse solutions to underdetermined linear systems. In: CISP, vol. 3, pp. 1660–1664. IEEE (2013)

  44. Yang, J., Wright, J.N., Huang, T.S., Ma, Y.: Image super-resolution via sparse representation. TIP 19, 2861–2873 (2010)

    MathSciNet  MATH  Google Scholar 

  45. Zeiler, M.D., Krishnan, D., Taylor, G.W., Fergus, R.: Deconvolutional networks. In: CVPR, pp. 2528–2535 (2010)

  46. Zeyde, R., Elad, M., Protter, M.: On single image scale-up using sparse-representations. In: Curves and Surfaces (2010)

  47. Zha, Z., Liu, X., Huang, X., Shi, H., Xu, Y., Wang, Q., Tang, L., Zhang, X.: Analyzing the group sparsity based on the rank minimization methods. In: ICME, pp. 883–888 (2017)

  48. Zhang, J., Cao, Y., Wang, Z.: A new image filtering method: nonlocal image guided averaging, pp. 2460–2464 (2014)

  49. Zhang, J., Cao, Y., Zha, Z., Zheng, Z., Chen, C.W., Wang, Z.: A unified scheme for super-resolution and depth estimation from asymmetric stereoscopic video. TCSVT 26, 479–493 (2016)

    Google Scholar 

  50. Zhang, J., Tao, D.: Famed-net: a fast and accurate multi-scale end-to-end dehazing network. TIP 29, 72–84 (2020)

    MathSciNet  Google Scholar 

  51. Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. TIP 26(7), 3142–3155 (2017)

    MathSciNet  MATH  Google Scholar 

  52. Zhang, Y., Li, K., Li, K., Wang, L., Zhong, B., Fu, Y.: Image super-resolution using very deep residual channel attention networks. In: ECCV (2018)

  53. Zuo, W., Meng, D., Zhang, L., Feng, X., Zhang, D.: A generalized iterated shrinkage algorithm for non-convex sparse coding. In: ICCV, pp. 217–224 (2013)

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Acknowledgements

This work is supported by NSFC (Grant No. 61871297).

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Correspondence to Lei Yu.

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He, J., Yu, L., Liu, Z. et al. Image super-resolution by learning weighted convolutional sparse coding. SIViP 15, 967–975 (2021). https://doi.org/10.1007/s11760-020-01821-1

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