Abstract
Sparse representation with training-based dictionary has been shown successful on super resolution(SR) but still have some limitations. Based on the idea of making the magnification of function curve without losing its fidelity, we proposed a function based dictionary on sparse representation for super resolution, called hybrid function sparse representation (HFSR). The dictionary we designed is directly generated by preset hybrid functions without additional training, which can be scaled to any size as is required due to its scalable property. We mixed approximated Heaviside function (AHF), sine function and DCT function as the dictionary. Multi-scale refinement is then proposed to utilize the scalable property of the dictionary to improve the results. In addition, a reconstruct strategy is adopted to deal with the overlaps. The experiments on ‘Set14’ SR dataset show that our method has an excellent performance particularly with regards to images containing rich details and contexts compared with non-learning based state-of-the art methods.
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References
Aharon, M., Elad, M., Bruckstein, A., et al.: K-svd: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311 (2006)
Babacan, S.D., Molina, R., Katsaggelos, A.K.: Variational bayesian super resolution. IEEE Trans. Image Process. 20(4), 984–999 (2011)
Dai, S., Han, M., Xu, W., Wu, Y., Gong, Y.: Soft edge smoothness prior for alpha channel super resolution. In: 2007 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8. IEEE (2007)
Deng, L.J., Guo, W., Huang, T.Z.: Single image super-resolution by approximated Heaviside functions. Inf. Sci. 348, 107–123 (2016). https://doi.org/10.1016/j.ins.2016.02.015
Dong, C., Loy, C.C., He, K., Tang, X.: Learning a deep convolutional network for image super-resolution. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8692, pp. 184–199. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10593-2_13
Dong, W., Zhang, L., Shi, G., Li, X.: Nonlocally centralized sparse representation for image restoration. IEEE Trans. Image Process. 22(4), 1620–1630 (2013)
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)
Donoho, D.L.: For most large underdetermined systems of linear equations the minimal \(\ell \)1-norm solution is also the sparsest solution. Commun. Pure and Appl. Math.: A J. Issued Courant Inst. Math. Sci. 59(6), 797–829 (2006)
Fattal, R.: Image upsampling via imposed edge statistics. ACM Trans. Graph. (TOG) 26(3), 95 (2007)
Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning low-level vision. Int. J. Comput. Vis. 40(1), 25–47 (2000)
Getreuer, P.: Contour stencils: total variation along curves for adaptive image interpolation. SIAM J. Imag. Sci. 4(3), 954–979 (2011)
Glasner, D., Bagon, S., Irani, M.: Super-resolution from a single image. In: 2009 IEEE 12th International Conference on Computer Vision, pp. 349–356. IEEE, Kyoto September 2009. https://doi.org/10.1109/ICCV.2009.5459271
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: Advances in Neural Information Processing Systems. pp. 2672–2680 (2014)
Kim, K.I., Kwon, Y.: Single-image super-resolution using sparse regression and natural image prior. IEEE Trans. Pattern Anal. Mach. Intell. 32(6), 1127–1133 (2010)
Ledig, C., et al.: Photo-realistic single image super-resolution using a generative adversarial network. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4681–4690 (2017)
Li, X., Orchard, M.T.: New edge-directed interpolation. IEEE Trans. Image Process. 10(10), 1521–1527 (2001)
Sajjadi, M.S., Scholkopf, B., Hirsch, M.: Enhancenet: single image super-resolution through automated texture synthesis. In: Proceedings of the IEEE International Conference on Computer Vision. pp. 4491–4500 (2017)
Sun, J., Xu, Z., Shum, H.Y.: Image super-resolution using gradient profile prior. In: 2008 IEEE Conference on Computer Vision and Pattern Recognition. pp. 1–8. IEEE (2008)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc.: Ser. B (Methodological) 58(1), 267–288 (1996)
Yang, J., Wright, J., Huang, T.S., Ma, Y.: Image super-resolution via sparse representation. IEEE Trans. Image Process. 19(11), 2861–2873 (2010). https://doi.org/10.1109/TIP.2010.2050625
Zeyde, R., Elad, M., Protter, M.: On single image scale-up using sparse-representations. In: Boissonnat, J.-D., et al. (eds.) Curves and Surfaces 2010. LNCS, vol. 6920, pp. 711–730. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27413-8_47
Zhang, L., Wu, X.: An edge-guided image interpolation algorithm via directional filtering and data fusion. IEEE Trans. Image Process. 15(8), 2226–2238 (2006)
Zhang, Y., Liu, J., Yang, W., Guo, Z.: Image super-resolution based on structure-modulated sparse representation. IEEE Trans. Image Process. 24(9), 2797–2810 (2015)
Zhang, Z., Li, F., Chow, T.W., Zhang, L., Yan, S.: Sparse codes auto-extractor for classification: a joint embedding and dictionary learning framework for representation. IEEE Trans. Signal Process. 64(14), 3790–3805 (2016)
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Bian, J., Lin, B., Zhang, K. (2019). Hybrid Function Sparse Representation Towards Image Super Resolution. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11679. Springer, Cham. https://doi.org/10.1007/978-3-030-29891-3_3
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