Abstract
This paper deals with the single image scale-up problem using sparse-representation modeling. The goal is to recover an original image from its blurred and down-scaled noisy version. Since this problem is highly ill-posed, a prior is needed in order to regularize it. The literature offers various ways to address this problem, ranging from simple linear space-invariant interpolation schemes (e.g., bicubic interpolation), to spatially-adaptive and non-linear filters of various sorts. We embark from a recently-proposed successful algorithm by Yang et. al. [1,2], and similarly assume a local Sparse-Land model on image patches, serving as regularization. Several important modifications to the above-mentioned solution are introduced, and are shown to lead to improved results. These modifications include a major simplification of the overall process both in terms of the computational complexity and the algorithm architecture, using a different training approach for the dictionary-pair, and introducing the ability to operate without a training-set by boot-strapping the scale-up task from the given low-resolution image. We demonstrate the results on true images, showing both visual and PSNR improvements.
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References
Yang, J., Wright, J., Huang, T., Ma, Y.: Image super-resolution as sparse representation of raw image patches. In: IEEE Computer Vision and Pattern Recognition (CVPR) (June 2008)
Yang, J., Wright, J., Huang, T., Ma, Y.: Image super-resolution via sparse representation. IEEE Trans. on Image Processing (to appear)
Farsiu, S., Robinson, D., Elad, M., Milanfar, P.: Advances and Challenges in Super-Resolution. International Journal of Imaging Systems and Technology 14(2), 47–57 (2004); special issue on high-resolution image reconstruction
Hou, H.S., Andrews, H.C.: Cubic spline for image interpolation and digital filtering. IEEE Transactions on Signal Processing 26, 508–517 (1978)
Irani, M., Peleg, S.: Improving Resolution by Image Registration. CVGIP: Graphical Models and Image Processing 53, 231–239 (1991)
Schultz, R.R., Stevenson, R.L.: A Bayesian Approach to Image Expansion for Improved Definition. IEEE Transactions on Image Processing 3(3), 233–242 (1994)
Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning Low-Level Vision. International Journal of Computer Vision 40(1), 25–47 (2000)
Li, X., Orchard, M.: New Edge-Directed Interpolation. IEEE Transactions on Image Processing 10, 1521–1527 (2001)
Chang, H., Yeung, D.-Y., Xiong, Y.: Super-resolution through neighbor embedding. In: IEEE Conference on Computer Vision and Pattern Classification (CVPR), vol. 1, pp. 275–282 (2004)
Elad, M., Datsenko, D.: Example-Based Regularization Deployed to Super-Resolution Reconstruction of a Single Image. The Computer Journal 50(4), 1–16 (2007)
Sun, J., Xu, Z., Shum, H.: Image super-resolution using gradient profile prior. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1–8 (2008)
Elad, M., Aharon, M.: Image denoising via learned dictionaries and sparse representation. In: International Conference on Computer Vision and Pattern Recognition, New York, June 17-22 (2006)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. on Image Processing 15(12), 3736–3745 (2006)
Bruckstein, A.M., Donoho, D.L., Elad, M.: From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images. SIAM Review 51(1), 34–81 (2009)
Elad, M.: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, Heidelberg (2010)
Wang, J., Zhu, S., Gong, Y.: Resolution enhancement based on learning the sparse association of image patches. Pattern Recognition Letters 31(1) (January 2010)
Lou, Y., Bertozzi, A., Soatto, S.: Direct sparse deblurring. J. Math. Imag. Vis. (August 13, 2010)
Zhang, X., Wu, X.: Image interpolation by adaptive 2-d autoregressive modeling and soft-decision estimation. IEEE Trans. Image Process. 17(6), 887–896 (2008)
Mallat, S., Yu, G.: Super-Resolution with Sparse Mixing Estimators. IEEE Trans. on Image Processing 19(11), 2889–2900 (2010)
Aharon, M., Elad, M., Bruckstein, A.M.: The K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Trans. on Signal Processing 54(11), 4311–4322 (2006)
Rubinstein, R., Zibulevsky, M., Elad, M.: Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit, Technical Report - CS Technion (April 2008)
Glasner, D., Bagon, S., Irani, M.: Super-Resolution from a Single Image. In: International Conference on Computer Vision, ICCV (October 2009)
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Zeyde, R., Elad, M., Protter, M. (2012). On Single Image Scale-Up Using Sparse-Representations. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_47
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DOI: https://doi.org/10.1007/978-3-642-27413-8_47
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