Abstract
Sparse representations provide a powerful framework for various image processing tasks, among which image recovery seems to be an already classical application. While most developments of image recovery applications are focused on finding the best dictionary, the possibility of using already existing sparse image representations tends to be ignored. This is the case of the JPEG compressed image representation, which is a sparse image representation in terms of the discrete cosine transform (DCT) dictionary. The development of sparse frameworks directly on the JPEG encoded image representation can lead to computationally efficient approaches. Here we introduce a DCT-based JPEG compressed domain formulation of the color image recovery process within a sparse representation framework and we prove mathematically and experimentally not only its numerical efficiency as compared to the pixel level formulation (the processing time is reduced up to 40 %), but also the good quality of the restoration results.
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Aharon, M., Elad, M., Bruckstein, A.M.: The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representations. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)
Mairal, J., Elad, M., Sapiro, G.: Sparse representation for color image restoration. IEEE Trans. Image Process. 17(1), 53–69 (2008)
Smith, B., Rowe, L.A.: A new family of algorithms for manipulating compressed images. IEEE Comput. Graph. Appl. 13(5), 34–42 (1993)
Fang, Y., Chen, Z., Lin, W., Lin, C.W.: Saliency detection in the compressed domain for adaptive image retargeting. IEEE Trans. Image Process. 21(9), 3888–3901 (2012)
Farinella, G.M., Battiato, S.: Scene classification in compressed and constrained domain. IEEE IET Comput. Vis., Inst. Eng. Tech. 5(5), 320–334 (2011)
Battiato, S., Farinella, G.M., Guarnera, M., Ravi, D., Tomaselli, V.: Instant scene recognition on mobile platform, In: European Conference on Computer Vision (ECCV). Lecture Notes in Computer Science (LNCS), vol. 7585, pp. 655–658, Florence, Italy, 7–13 October (2012)
Wang, X., Wang, H., Huang, Y.: Fast block edge direction analysis in DCT Domain. In: IEEE International Conference on Wireless Communications and Signal Processing, pp. 703–707 (2010)
Kakarala, R., Hebbalaguppe, R.: A method for fusing a pair of images in the JPEG domain. J. Real-Time Image Process. (2011). doi:10.1007/s11554-011-0231-8
Dong, L., Kong, X., Wang, B., You, X.G.: Double compression detection based on Markov model of the first digits of DCT coefficients. In: Proceedings of the 6th International Conference on Image and Graphics, pp. 234–237 (2011)
Huang, F., Huang, J., Shi, Y.Q.: Detecting double JPEG compression with the same quantization matrix. IEEE Trans. Inf. Forensics Secur. 5(4), 848–856 (2010)
Lukas, J., Fridrich, J.: Estimation of primary quantization matrix in double compressed JPEG images. In: Proceedings of Digital Forensic Research Workshop, Cleveland, OH (2003)
Pavlidis, G., Tsekeridou, S., Chamzas, C.: JPEG-matched data filling of sparse images. In: IEEE International Conference on Image Processing (ICIP), Singapore, vol. 1, pp. 493–496 (2004)
Farinella, G.M., Battiato, S.: On the application of structured sparse model selection to JPEG compressed images. In: Proceedings of IAPR 3rd Computational Color Imaging Workshop, Milan, Italy. Lecture Notes in Computer Science, vol. 6626, pp. 137–151 (2011).
Guleryuz, O.G.: Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising—Part I: Theory. IEEE Trans. Image Process. 15, 539–554 (2006)
Guleryuz, O.G.: Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising—Part II: Adaptive algorithms. IEEE Trans. Image Process. 15, 555–571 (2006)
Sapiro, G.: Learning dictionaries and sparse image representation. SIAM J. Imaging Sci. 43(7), 1–2 (2010)
Yu, N., Qiu, T., Ren, F.: Denoising for multiple image copies through joint sparse representation. J. Math. Imaging Vis. (2012). doi:10.1007/s10851-012-0343-1
Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41 3397–3415 (1993)
Rath, G., Guillemot, C.: A complementary matching pursuit algorithm for sparse approximation. In: Proceedings of European Signal Processing Conference, Lausanne, Switzerland (2008)
Cislariu, M., Gordan, M., Vlaicu, A., Florea, C., Suteu, S.C.: Defect detection and restoration of heritage images. Acta Tech. Napoc., Electron.-Telecomun. J. 52(4), 49–54 (2011)
Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T.S., Yan, S.: Sparse representation for computer vision and pattern recognition. In: Proceedings of the IEEE, vol. 98, pp. 1031–1044 (2010)
Wallace, G.K.: The JPEG still picture compression standard. IEEE Trans. Consum. Electron. 38(1), 18–34 (1992)
Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Xu, Z., Wu, H.R., Qiu, B., Yu, X.: Geometric features-based filtering for suppression of impulse noise in color images. IEEE Trans. Image Process. 18(8), 1742–1759 (2009)
KODAK test images database. (Online) http://r0k.us/graphics/kodak/
Ponomarenko, N., Lukin, V., Zelensky, A., Egiazarian, K., Carli, M., Battisti, F.: TID2008—a database for evaluation of full-reference visual quality assessment metrics. Adv. Modern Radioelectron. 10, 30–45 (2009)
Criminisi, A., Perez, P., Toyama, K.: Region filling and object removal by exemplar-based image inpainting. IEEE Trans. Image Process. 13(9), 1200–1212 (2004)
Bertalmio, M., Sapiro, G.: Image inpainting. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, New York, USA, pp. 417–424 (2000)
Chen, T., Wu, H.: Adaptive impulse detection using center-weighted median filter. IEEE Signal Process. Lett. 8(1), 1–3 (2001)
Hore, E.S., Qiu, B., Wu, H.R.: Prediction based image restoration using a multiple window configuration. Opt. Eng. 41, 1855–1865 (2002)
Camacho, J., Morillas, S., Latorre, P.: Efficient impulsive noise suppression based on statistical confidence limits. J. Imaging Sci. Technol. 50(5), 427–436 (2006)
Morillas, S., Gregori, V., Peris-Fajarnés, G., Latorre, P.: A fast impulsive noise color image filter using fuzzy metrics. Real-Time Imaging 11(5–6), 417–428 (2005)
Koschan, A., Abidi, M.: A comparison of median filter techniques for noise removal in color images. In: Proceedings of 7th German Workshop on Color Image Processing, Erlangen, Germany. Report University of Erlangen-Nurnberg, Institute of Computer Science, vol. 34, pp. 69–79 (2001).
Bertalmio, M., Caselles, V., Masnou, S., Sapiro, G.: Inpainting. In: Encyclopedia of Computer Vision. Springer, Berlin (2011). math.univ-lyon1.fr/~masnou/fichiers/publications/survey.pdf
Filipovic, M., Kopriva, I., Cichocki, A.: Inpainting color images in learned dictionary. In: Proceedings of the 20th European Signal Processing Conference (EUSIPCO), 27–31 Aug. 2012, Bucharest, Romania, pp. 66–70 (2012)
Acknowledgements
This paper was supported by the project “Development and support of multidisciplinary postdoctoral programs in major technical areas of national strategy of Research – Development – Innovation” 4D-POSTDOC, contract no. POSDRU/89/1.5/S/52603, project co-funded by the European Social Fund through Sectoral Operational Program Human Resources Development 2007–2013.
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Florea, C., Gordan, M., Vlaicu, A. et al. Computationally Efficient Formulation of Sparse Color Image Recovery in the JPEG Compressed Domain. J Math Imaging Vis 49, 173–190 (2014). https://doi.org/10.1007/s10851-013-0449-0
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DOI: https://doi.org/10.1007/s10851-013-0449-0