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Adapted Total Variation for Artifact Free Decompression of JPEG Images

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Abstract

The widely used JPEG lossy baseline coding system is known to produce, at low bit rates, blocking effects and Gibbs phenomenon. This paper develops a method to get rid of these artifacts without smoothing images and without removing perceptual features. This results in better looking pictures and improved PSNR. Our algorithm is based on an adapted total variation minimization approach constrained by the knowledge of the input intervals the unquantized cosine coefficients belong to. In this way, we reconstruct an image having the same quantized coefficients than the original one, but which is minimal in term of the total variation. This discourages blocking effects and Gibbs phenomenon to appear while edges are kept as sharp as possible. Although the proposed subgradient method is converging in infinite time, experiments show that best results are obtained with a very few number of iterations. This leads to a simple and fast algorithm that may be applied to the great set of JPEG images to decompress them more efficiently.

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Author information

Authors and Affiliations

  1. ENS, 45 rue d’Ulm, 75005, Paris, France

    François Alter

  2. LAMFA, Université de Picardie, 33 rue Saint Leu, 80039, Amiens Cedex 1, France

    Sylvain Durand

  3. LMAM, Université de Bretagne Sud, Campus de Tohannic-Y. Coppens, BP 573, 56017, Vannes, France

    Jacques Froment

Authors
  1. François Alter
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  2. Sylvain Durand
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  3. Jacques Froment
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Corresponding author

Correspondence to Jacques Froment.

Additional information

This work was also supported in part by CNES, 18 avenue E. Belin, 31055 Toulouse Cedex, France and Science Pratique SA, 47 avenue Carnot, 94230 Cachan, France under Grant 762/00/CNES/8319; by CMLA, ENS Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France; by DOLabs, 3 rue Nationale, 92100 Boulogne-Billancourt, France and by MAP5, UFR mathématiques et informatique, Université Paris 5, 45 rue des Saints Pères, 75270 Paris Cedex 06, France.

François Alter was at École Normale Supérieure Ulm in Paris from 1998 to 2003, and entered the Corps des Mines attached to the French minister in charge of industry in 2003. He received M.Sc. degree in Pure Mathematics from Paris 6 University in 2001. Since 2002, he has been preparing his Ph.D. in Image Processing and Analysis at CMLA in Cachan, France. His research interests are Geometric Partial Differential Equations and Stochastic Perception Theory.

Sylvain Durand received his PhD in applied mathematics, in 1993, from Paris-Dauphine University, France. In 1994 and 1995, he held a postdoctoral position at Washington University of St. Louis, Missouri. He is currently assistant professor at Jules Verne University of Picardie, France. His research interests include mathematical aspects of image processing.

Jacques Froment received the Ph.D. degree in applied mathematics from Paris-Dauphine University, France, in 1990. During the academic year 1990/1991, he was an associate research scientist at the Courant Institute of Mathematical Sciences in NYU’s computer science department. From 1991 to 2002, he was an assistant professor in the department of mathematics at Paris 5 University, France. He is currently professor of applied mathematics at the University of Bretagne Sud, Vannes, France. His research interests include mathematical models in computer vision and representation of meaningful information with applications to image compression and restoration.

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Alter, F., Durand, S. & Froment, J. Adapted Total Variation for Artifact Free Decompression of JPEG Images. J Math Imaging Vis 23, 199–211 (2005). https://doi.org/10.1007/s10851-005-6467-9

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