A total variation-based JPEG decompression model

SIAM Journal on Imaging Sciences

Volumn 5, Issue 1, 2012, Pages 366-393

  Bredies, K ^a   Holler, M ^a  

^a UNIVERSITY OF GRAZ   (Austria)

Author keywords

Artifact free JPEG decompression; Image reconstruction; Optimality system; Primaldual gap; Total variation

Indexed keywords

ARTIFACT-FREE JPEG DECOMPRESSION; COMPRESSED IMAGES; COMPUTATION TIME; CONVEX SET; GRAPHICS PROCESSING UNIT; INFINITE DIMENSIONAL; OPTIMALITY CONDITIONS; OPTIMALITY SYSTEM; ORTHONORMAL BASIS; PRIMAL DUAL ALGORITHMS; PRIMAL-DUAL; REAL-TIME APPLICATION; RECONSTRUCTION QUALITY; SOURCE IMAGES; STOPPING CRITERIA; TOTAL VARIATION; VARIATIONAL MODELS;

COMPUTER GRAPHICS; IMAGE RECONSTRUCTION; PROGRAM PROCESSORS; SET THEORY;

COMPUTER GRAPHICS EQUIPMENT;

EID: 84865278612     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/110833531     Document Type: Article

References (31)

1. R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, InverseProblems, 10 (1994), pp. 1217-1229.
2. F. Alter, S. Durand, and J. Froment, Adapted total variation for artifact free decompression ofJPEG images, J. Math. Imaging Vision, 23 (2005), pp. 199-211.
3. L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, The Clarendon Press, Oxford University Press, New York, 2000.
4. G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4), 135 (1983), pp. 293-318.
5. H. Attouch and H. Brezis, Duality for the sum of convex functions in general Banach spaces, inAspects of Mathematics and Its Applications, North-Holland, Amsterdam, 1986, pp. 125-133.
6. K. Bredies, K. Kunisch, and T. Pock, Total generalized variation, SIAM J. Imaging Sci., 3 (2010), pp. 492-526.
7. E. Casas, K. Kunisch, and C. Pola, Regularization by functions of bounded variation and applicationto image enhancement, Appl. Math. Optim., 40 (1999), pp. 229-257.
8. A. Chambolle and P.-L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), pp. 167-188.
9. A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applicationsto imaging, J. Math. Imaging Vision, 40 (2011), pp. 120-145.
10. 1 function approximation, SIAMJ. Appl. Math, 65 (2005), pp. 1817-1837.
11. P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, MultiscaleModel. Simul., 4 (2005), pp. 1168-1200.
12. 1TV image restoration, SIAM J. Imaging Sci., 2 (2009), pp. 1168-1189.
13. I. Ekeland and R. Témam, Convex Analysis and Variational Problems, Classics Appl. Math. 28, SIAM, Philadelphia, 1999.
14. L. C. Evans, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, 1992.
15. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equation. Theory and Algorithms, Springer, Berlin, 1986.
16. M. Hintermüller and K. Kunisch, Total bounded variation regularization as a bilaterally constrainedoptimization problem, SIAM J. Appl. Math., 64 (2004), pp. 1311-1333.
17. 1-TV-based image restoration, Inverse Problems, 26(2010), 085005.
18. T. Kartalov, Z. A. Ivanovski, L. Panovski, and L. J. Karam, An adaptive POCS algorithm for compressionartifacts removal, in Proceedings of the 9th International Symposium on Signal Processingand Its Applications, 2007, pp. 1-4.
19. NASA, Hubblesite, Space Telescope Science Institute, Baltimore, MD, http://hubblesite.org/gallery/album/nebula/pr2004032d/titles/true/hires/true/.
20. NASA, Photojournal Image Gallery, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, http://photojournal.jpl.nasa.gov/favorites/PIA03153.
21. A. Nosratinia, Enhancement of JPEG-compressed images by re-application of JPEG, J. VLSI SignalProcess. Syst., 27 (2001), pp. 69-79.
22. NVIDIA CUDA Programming Guide Version 2.0, NVIDIA Corporation, Santa Clara, CA, 2008.
23. L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
24. M.-Y. Shen and C.-C. J. Kuo, Review of postprocessing techniques for compression artifact removal, J. Visual Commun. Image Representation, 9 (1998), pp. 2-14.
25. S. Singh, V. Kumar, and H. K. Verma, Reduction of blocking artifacts in JPEG compressed images, Digit. Signal Process., 17 (2007), pp. 225-243.
26. A. Vretblad, Fourier Analysis and Its Applications, Springer, New York, 2003.
27. G. K. Wallace, The JPEG still picture compression standard, Comm. ACM, 34 (1991), pp. 30-44.
28. C. Weerasinghe, A. W.-C. Liew, and H. Yan, Artifact reduction in compressed images based onregion homogeneity constraints using the projection onto convex sets algorithm, IEEE Trans. CircuitsSyst. Video Technol., 12 (2002), pp. 891-897.
29. S. Zhong, Image coding with optimal reconstruction, in Proceedings of the International Conference onImage Processing, Vol. 1, IEEE Computer Society, Washington, DC, 1997, pp. 161-164.
30. W. P. Ziemer, Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation, Springer, New York, 1989.
31. J. J. Zou and H. Yan, A deblocking method for BDCT compressed images based on adaptive projections, IEEE Trans. Circuits Syst. Video Technol., 15 (2005), pp. 430-435.