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Spatially dependent regularization parameter selection in total generalized variation models for image restoration. (English) Zbl 1278.68327
Summary: In this paper, the automated spatially dependent regularization parameter selection framework for multi-scale image restoration is applied to total generalized variation (TGV) of order 2. Well-posedness of the underlying continuous models is discussed and an algorithm for the numerical solution is developed. Experiments confirm that due to the spatially adapted regularization parameter, the method allows for a faithful and simultaneous recovery of fine structures and smooth regions in images. Moreover, because of the TGV regularization term, the adverse staircasing effect, which is a well-known drawback of the total variation regularization, is avoided.

MSC:
68U10 Computing methodologies for image processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65K10 Numerical optimization and variational techniques
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References:
[1] Bertalmio M., J. Sci. Comput. 19 pp 95– (2003) · Zbl 1034.49036
[2] Blomgren P., Proceedings of SPIE 1997 (1997)
[3] Bovik , A. 2000 . ” Handbook of Image and Video Processing ” . San Diego : Academic Press . · Zbl 0967.68155
[4] Bredies , K. and Valkonen , T. Inverse problems with second-order total generalized variation constraints . Proceedings of SampTA 2011 – 9th International Conference on Sampling Theory and Applications . Singapore . · Zbl 1322.94024
[5] Bredies K., SIAM J. Imaging Sci. 3 (3) pp 492– (2010) · Zbl 1195.49025
[6] Chambolle A., Numer. Math. 76 pp 167– (1997) · Zbl 0874.68299
[7] Chambolle A., J. Math. Imaging Vision 40 (1) pp 120– (2011) · Zbl 1255.68217
[8] Chan T. F., SIAM J. Sci. Comput. 22 pp 503– (2000) · Zbl 0968.68175
[9] Dong Y. Q., J. Math. Imaging Vision 40 pp 82– (2011) · Zbl 1255.68230
[10] Knoll F., Magn. Reson. Med. 65 (22) pp 480– (2011)
[11] Liao H., J. Opt. Soc. Am. A 26 (11) pp 2311– (2009)
[12] Osher S., SIAM Multiscale Model. Simul. 4 pp 460– (2005) · Zbl 1090.94003
[13] Ring W., Math. Model. Numer. Anal. 34 (4) pp 799– (2000) · Zbl 1018.49021
[14] Rudin L. I., Phys. D 60 pp 259– (1992) · Zbl 0780.49028
[15] Strong D., Tech. Rep (1996)
[16] Tadmor E., Multiscale Model. Simul. 2 pp 554– (2004) · Zbl 1146.68472
[17] Temam R., Méthodes Mathématiques de l’Informatique [Mathematical Methods of Information Science]
[18] Tikhonov , A. and Arsenin , V. 1977 . ” Solutions of Ill-Posed Problems ” . Washington , DC : Winston and Sons . · Zbl 0354.65028
[19] Vogel C. R., Frontiers in Applied Mathematics 23 (2002)
[20] Wen Y.-W., IEEE Trans. Image Process. 21 (4) pp 1770– (2012) · Zbl 1373.94440
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