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Maximum Entropy Principle in Image RestorationPETROVICI, M.-A. , DAMIAN, C. , COLTUC, D.
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image processing, image reconstruction, image representation, image restoration, image sampling
entropy(20), maximum(18), image(13), reconstruction(7), method(6), methods(5), data(5), astronomical(5), restoration(4), imaging(4)
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About this article
Date of Publication: 2018-05-31
Volume 18, Issue 2, Year 2018, On page(s): 77 - 84
ISSN: 1582-7445, e-ISSN: 1844-7600
Digital Object Identifier: 10.4316/AECE.2018.02010
Web of Science Accession Number: 000434245000010
SCOPUS ID: 85047876823
Many imaging systems are faced with the problem of estimating a true image from a degraded dataset. In such systems, the image degradation is translated into a convolution with a Point Spread Function (PSF) and addition of noise. Often, the image recovery by inverse filtering is not possible because the PSF matrix is ill-conditioned. Maximum Entropy (MaxEnt) is an alternative method, which uses the entropy concept for estimating the true image. This paper presents MaxEnt method, starting with the historical references of the entropy concept and finalizing with its application in image restoration and reconstruction. The statistical model of MaxEnt for images is discussed and the connection of MaxEnt with the Bayesian inference is explained. MaxEnt is evaluated by using a modified version of Cornwell algorithm. Two cases are considered: images degraded by various PSF kernels in presence of additive noise and images resulted from incomplete datasets. The tests show PSNR gains ranging from 1 to 7dB for the degraded images and images reconstructed at 25dB from datasets with up to 80% missing pixels.
|References|||||Cited By «-- Click to see who has cited this paper|
| J.-L. Starck, F. Murtagh, "Astronomical image and data analysis", pp.71-110, Springer Science & Business Media, 2007, |
 A. Giffin, "Maximum entropy: the universal method for inference", pp. 20-25, ProQuest, Umi Dissertation Publishing, 2011.
 C. Shannon, "A mathematical theory of communication." Bell System Technical Journal, no.27, pp. 379-423, 1948,
[CrossRef] [SCOPUS Times Cited 14361]
 E. T. Jaynes, "Information theory and statistical mechanics." Physical review, no.106, p. 620, 1957,
[CrossRef] [SCOPUS Times Cited 6438]
 B. R. Frieden, "Restoring with Maximum Likelihood and Maximum Entropy", JOSA, no.62, pp.511-518, 1972,
[CrossRef] [SCOPUS Times Cited 463]
 S. F. Gull, G. J. Daniell,"Image reconstruction from incomplete and noisy data. " Nature, no. 272, pp. 686-690, 1978,
[CrossRef] [Web of Science Times Cited 814] [SCOPUS Times Cited 695]
 J. Skilling , "Maximum Entropy and Bayesian Methods", Kluwer, pp. 45-52, 1989,
 N. Weir, "A multi-channel method of maximum entropy image restoration". Astronomical Data Analysis Software and Systems I, vol. 25, p. 186, 1992.
 Tj. R. Bontekoe, E. Koper, and D. J. M. Kester, "Pyramid maximum entropy images of IRAS survey data.", Astronomy and Astrophysics no.284, pp.1037-1053, 1994.
 E. Pantin, J. L. Starck, "Deconvolution of astronomical images using the multiscale maximum entropy method. ", Astronomy and Astrophysics Supplement Series, no. 118, pp. 575-585, 1996,
 J. Guan, L. M. Song, Z. X. Huo, "Application of a multiscale maximum entropy image restoration algorithm to HXMT observations. " Chinese physics C, pp. 0-0, 2016,
[CrossRef] [Web of Science Times Cited 1] [SCOPUS Times Cited 2]
 B. Zhao, G. Qin, P.Liu, "A Robust Image Tampering Detection Method Based on Maximum Entropy Criteria." Entropy 17.12 , 2015 , pp. 7948-7966,
[CrossRef] [Web of Science Times Cited 3] [SCOPUS Times Cited 3]
 M. Willis, B. D. Jeffs, D. G. Long, "A new look at maximum entropy image reconstruction." Signals, Systems, and Computers, 1999. Conference Record of the Thirty-Third Asilomar Conference on. IEEE, vol. 2, pp. 1272-1276, 1999,
[CrossRef] [SCOPUS Times Cited 3]
 J. Skilling, R. Bryan, "Maximum entropy image reconstruction: general algorithm. " Monthly notices of the royal astronomical society, no. 211, pp.111-124, 1984,
[CrossRef] [Web of Science Times Cited 782]
 A. Caticha, A. Giffin, "Updating probabilities." AIP Conference Proceedings, vol. 872, no. 1. AIP, 2006,
[CrossRef] [SCOPUS Times Cited 80]
 E. T. Jaynes, "On the rationale of maximum-entropy methods. " Proceedings of the IEEE, no. 70, pp. 939-952, 1982,
[CrossRef] [Web of Science Times Cited 844] [SCOPUS Times Cited 923]
 A. Jannetta, J. C. Jackson, C. J. Kotre, I. P. Birch, K. J. Robson, R. Padgett, "Mammographic image restoration using maximum entropy deconvolution. " Physics in Medicine and Biology, no. 49, p. 4997, 2004,
[CrossRef] [Web of Science Times Cited 8] [SCOPUS Times Cited 10]
 M. K. Charter, W. T. Grandy Jr, L. H. Schick, "Maximum Entropy and Bayesian Methods.", ed. PF Fougere, pp. 325-339, Dordrecht: Kluwer, 1990,
 B. R. Frieden, "Image enhancement and restoration." Picture Processing and Digital Filtering. Springer Berlin Heidelberg, pp.177-248, 1975,
 T. Cornwell, K. Evans, "A simple maximum entropy deconvolution algorithm." Astronomy and Astrophysics, no.143, pp. 77-83, 1985.
 N. I. Gould, S. Leyffer, "An introduction to algorithms for nonlinear optimization." Frontiers in numerical analysis. Springer Berlin Heidelberg, pp. 109-197, 2003,
 A. Mohammad-Djafari,"Entropy, information theory, information geometry and Bayesian inference in data, signal and image processing and inverse problems." Entropy no.17.6, pp. 3989-4027, 2015,
[CrossRef] [Web of Science Times Cited 9] [SCOPUS Times Cited 21]
 K. Maisinger, M. P. Hobson, A. N. Lasenby , "Maximum-entropy image reconstruction using wavelets. " Monthly Notices of the Royal Astronomical Society, no. 347(1), pp. 339-354, 2004,
[CrossRef] [Web of Science Times Cited 33] [SCOPUS Times Cited 35]
 T. Hedrich, et al. , "Comparison of the spatial resolution of source imaging techniques in high-density EEG and MEG." NeuroImage, no.157, pp. 531-544, 2017,
[CrossRef] [Web of Science Times Cited 20] [SCOPUS Times Cited 23]
 J. J. Martín-Sotoca, A. Saa-Requejo, J. B. Grau, A. Paz-González, A. M. Tarquis,, "Combining global and local scaling methods to detect soil pore space." Journal of Geochemical Exploration, vol. 189, pp. 72-84, 2018,
[CrossRef] [Web of Science Times Cited 2] [SCOPUS Times Cited 2]
 D. Gagliardi, et al., "Estimation of the effective bone-elasticity tensor based on µCT imaging by a stochastic model. A multi-method validation." European Journal of Mechanics-A/Solids, vol. 69, pp. 147-167, 2018,
[CrossRef] [Web of Science Times Cited 1] [SCOPUS Times Cited 1]
 Y. Li, et al., "Characterization of macropore structure of Malan loess in NW China based on 3D pipe models constructed by using computed tomography technology." Journal of Asian Earth Sciences, vol. 154, pp. 271-279, 2018,
[CrossRef] [Web of Science Times Cited 17] [SCOPUS Times Cited 18]
 Q. L. Yu, et al., "Transverse phase space reconstruction study in Shanghai soft X-ray FEL facility." Nuclear Science and Techniques, vol. 29, no. 1, 2018,
[CrossRef] [Web of Science Times Cited 4] [SCOPUS Times Cited 3]
 J. B.Heymann, "Tomographic Reconstruction from Electron Micrographs." Cellular Imaging. Springer, Cham, pp. 209-236, 2018,
 S. Shentu, et al., "Maximum entropy method for ocean acoustic tomography." Signal Processing, Communications and Computing (ICSPCC), 2017 IEEE International Conference on. IEEE, 2017,
[CrossRef] [SCOPUS Times Cited 1]
 M. A. Petrovici, C. Damian, D. Coltuc, "Image reconstruction from incomplete measurements: Maximum Entropy versus L1 norm optimization." Signals, Circuits and Systems (ISSCS), 2017 International Symposium on. IEEE, 2017,
[CrossRef] [SCOPUS Times Cited 1]
 H. Costin, S. Bejinariu, D. Costin, "Biomedical Image Registration by means of Bacterial Foraging Paradigm", International Journal of Computers, Communications & Control (IJCCC), vol. 11, no. 3, pp. 329-345, 2016,
[CrossRef] [Web of Science Times Cited 3]
 G. Steidl, T. Teuber, "Removing multiplicative noise by Douglas-Rachford splitting methods", Journal of Mathematical Imaging and Vision, vol. 36, no.2, pp.168-184, 2010,
[CrossRef] [Web of Science Times Cited 168] [SCOPUS Times Cited 184]
 G. Aubert, J. F. Aujol, "A variational approach to removing multiplicative noise", SIAM Journal on Applied Mathematics, vol.68, no.4, pp.925-946, 2008,
[CrossRef] [Web of Science Times Cited 292] [SCOPUS Times Cited 341]
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