| 2/2018 - 10 |
Maximum Entropy Principle in Image RestorationPETROVICI, M.-A.   , DAMIAN, C. , COLTUC, D. |
View the paper record and citations in  |
| Click to see author's profile in SCOPUS, IEEE Xplore, Web of Science |
Download PDF  (1,479 KB) | Citation | Downloads: 1,851 | Views: 3,865 |
Author keywords
image processing, image reconstruction, image representation, image restoration, image sampling
References keywords
entropy(20), maximum(18), image(13), reconstruction(7), method(6), methods(5), data(5), astronomical(5), restoration(4), imaging(4)
Blue keywords are present in both the references section and the paper title.
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
Abstract
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 This paper presents MaxEnt method, starting with the historical references of the entropy concept and finalizing with its application in image restoration and reconstruction.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 |
| [1] J.-L. Starck, F. Murtagh, "Astronomical image and data analysis", pp.71-110, Springer Science & Business Media, 2007, [CrossRef] [2] A. Giffin, "Maximum entropy: the universal method for inference", pp. 20-25, ProQuest, Umi Dissertation Publishing, 2011. [3] C. Shannon, "A mathematical theory of communication." Bell System Technical Journal, no.27, pp. 379-423, 1948, [CrossRef] [SCOPUS Times Cited 34796] [4] E. T. Jaynes, "Information theory and statistical mechanics." Physical review, no.106, p. 620, 1957, [CrossRef] [SCOPUS Times Cited 8878] [5] B. R. Frieden, "Restoring with Maximum Likelihood and Maximum Entropy", JOSA, no.62, pp.511-518, 1972, [CrossRef] [SCOPUS Times Cited 522] [6] 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 886] [SCOPUS Times Cited 799] [7] J. Skilling , "Maximum Entropy and Bayesian Methods", Kluwer, pp. 45-52, 1989, [CrossRef] [8] N. Weir, "A multi-channel method of maximum entropy image restoration". Astronomical Data Analysis Software and Systems I, vol. 25, p. 186, 1992. [9] 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. [10] 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, [CrossRef] [11] 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 2] [SCOPUS Times Cited 2] [12] 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 6] [SCOPUS Times Cited 6] [13] 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] [14] 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 871] [15] A. Caticha, A. Giffin, "Updating probabilities." AIP Conference Proceedings, vol. 872, no. 1. AIP, 2006, [CrossRef] [SCOPUS Times Cited 109] [16] 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 1067] [SCOPUS Times Cited 1212] [17] 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 12] [18] M. K. Charter, W. T. Grandy Jr, L. H. Schick, "Maximum Entropy and Bayesian Methods.", ed. PF Fougere, pp. 325-339, Dordrecht: Kluwer, 1990, [CrossRef] [19] B. R. Frieden, "Image enhancement and restoration." Picture Processing and Digital Filtering. Springer Berlin Heidelberg, pp.177-248, 1975, [CrossRef] [20] T. Cornwell, K. Evans, "A simple maximum entropy deconvolution algorithm." Astronomy and Astrophysics, no.143, pp. 77-83, 1985. [21] N. I. Gould, S. Leyffer, "An introduction to algorithms for nonlinear optimization." Frontiers in numerical analysis. Springer Berlin Heidelberg, pp. 109-197, 2003, [CrossRef] [22] 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 29] [SCOPUS Times Cited 41] [23] 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 36] [SCOPUS Times Cited 39] [24] 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 84] [SCOPUS Times Cited 94] [25] 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 4] [SCOPUS Times Cited 4] [26] 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 6] [SCOPUS Times Cited 7] [27] 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 75] [SCOPUS Times Cited 82] [28] 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 7] [SCOPUS Times Cited 6] [29] J. B.Heymann, "Tomographic Reconstruction from Electron Micrographs." Cellular Imaging. Springer, Cham, pp. 209-236, 2018, [CrossRef] [30] 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 2] [31] 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 4] [32] 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 5] [SCOPUS Times Cited 6] [33] 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 234] [SCOPUS Times Cited 251] [34] 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 448] [SCOPUS Times Cited 520] Web of Science® Citations for all references: 3,768 TCR SCOPUS® Citations for all references: 47,395 TCR Web of Science® Average Citations per reference: 108 ACR SCOPUS® Average Citations per reference: 1,354 ACR TCR = Total Citations for References / ACR = Average Citations per Reference We introduced in 2010 - for the first time in scientific publishing, the term "References Weight", as a quantitative indication of the quality ... Read more Citations for references updated on 2024-10-13 13:50 in 205 seconds. Note1: Web of Science® is a registered trademark of Clarivate Analytics. Note2: SCOPUS® is a registered trademark of Elsevier B.V. Disclaimer: All queries to the respective databases were made by using the DOI record of every reference (where available). Due to technical problems beyond our control, the information is not always accurate. Please use the CrossRef link to visit the respective publisher site. |
Copyright ©2001-2024
Faculty of Electrical Engineering and Computer Science
Stefan cel Mare University of Suceava, Romania
All rights reserved: Advances in Electrical and Computer Engineering is a registered trademark of the Stefan cel Mare University of Suceava. No part of this publication may be reproduced, stored in a retrieval system, photocopied, recorded or archived, without the written permission from the Editor. When authors submit their papers for publication, they agree that the copyright for their article be transferred to the Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University of Suceava, Romania, if and only if the articles are accepted for publication. The copyright covers the exclusive rights to reproduce and distribute the article, including reprints and translations.
Permission for other use: The copyright owner's consent does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific written permission must be obtained from the Editor for such copying. Direct linking to files hosted on this website is strictly prohibited.
Disclaimer: Whilst every effort is made by the publishers and editorial board to see that no inaccurate or misleading data, opinions or statements appear in this journal, they wish to make it clear that all information and opinions formulated in the articles, as well as linguistic accuracy, are the sole responsibility of the author.
Faculty of Electrical Engineering and Computer Science
Stefan cel Mare University of Suceava, Romania
All rights reserved: Advances in Electrical and Computer Engineering is a registered trademark of the Stefan cel Mare University of Suceava. No part of this publication may be reproduced, stored in a retrieval system, photocopied, recorded or archived, without the written permission from the Editor. When authors submit their papers for publication, they agree that the copyright for their article be transferred to the Faculty of Electrical Engineering and Computer Science, Stefan cel Mare University of Suceava, Romania, if and only if the articles are accepted for publication. The copyright covers the exclusive rights to reproduce and distribute the article, including reprints and translations.
Permission for other use: The copyright owner's consent does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific written permission must be obtained from the Editor for such copying. Direct linking to files hosted on this website is strictly prohibited.
Disclaimer: Whilst every effort is made by the publishers and editorial board to see that no inaccurate or misleading data, opinions or statements appear in this journal, they wish to make it clear that all information and opinions formulated in the articles, as well as linguistic accuracy, are the sole responsibility of the author.
