PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

X-ray Computed Tomography using a Sparsity Enforcing Prior Model Based on Haar Transformation in a Bayesian Framework

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
X-ray Computed Tomography (CT) has become a hot topic in both medical and industrial applications in recent decades. Reconstruction by using a limited number of projections is a significant research domain. In this paper, we propose to solve the X-ray CT reconstruction problem by using the Bayesian approach with a hierarchical structured prior model basing on the multilevel Haar transformation. In the proposed model, the multilevel Haar transformation is used as the sparse representation of a piecewise continuous image, and a generalized Student-t distribution is used to enforce its sparsity. The simulation results compare the performance of the proposed method with some state-of-the-art methods.
Wydawca
Rocznik
Strony
449--480
Opis fizyczny
Bibliogr. 68 poz., rys., tab., wykr.
Twórcy
autor
  • Laboratoire des Signaux et Système, CentraleSupélec, CNRS, Université Paris Sud, Université Paris-Saclay, 3, Rue Joliot-Curie, 91192 Gif-sur-Yvette, France
  • Laboratoire des Signaux et Système, CentraleSupélec, CNRS, Université Paris Sud, Université Paris-Saclay, 3, Rue Joliot-Curie, 91192 Gif-sur-Yvette, France
autor
  • Laboratoire des Signaux et Système, CentraleSupélec, CNRS, Université Paris Sud, Université Paris-Saclay, 3, Rue Joliot-Curie, 91192 Gif-sur-Yvette, France
Bibliografia
  • [1] Abrams HL, McNeil BJ. Medical implications of computed tomography (CAT scanning). New England Journal of Medicine, 1978;298(6):310–318.
  • [2] Arridge SR. Optical tomography in medical imaging. Inverse problems, 1999;15(2):R41. URL http://stacks.iop.org/0266-5611/15/2/022.
  • [3] Hanke R, Fuchs T, Uhlmann N. X-ray based methods for non-destructive testing and material characterization. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2008;591(1):14–18. URL https://doi.org/10.1016/j.nima.2008.03.016.
  • [4] Halmshaw R, Honeycombe R, Hancock P. Non-destructive testing. Arnold, 1991.
  • [5] Kalender WA. X-ray Computed Tomography. Physics in Medicine and Biology, 2006;51(13):R29. doi:10.1088/0031-9155/51/13/R03.
  • [6] Natterer F, Wubbeling F. A propagation-backpropagation method for ultrasound tomography. Inverse problems, 1995;11(6):1225. URL http://stacks.iop.org/0266-5611/11/i=6/a=007.
  • [7] Bolomey JC, Pichot C. Microwave tomography: from theory to practical imaging systems. International Journal of Imaging Systems and Technology, 1990;2(2):144–156. doi:10.1002/ima.1850020210.
  • [8] Nelson J, Milner T, Tanenbaum B, Goodman D, Van Gemert M. Infra-red tomography of port-wine-stain blood vessels in human skin. Lasers in Medical Science, 1996;11(3):199–204.
  • [9] Crowther R, DeRosier D, Klug A. The reconstruction of a three-dimensional structure from projections and its application to electron microscopy. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 317. The Royal Society, 1970 pp. 319–340. doi:10.1098/rspa.1970.0119.
  • [10] Bracewell RN, Riddle A. Inversion of fan-beam scans in radio astronomy. The Astrophysical Journal, 1967;150:427. doi:10.1086/149346.
  • [11] Berry M, Gibbs D. The interpretation of optical projections. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 314. The Royal Society, 1970 pp. 143–152. doI:10.1098/rspa.1970.0001.
  • [12] Clackdoyle R, Defrise M. Tomographic reconstruction in the 21st century. IEEE Signal Processing Magazine, 2010;27(4):60–80. doi:10.1109/MSP.2010.936743.
  • [13] Deans SR. The Radon transform and some of its applications. Courier Corporation, 2007. ISBN-0486462412, 9780486462417.
  • [14] Chetih N, Messali Z. Tomographic image reconstruction using Filtered Back Projection (FBP) and Algebraic Reconstruction Technique (ART). In: Control, Engineering & Information Technology (CEIT), 2015 3rd International Conference on. IEEE, 2015 pp. 1–6. doi:10.1109/CEIT.2015.7233031.
  • [15] Ludwig D. The Radon transform on Euclidean space. Communications on Pure and Applied Mathematics, 1966;19(1):49–81.
  • [16] Beylkin G. Discrete radon transform. IEEE transactions on acoustics, speech, and signal processing, 1987;35(2):162–172. doi:10.1109/TASSP.1987.1165108.
  • [17] Feldkamp L, Davis L, Kress J. Practical cone-beam algorithm. JOSA A, 1984;1(6):612–619. doi:10.1364/JOSAA.1.000612.
  • [18] Alifanov OMl, Artiukhin EA, Rumiantsev SV. Extreme methods for solving ill-posed problems with applications to inverse heat transfer problems. Begell house New York, 1995. ISBN-156700038X, 9781567000382.
  • [19] O’Sullivan F. A statistical perspective on ill-posed inverse problems. Statistical science, 1986, pp. 502–518. URL http://www.jstor.org/stable/2245801.
  • [20] Gordon R. A tutorial on ART (algebraic reconstruction techniques). IEEE Transactions on Nuclear Science, 1974;21(3):78–93. doi:10.1109/TNS.1974.6499238.
  • [21] Gordon R, Bender R, Herman GT. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography. Journal of theoretical Biology, 1970;29(3):471–481.
  • [22] Trampert J, Leveque JJ. Simultaneous iterative reconstruction technique: physical interpretation based on the generalized least squares solution. J. Geophys. Res, 1990;95(12):553–9. doi:10.1029/JB095iB08p12553.
  • [23] Bangliang S, Yiheng Z, Lihui P, Danya Y, Baofen Z. The use of simultaneous iterative reconstruction technique for electrical capacitance tomography. Chemical Engineering Journal, 2000;77(1):37–41. URL https://doi.org/10.1016/S1385-8947(99)00134-5.
  • [24] Ben-Israel A, Greville TN. Generalized inverses: theory and applications, volume 15. Springer Science & Business Media, 2003. doi:10.1007/b97366.
  • [25] Rit S, Sarrut D, Desbat L. Comparison of analytic and algebraic methods for motion-compensated conebeam CT reconstruction of the thorax. IEEE Transactions on Medical Imaging, 2009. 28(10):1513–1525.
  • [26] Chambolle A, Lions PL. Image recovery via total variation minimization and related problems. Numerische Mathematik, 1997;76(2):167–188. doi:10.1007/s002110050258.
  • [27] Goldstein T, Osher S. The Split Bregman method for L1-regularized problems. SIAM Journal on Imaging Sciences, 2009;2(2):323–343. URL https://doi.org/10.1137/080725891.
  • [28] Chan TF, Golub GH, Mulet P. A nonlinear primal-dual method for Total Variation-based image restoration. SIAM Journal on Scientific Computing, 1999;20(6):1964–1977. URL https://doi.org/10.1137/S1064827596299767.
  • [29] Wahlberg B, Boyd S, Annergren M, Wang Y. An ADMM algorithm for a class of total variation regularized estimation problems. IFAC Proceedings Volumes, 2012;45(16):83–88. URL https://doi.org/10.3182/20120711-3-BE-2027.00310.
  • [30] Rolfs B, Rajaratnam B, Guillot D, Wong I, Maleki A. Iterative thresholding algorithm for sparse inverse covariance estimation. In: Advances in Neural Information Processing Systems. 2012 pp. 1574–1582. arXiv:1211.2532 [stat.CO]
  • [31] Tao S, Boley D, Zhang S. Local Linear Convergence of ISTA and FISTA on the LASSO Problem. SIAM Journal on Optimization, 2016;26(1):313–336. URL https://doi.org/10.1137/151004549.
  • [32] Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on pure and applied mathematics, 1989;42(5):577–685. doi:10.1002/cpa.3160420503.
  • [33] Ramani S, Liu Z, Rosen J, Nielsen JF, Fessler JA. Regularization parameter selection for nonlinear iterative image restoration and MRI reconstruction using GCV and SURE-based methods. IEEE Transactions on Image Processing, 2012;21(8):3659–3672. doi:10.1109/TIP.2012.2195015.
  • [34] Galatsanos NP, Katsaggelos AK. Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation. IEEE Transactions on Image Processing, 1992;1(3):322–336. doi:10.1109/83.148606.
  • [35] Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005;67(2):301–320. doi:10.1111/j.1467-9868.2005.00503.x.
  • [36] Wang G, Schultz L, Qi J. Statistical image reconstruction for muon tomography using a Gaussian scale mixture model. IEEE Transactions on Nuclear Science, 2009;56(4):2480–2486. doi:10.1109/TNS.2009.2023518.
  • [37] Ramani S, Fessler JA. Statistical X-ray CT reconstruction using a splitting-based iterative algorithm with orthonormal wavelets. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI). IEEE, 2012 pp. 1008–1011. doi:10.1109/ISBI.2012.6235728.
  • [38] Redner RA, Walker HF. Mixture densities, maximum likelihood and the EM algorithm. SIAM review, 1984;26(2):195–239.
  • [39] Moon TK. The expectation-maximization algorithm. IEEE Signal processing magazine, 1996;13(6):47–60. doi:10.1109/79.543975.
  • [40] Shepp LA, Vardi Y. Maximum likelihood reconstruction for emission tomography. IEEE transactions on medical imaging, 1982;1(2):113–122.
  • [41] Tregouet D, Escolano S, Tiret L, Mallet A, Golmard J. A new algorithm for haplotype-based association analysis: the Stochastic-EM algorithm. Annals of human genetics, 2004;68(2):165–177. doi:10.1046/j.1529-8817.2003.00085.x.
  • [42] Hudson HM, Larkin RS. Accelerated image reconstruction using ordered subsets of projection data. IEEE transactions on medical imaging, 1994;13(4):601–609. doi:10.1109/42.363108.
  • [43] Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis, volume 2. Chapman & Hall/CRC Boca Raton, FL, USA, 2014. ISBN-9781584883883.
  • [44] Qi J, Leahy RM. Resolution and noise properties of MAP reconstruction for fully 3-D PET. IEEE transactions on medical imaging, 2000;19(5):493–506. doi:10.1109/42.870259.
  • [45] Ericson WA. A note on the posterior mean of a population mean. Journal of the Royal Statistical Society. Series B (Methodological), 1969, pp. 332–334.
  • [46] Fox CW, Roberts SJ. A tutorial on variational Bayesian inference. Artificial intelligence review, 2012;38(2):85–95. URL https://doi.org/10.1007/s10462-011-9236-8.
  • [47] Tzikas DG, Likas AC, Galatsanos NP. The variational approximation for Bayesian inference. IEEE Signal Processing Magazine, 2008;25(6):131–146. doi:10.1109/MSP.2008.929620.
  • [48] Chen J, Cong J, Vese LA, Villasenor J, Yan M, Zou Y. A hybrid architecture for compressive sensing 3-D CT reconstruction. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2012;2(3):616–625. doi:10.1109/JETCAS.2012.2221530.
  • [49] Noël PB, Walczak AM, Xu J, Corso JJ, Hoffmann KR, Schafer S. GPU-based cone beam computed tomography. Computer methods and programs in biomedicine, 2010;98(3):271–277. URL https://doi.org/10.1016/j.cmpb.2009.08.006.
  • [50] Gac N, Mancini S, Desvignes M, Houzet D. High speed 3D tomography on CPU, GPU, and FPGA. EURASIP Journal on Embedded systems, 2008;5:1–5:12. doi:10.1155/2008/930250.
  • [51] Wang L, Mohammad-Djafari A, Gac N, Dumitru M. Computed tomography reconstruction based on a hierarchical model and variational Bayesian method. In: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016 pp. 883–887. doi:10.1109/ICASSP.2016.7471802.
  • [52] Elad M, Aharon M. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image processing, 2006;15(12):3736–3745. doi:10.1109/TIP.2006.881969.
  • [53] Chen Y, Nasrabadi NM, Tran TD. Hyperspectral image classification using dictionary-based sparse representation. IEEE Transactions on Geoscience and Remote Sensing, 2011;49(10):3973–3985. doi:10.1109/TGRS.2011.2129595.
  • [54] Flury BN, Gautschi W. An algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing, 1986;7(1):169–184.
  • [55] Montgomery D, Zippin L. Topological transformation groups, volume 95. Interscience Publishers New York, 1955.
  • [56] Ahmed N, Natarajan T, Rao KR. Discrete cosine transform. IEEE transactions on Computers, 1974; 100(1):90–93. doi:10.1109/T-C.1974.223784.
  • [57] Nadarajah S. A generalized normal distribution. Journal of Applied Statistics, 2005;32(7):685–694. URL http://dx.doi.org/10.1080/02664760500079464.
  • [58] Rasmussen CE. The infinite Gaussian mixture model. In: NIPS, volume 12. 1999 pp. 554–560.
  • [59] Aristophanous M, Penney BC, Martel MK, Pelizzari CA. A Gaussian mixture model for definition of lung tumor volumes in positron emission tomography. Medical physics, 2007;34(11):4223–4235. doi:10.1118/1.2791035.
  • [60] Klebanov LB. Heavy tailed distributions. Matfyzpress, 2003.
  • [61] Gomes CP, Selman B, Crato N, Kautz H. Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. Journal of automated reasoning, 2000;24(1-2):67–100. doi:10.1023/A:1006314320276.
  • [62] Lange KL, Little RJ, Taylor JM. Robust statistical modeling using the t distribution. Journal of the American Statistical Association, 1989;84(408):881–896. doi:10.2307/2290063.
  • [63] Tzikas DG, Likas AC, Galatsanos NP. Variational Bayesian sparse kernel-based blind image deconvolution with Student’s-t priors. IEEE transactions on image processing, 2009;18(4):753–764. doi:10.1109/TIP.2008.2011757.
  • [64] Dumitru M. A Bayesian approach for periodic components estimation for chronobiological signals. 2016. URL https://tel.archives-ouvertes.fr/tel-01318048.
  • [65] Boyd S, Vandenberghe L. Convex optimization. Cambridge university press, 2004. ISBN-978-0-521-83378-3.
  • [66] Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 2004;13(4):600–612. doi:10.1109/TIP.2003.819861.
  • [67] Selesnick IW, Baraniuk RG, Kingsbury NC. The dual-tree complex wavelet transform. IEEE signal processing magazine, 2005;22(6):123–151. doi:10.1109/MSP.2005.1550194.
  • [68] Palenstijn WJ, Batenburg KJ, Sijbers J. The ASTRA tomography toolbox. In: 13th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, volume 2013, 2013. URL http://gsii.usal.es/ CMMSE/.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ebbf0e53-8afe-4b4f-b5b7-0713919a848a
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.