Medical image noise reduction using the Sylvester-Lyapunov equation

IEEE Transactions on Image Processing

Volumn 17, Issue 9, 2008, Pages 1522-1539

  Sanches, João M ^a   Nascimento, Jacinto C ^a   Marques, Jorge S ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Despeckling; Image denoising; Medical imaging

Indexed keywords

ACOUSTIC NOISE MEASUREMENT; ALGORITHMS; BAYESIAN NETWORKS; BOOLEAN FUNCTIONS; COMPUTERIZED TOMOGRAPHY; CONFORMAL MAPPING; CONTROL THEORY; DIAGNOSIS; DIAGNOSTIC RADIOGRAPHY; EDGE DETECTION; FLUORESCENCE MICROSCOPY; IMAGE ANALYSIS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MAGNETIC RESONANCE IMAGING; MICROSCOPIC EXAMINATION; PHASE NOISE; POISSON DISTRIBUTION; POSITRON ANNIHILATION SPECTROSCOPY; POSITRON EMISSION TOMOGRAPHY; RESONANCE; SIGNAL FILTERING AND PREDICTION; TELECOMMUNICATION NETWORKS; THREE DIMENSIONAL; TOMOGRAPHY; ULTRASONIC IMAGING;

DESPECKLING; IMAGE DENOISING; MULTIPLICATIVE NOISES;

MEDICAL IMAGING;

ALGORITHM; ARTICLE; ARTIFACT; COMPUTER ASSISTED DIAGNOSIS; DIAGNOSTIC IMAGING; EVALUATION; IMAGE ENHANCEMENT; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ALGORITHMS; ARTIFACTS; DIAGNOSTIC IMAGING; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 50849115225     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2008.2001398     Document Type: Article

References (78)

1. J. Stoitsis, S. Golemati, K. S. Nikita, and A. N. Nicolaides, "Characterization of carotid atherosclerosis based on motion and texture features and clustering using fuzzy c-means," presented at the 26th Int. Conf. IEEE EMBS, 2004.
2. C. I. Christodoulou, C. S. Pattichis, M. Pantziaris, and A. Nicolaides, "Texture-based classification of atherosclerotic carotid plaques," IEEE Trans. Med. Imag., vol. 22, no. 7, pp. 902-912, Jul. 2003.
3. J. Bleck, U. Ranft, M. Gebel, H. Hecker, M. Westhoff-Beck, C. Thiesemann, S. Wagner, and M. Manns, "Random field models in textural analysis of ultrasonic images of the liver," IEEE Trans. Med. Imag. vol. 15, no. 6, pp. 796-801, Dec. 1996.
4. J. A. Noble and D. Boukerroui, "Ultrasound image segmentation: A survey," IEEE Trans. Med. Imag., vol. 25, no. 8, pp. 987-1010, Aug. 2006.
5. J. L. P. Dzung, L. Pham, and C. Xu, "Current methods in medical image segmentation," Annu. Rev. Biomed. Eng., vol. 2, 2000.
6. A. Hua and L. Yezzi, "Vessels as 4D curves: Global minimal 4D paths to extract 3D tubular surfaces," presented at the Int. Conf. Computer Vision and Pattern Recognition Workshop, Jun. 2006.
7. T.-S. Lee, W. Segars, and B. Tsui, "Study of parameters characterizing space-time gibbs priors for 4D map-rbi-em in gated myocardial perfusion spect," in Proc. IEEE Nuclear Science Symp. Conf. Record, 2005, vol. 4, pp. 2124-2128.
8. T. Deschamps, R. Malladi, and I. Ravve, "Fast evolution of image manifolds and application to filtering and segmentation in 3D medical images," IEEE Trans. Vis. Comput. Graph., vol. 10, pp. 525-535, 2004.
9. J. Montagnat and H. Delingette, "Space and time shape constrained deformable surfaces for 4D medical image segmentation," in Proc. 3rd Int. Conf. Med. Imag. Comput. and Computer-Assisted Intervention, 2000.
10. T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing, 2000.
11. A. K. Jain, Fundamentals of Digital Image Processing, 1989.
12. A. Toprak and I. Gler, "Suppression of impulse noise in medical images with the use of fuzzy adaptive median filter," J. Med. Syst., vol. 30, no. 6, 2006.
13. F. Anscombe, "The transformation of poisson, binomial and negative-binomial data," Biometrika, vol. 15, pp. 246-254, 1948.
14. J. Abbot and F. Thurstone, "Acoustic speckle: Theory and experimental analysis," Ultrasound Imag., vol. 1, pp. 303-324, 1979.
15. B. Zagar and H. Weiss, "Processing of laser speckle interferometer signals for high precision strain measurement," in Proc. 8th Int. Symp. Artificial Intelligence Based Measurement and Control, 1991, vol. 1, pp. 99-105.
16. C. Burckhardt, "Speckle in ultrasound B-mode scans," IEEE Trans. Son. Ultrason., vol. SU-25, no. 1, pp. 1-6, Jan. 1978.
17. P. Xu, "Despeckling sar-type multiplicative noise," Int. J. Remote Sens., vol. 20, no. 13, pp. 2577-2596, Sep. 1999.
18. J. M. Ollinger and J. A. Fessler, "Positron emission tomography," IEEE Signal Process. Mag., vol. 14, no. 1, pp. 43-55, Jan. 1997.
19. G. E. Hagberg, G. Zito, F. Patria, and J. N. Sanes, "Improved detection of event-related functional MRI signals using probability functions," NeuroImage, vol. 2, pp. 1193-1205, 2001.
20. G. van Kempen, L. van Vliet, and P. Verveer, "Application of image restoration methods for confocal fluorescence microscopy," in Proc. SPIE 3-D Microscopy: Image Acquisition and Processing IV, 1997, vol. 2984.
21. E. Saleh and M. Teich, N. Y. Wiley, Ed., in Proc. Fundamentals of Photonics, 1991.
22. P. Gravel, G. Beaudoin, and J. A. D. Guise, A method for modeling noise in medical images," IEEE Trans. Med. Imag., vol. 23, no. 10, pp. 1221-1232, Oct. 2004.
23. P. Bao and L. Zhang, "Noise reduction for magnetic resonance images via adaptative multiscale products thresholding," IEEE Trans. Med. Imag. vol. 22, no. 9, Sep. 2003.
24. T. K. Keyes and W. T. Tucker, "The k-distribution for modeling the envelope amplitude of a backscattered signal," IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 46, no. 4, pp. 883-887, Jul. 1999.
25. P. Shankar, "A general statistical model for ultrasonic backscattering from tissues," IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 47, no. 5, pp. 727-736, May 2000.
26. J. M. Sanches and J. S. Marques, "Compensation of log-compressed images for 3d ultrasound," Ultrasound Med. Biol., vol. 29, no. 2, pp. 239-253, 2003.
27. O. V. Michailovich and A. Tannenbaum, "Despeckling of medical ultrasound images," IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 53, no. 1, pp. 64-78, Jan. 2006.
28. R. H. Bartels and G. W. Stewart, "Solution of the matrix equation AX+ XB = C[F4]," Commun. ACM, vol. 15, no. 9, pp. 820-826, 1972.
29. A. Barraud, "A numerical algorithm to solve A XA - X = Q," IEEE Trans. Autom. Control, vol. AC-22, 1977.
30. P. C. Tay, S. T. Acton, and J. A. Hossack, "Ultrasound despeckling using an adaptive window stochastic approach," in Proc. Int. Conf. Image Processing, 2006, pp. 2549-2552.
31. R. F. Wagner, S. W. Smith, J. M. Sandrik, and H. Lopez, "Statistics of speckle in ultrasound b-scans," IEEE Trans. Son. Ultrason., vol. 30, no. 3, pp. 156-163, May 1983.
32. J. Dainty, "Laser speckle and related phenomena," in Laser Speckle and Related Phenomena. New York: Springer-Verlag, 1984, vol. 9, p. 146, XVII, 342 figs., Also Topics in Applied Physics.
33. R. F. Wagner, M. F. Insana, and S. W. Smith, "Fundamental correlation lengths of coherent speckle in medical ultrasonic images," IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 35, no. 1, pp. 34-44, Jan. 1988.
34. C. Loizou, C. Pattichis, C. Christodoulou, R. H. Istepanian, M. Pantziaris, and A. Nicolaides, "Comparative evaluation of despeckle filtering in ultrasound imaging of the carotid artery," IEEE Trans. Visual. Comput. Graph., vol. 52, no. 10, pp. 1653-1669, Oct. 2005.
35. T. Huang, G. Yang, and G. Tang, "A fast two-dimensional median filtering algorithm," IEEE Trans. Acoust., Speech, Signal Process. vol. ASSP-27, no. 1, pp. 13-18, Jan. 1979.
36. T. Loupas, W. McDicken, and P. Allan, "An adaptive weighted median filter for speckle suppression in medical ultrasonic images," IEEE Trans. Circuits Syst., vol. 36, no. 1, pp. 129-135, Jan. 1989.
37. P. C. Tay, S. T. Acton, and J. A. Hossack, "A stochastic approach to ultrasound despeckling," in Proc. 3rd IEEE Int. Symp. Biomedical Imaging: Macro to Nano, 2006, pp. 221-224.
38. D. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, Mar. 1994.
39. S. Zhong and V. Cherkassky, "Image denoising using wavelet thresholding and model selection," in Proc. Int. Conf. Image Processing, 2000, vol. 3, pp. 262-265.
40. A. Achim, A. Bezerianos, and P. Tsakalides, "Novel bayesian multi-scale method for speckle removal in medical ultrasound images," IEEE Trans. Med. Imag., vol. 20, no. 8, pp. 772-783, Aug. 2001.
41. S. Gupta, L. Kaur, R. C. Chauhan, and S. C. Saxena, "A wavelet based statistical approach for speckle reduction in medical ultrasound images," Med. Biol. Eng. Comput., vol. 42, pp. 534-537, 2004.
42. M. Figueiredo and R. Nowak, "A bound optimization approach to wavelet-based image deconvolution," presented at the IEEE Int. Conf. Image Processing, Sep. 2005.
43. A. F. Laine, "Wavelets in temporal and spatial processing of biomedical images," Annu. Rev. Biomed. Eng., vol. 2, pp. 511-550, 2000.
44. Y. Jin, E. Angelini, and A. Laine, Wavelets in Medical Image Processing: Denoising, Segmentation, and Registration, Handbook of Medical Image Analysis: Advanced Segmentation and Registration Models New York: Springer, 2004.
45. H. L. V. Trees, Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise. Melbourne, FL: Krieger, 1992.
46. H. Guo, J. E. Odergard, M. Lang, R. A. Gopinath, I. W. Selesnick, and C. Burrus, "Wavelet based speckle reduction with application to sar based atd/r," in Proc. Int. Conf. Image Processing, 1994, pp. 75-79.
47. C. R. Vogel, Computational Methods for Inverse Problems, 2002.
48. X. Huang, A. Madoc, and A. Cheetham, "Wavelet-based bayesian estimator for poisson noise removal from images," in Proc. Int. Conf. Multimedia and Expo, Jul. 2003, vol. 1, pp. I-593-I-596.
49. D. Gleich and M. Datcu, "Gauss-markov model for wavelet-based sar image despeckling," IEEE Signal Process. Lett., vol. 13, no. 6, pp. 365-368, Jun. 2006.
50. J. Xu and S. Osher, "Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising," IEEE Trans. Image Process., vol. 16, no. 2, pp. 534-544, Feb. 2007.
51. J. Hadamard, "Sur les problémes aux dérivées partielles et leur signification physique," Princeton Univ. Bull., pp. 49-52, 1902.
52. L. A. Shepp and Y. Vardi, "Maximum likelihood reconstruction in positron emission tomography," IEEE Trans. Med. Imag., vol. 1, no. 2, pp. 113-122, Feb. 1982.
53. J. Besag, "On the statistical analysis of dirty pictures," J. Roy. Statist. Soc. B, vol. 48, no. 3, pp. 259-302, 1986.
54. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the bayesian restoration of images," Readings in Computer Vision: Issues, Problems, Principles, and Paradigms, pp. 564-584, 1987.
55. S. Geman and D. McClure, Bayesian Image Analysis: An Application to Single Photon Emission Tomography, pp. 12-18, 1985.
56. S. Z. Li, "Close-form solution and parameter selection for convex minimization-based edge-preserving smoothing," IEEE Trans. Pattern Anal. Mach. Intell., vol. 20, no. 9, pp. 916-932, Sep. 1998.
57. E. Rignot and R. Chelappa, "Segmentation of polarimetric synthetic aperture radar data," IEEE Trans. Image Process., vol. 1, no. 1, pp. 281-300, Jan. 1992.
58. S. D. Conte and C. de Boor, Elementary Numerical Analysis. New York: McGraw-Hill, 1981.
59. V. Balakrishnan and E. F., Eds., "Linear matrix inequalities in control theory and applications," Int. J. Robust and Nonlinear Control, vol. 6, no. 9/10, pp. 896-1099, Nov-Dec. 1996.
60. D. Calvetti and L. Reichel, "Application of adi iterative methods to the restoration of noisy images," SIAM J. Matrix Anal. Appl., vol. 17, no. 1, pp. 165-186, 1996.
61. J. D. Gardiner, A. J. Laub, J. J. Amato, and C. B. Moler, "Solution of the sylvester matrix equation axbt + cxdt = c," ACM Trans. Math. Softw., vol. 18, no. 2, pp. 223-231, 1992.
62. K. Lange, Optimization, ser. Springer Texts in Statistics.. New York: Springer, Jun. 2004.
63. R. Pan and S. J. Reeves, "Efficient huber-markov edge-preserving image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 3728-3735, Dec. 2006.
64. J. Dias, "Fast gem wavelet-based image deconvolution algorithm," presented at the Int. Conf. Image Processing, 2003.
65. P. Benner, Factorized Solution of Sylvester Equations With Applications in Control, May 2004.
66. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," presented at the Annu. Allerton Conf. Communication, Control and Computing, Oct. 1993.
67. R. M. Willett and R. D. Nowak, "Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging," IEEE Trans. Med. Imag., vol. 22, no. 3, pp. 332-350, Mar. 2003.
68. J. Nascimento and J. S. Marques, "Robust shape tracking in the presence of cluttered background," IEEE Trans. Multimedia, vol. 6, no. 6, pp. 852-861, Dec. 2004.
69. A. Hammoude, "Computer-assited endocardial border identification from a sequence of two-dimensional echocardiographic images," Ph.D. dissertation, Univ. Washington, Seattle, WA, 1988.
70. J. A. Jensen and N. B. Svendsen, "Calculation of pressure fields from arbitrarily shaped apodized and excited ultrasound transducers," IEEE Trans. Ultrason., Ferroelect., Freq. Control, vol. 39, no. 2, pp. 262-267, Feb. 1992.
71. K. Timmermann and R. Nowak, "Multiscale bayesian estimation of poisson intensities," in Proc. 31st Asilomar Conf. Signals, Systems, Comput. 1997, pp. 85-90.
72. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, "Comparing images using Hausdorff distance," IEEE Trans. Pattern Anal. Mach. Intell., vol. 15, pp. 850-863, 1993.
73. M. J. Black and A. Rangarajan, "On the unification of line processes, outlier rejection, and robust statistics with applications in early vision," Int. J. Comput. Vis., vol. 19, no. 1, pp. 57-91, 1996.
74. C. Bouman and K. Sauer, "A generalized gaussian image model for edge-preserving MAP estimation," IEEE Trans. Image Process., vol. 2, no. 3, pp. 296-310, Jul. 1993.
75. C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," in Proc. IEEE Int. Conf. Image Processing, vol. 7, no. 7, pp. 813-824.
76. J. Sanches and J. Marques, "Image reconstruction using the Benford law," presented at the IEEE Proc. Int. Conf. Image Processing, 2006.
77. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imag. Vis., vol. 20, no. 1-2, pp. 89-97, 2004.
78. J. Jolion, "Image and the benford's law," J. Math. Imag. Vis., vol. 14, pp. 73-81, 2001.