Abstract
A three-dimensional filtering algorithm for CT images (HeNLM-LA3D) has been proposed that is based on expanding the pixel neighborhood into Hermite functions, which form an orthonormal basis. Accounting for Hermite functions properties, pixel neighborhoods are oriented according to principal components of the structure tensor. The filtering parameter is adaptively adjusted to local estimates of the noise level. A noise estimation algorithm is proposed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. National Bureau of Standards, 1964; Dover, New York, 1965).
A. Buades, “A non-local algorithm for image denoising,” in Proc. IEEE Computer Society Conf. on Computer Vision and Pattern Recognition (Madison, WI, 2005), Vol. 2, pp. 60–65.
J. Canny, “A computational approach to edge detection,” IEEE PAMI 8, 34–43 (1986).
W. Forstner, “Image preprocessing for feature extraction in digital intensity, color and range images,” Springer Lecture Notes Earth Sci. 95, 165–189 (2000).
M. K. Kalra, C. Wittram, M. M. Maher, A. Sharma, G. B. Avinash, K. Karau, T. L. Toth, E. Halpern, S. Saini, and J. A. Shepard, “Can noise reduction filters improve low-radiation-dose chest CT images? Pilot study,” Radiology 228, 257–264 (2003).
M. F. Kijewski and P. F. Judy, “The noise power spectrum of CT images,” Phys. Med. Biol. 32 (5), 565–575 (1987).
H. Knutsson, “Representing local structure using tensors,”in Proc. 6th Scandinavian Conf. on Image Analysis (Oulu Univ., Oulu, 1989), pp. 244–251.
A. S. Krylov, A. V. Kutovoi, and Wee Kheng Leow, “Texture parameterization with hermite functions,” in Proc. 12th Int. Conf. Graphicon’2002 (Nizhny Novgorod, 2002), pp. 190–194.
T. Lindeberg, Scalepace Theory in Computer Vision (Kluwer Acad. Publ., Dordrecht, 1994).
N. Mamaev, A. Lukin, D. Yurin, M. Glazkova, and V. Sinitsin, “Hermite functions expansion based nonlocal means algorithm for CT applications,” in Proc. of 11th Int. Conference “Pattern Recognition and Image Analysis: New Information Technologies” (Samara, 2013), Vol. 2, pp. 638–641.
A. Manzanera, “Local jet based similarity for NLmeans filtering,” in Proc. 20th Int. Conf. on Computer Vision and Pattern Recognition (ICPR) (Istanbul, 2010), pp. 2668–2671.
F. Natterer, The Mathematics of Computerized Tomography (SIAM: Soc. for Industrial and Applied Mathematics, Philadelphia, July 2001), p. 222
T. H. Newton and D. G. Potts, Radiology of the Skull and Brain, Vol. 5: Technical Aspects of Computed Tomography (C. V. Mosby Co., St. Louis, 1981), p. 585.
St. Pyatykh, J. Hesser, and Lei Zheng. “Noise level estimation by principal component analysis,” IEEE Trans. Image Processing 22 (2), 687–699 (2013).
M. V. Storozhilova, A. S. Lukin, D. V. Yurin, and V. E. Sinitsyn, “2.5D extension of neighborhood filters for noise reduction in 3D medical CT images,” Lecture Notes Comput. Sci. 7870, 1–16 (2013).
C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proc. 6th Int. Conf. on Computer Vision (ICCV’98) (Bombay, 1998), pp. 839–846.
S. Wang, Y. Xia, Q. Liu, J. Luo, Y. Zhu, and D. D. Feng, “Gabor feature based nonlocal means filter for textured image denoising,” J. Visual Commun. Image Repr. 23 (7), 1008–1018 (2012).
L. P. Yaroslavsky and V. Kim, “Rank algorithms for picture processing, computer vision,” Graph. Image Processing 35, 234–258 (1986).
Author information
Authors and Affiliations
Corresponding author
Additional information
The paper was translated by the authors.
This paper uses the materials of the report submitted at the 11th International Conference “Pattern Recognition and Image Analysis: New Information Technologies,” Samara, Russia, September 23–28, 2013.
Nikolay V. Mamaev (1993) is a student at the chair of Mathematical Physics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russia.
Areas of interest: mathematical methods of image processing, computer vision, image filtering and enhancement, noise suppression, medical image processing.
Alexey S. Lukin (1981), Ph. D., is a researcher at the Laboratory of Mathematical Methods of Image Processing, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russia.
Areas of interest: mathematical methods of image and audio processing, noise reduction, adaptive spectral analysis, multiresolution filter banks.
Dmitry V. Yurin (1965), Ph. D., is a senior researcher at the laboratory of Mathematical Methods of Image Processing, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russia.
Areas of interest: mathematical methods of image processing, computer vision, primary feature detection, image filtering, 3D recovery, image segmentation, image registration and mosaicing, modern programming techniques.
Rights and permissions
About this article
Cite this article
Mamaev, N.V., Lukin, A.S. & Yurin, D.V. HeNLM-LA3D: A three-dimensional locally adaptive Hermite functions expansion based non-local means algorithm for CT applications. Pattern Recognit. Image Anal. 25, 658–668 (2015). https://doi.org/10.1134/S105466181504015X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S105466181504015X