Computer Tomography image filtering

Nikolay Mamaev, Alexey Lukin, Dmitry Yurin

Non-Local Means [1] is well-known algorithm for image filtering. But it doesn't consider the rotation of pixels neighborhood then pixels neighborhoods are compared. Hermite functions can be used for pixel neighborhood decomposition and for formation of feature vector describing the neighborhood. Also obtained feature vector can be translated into invariant form that takes into account the rotation of pixel neighborhood. The subject of our research is to develop effective algorithm for image filtering based on local pixels neighborhood decomposition by using Hermite functions. Comparison of NLM [1], LJNLM-LR [2] and our new proposed algorithm (HeNLM):

Original phantom image simulated human body.

Phantom image with added Gaussian noise (sigma = 3000).

Noised image filtered by Non-Local Means algorithm. PSNR = 40.8627

Noised image filtered by Local Jets based Non-Local Means algorithm. PSNR = 41.9012

Noised image filtered by our algorithm (HeNLM). PSNR = 42.1067

Some local PSNRs on the phantom image:
Detail 1

Detail 2

Detail 3


NLM 31.985 31.9863 30.0026 42.252 49.0291
LJNLM-LR 34.1288 33.9722 31.5183 43.1465 46.7268
HeNLM 34.171 33.9081 31.799 43.0914 47.414

[1] A. Buades. “A non-local algorithm for image denoising” // IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, -V. 2, -P. 60–65.
[2] A. Manzanera. “Local Jet based similarity for NL-Means filtering” // 20th International Conference on Computer Vision and Pattern Recognition (ICPR), 2010, -P. 2668–2671.



N. Mamaev, A. Lukin, D. Yurin. “HeNLM-3D: A 3D Computer Tomography Image Denoising Algorithm” // In: The 12th International Conference on Pattern Recognition and Information Processing. United Institute of Informatics Problems of the National Academy of Sciences of Belarus, 28–30 May 2014, Minsk, Belarus, 2014, pp. 176−180. PDF.

N. V. Mamaev, A. S. Lukin, D. V. Yurin. “HeNLM–LA: a Locally Adaptive Nonlocal Means Algorithm Based on Hermite Functions Expansion” // Programming and Computer Software, Vol. 40, No. 4, Pleiades Publishing, Ltd., 2014, pp. 199−207. PDF_(draft,en).


M. V. Storozhilova, A. S. Lukin, D. V. Yurin, V. E. Sinitsyn. “2.5D Extension of Neighborhood Filters for Noise Reduction in 3D Medical CT Images” // Lecture Notes in Computer Science, Vol. 7870, 2013, pp. 1−16. Springer.

А. С. Лукин, М. В. Сторожилова, Д. В. Юрин. «Методы анализа качества фильтрации шума на изображениях компьютерной томографии» // в: Труды 15-й международной конференции "Цифровая обработка сигналов и её применение" (DSPA'2013), т. 2. 2013, с. 85−88. PDF.

Н. В. Мамаев, А. С. Лукин, Д. В. Юрин, М. А. Глазкова, В. Е. Синицын. «Алгоритм нелокального среднего на основе разложения по функциям Эрмита в задачах компьютерной томографии» // в: 23-я международная конференция по компьютерной графике и зрению GraphiCon'2013. Россия, Владивосток, 2013, с. 254−258. PDF.

M. V. Storozhilova, A. S. Lukin, D. V. Yurin. “Methods of noise filtering quality assessment for CT images” // In: Proceedings of 15-th International Conference "Digital Signal Processing and its Applications" (DSPA'2013), Vol. 2. Moscow, Russia, 2013, p. 88.


M. V. Storozhilova, A. S. Lukin, D. V. Yurin, V. E. Sinitsyn. “Two approaches for noise filtering in 3D medical CT-images” // In: 22-th International Conference on Computer Graphics GraphiCon'2012. Moscow, Russia, 2012, pp. 68−72. PDF.