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HeNLM-LA3D: A three-dimensional locally adaptive Hermite functions expansion based non-local means algorithm for CT applications

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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.

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Author information

Correspondence to N. V. Mamaev.

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.

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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

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Keywords

  • computed tomography
  • image filtering
  • non-local means
  • local jets method
  • Hermite functions
  • 3D filtering
  • locally adaptive algorithm