Journal of Mathematical Imaging and Vision

, Volume 54, Issue 3, pp 301–319 | Cite as

Extended Shearlet HMT Model-Based Image Denoising Using BKF Distribution

  • Xiang-Yang WangEmail author
  • Na Zhang
  • Hong-Liang Zheng
  • Yang-Cheng Liu


Images are often corrupted by noise in the procedures of image acquisition and transmission. It is a challenging work to design an edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method; it not only can exactly compute the Shearlet coefficients based on a multiresolution analysis, but also can represent images with very few coefficients. In this paper, we propose a new image denoising approach in extended DST domain, which combines hidden Markov tree (HMT) model and Bessel K Form (BKF) distribution. Firstly, the marginal statistics of extended DST coefficients are studied, and their distribution is analytically calculated by modeling extended DST coefficients with BKF probability density function. Then, an extended Shearlet HMT model is established for capturing the intra-scale, inter-scale, and cross-orientation coefficients dependencies. Finally, an image denoising approach based on the extended Shearlet HMT model is presented. Extensive experimental results demonstrate that our extended Shearlet HMT denoising approach can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed approach can preserve edges very well while removing noise.


Image denoising Hidden Markov tree (HMT) Extended discrete Shearlet transform (extended DST) Bessel K Form (BKF) distribution 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 61472171 & 61272416, and Liaoning Research Project for Institutions of Higher Education of China under Grant No. L2013407.

Compliance with Ethical Standards

Ethical standard

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Conflict of interest

The authors declare that they have no conflict of interest.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Xiang-Yang Wang
    • 1
    Email author
  • Na Zhang
    • 1
  • Hong-Liang Zheng
    • 1
  • Yang-Cheng Liu
    • 1
  1. 1.School of Computer and Information TechnologyLiaoning Normal UniversityDalianPeople’s Republic of China

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