Thresholding Neural Network Image Enhancement Based on 2-D Non-separable Quaternionic Filter Bank

  • Vladislav V. Avramov
  • Eugene V. Rybenkov
  • Nick A. PetrovskyEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1055)


The thresholding neural network with a 2-D non-separable paraunitary filter bank based on quaternion multipliers (2-D NSQ-PUFB) for image enhancement is proposed. Due to the high characteristics of the multi-bands 2-D NSQ-PUFB (structure “64in-64out”, \(CG_{2D} = {{17,15\,\mathrm{\text {dB}}}}\), prototype filter bank (\( 8 \times 24 \)Q-PUFB), which forms the basis of the TNN, the results of noise editing in comparison with the approaches based on the two-channel wavelet transform in terms of PSNR are \({{1\,\mathrm{\text {dB}}}}\)\({{1.5\,\mathrm{\text {dB}}}}\) higher.


Image enhancement Thresholding neural network 2-D non-separable quaternionic filter bank 


  1. 1.
    Bhutada, G., Anand, R., Saxena, S.: Image enhancement by wavelet-based thresholding neural network with adaptive learning rate. IET Image Process. 5(7), 573 (2011). Scholar
  2. 2.
    Krim, H., Tucker, D., Mallat, S., Donoho, D.: On denoising and best signal representation. IEEE Trans. Inf. Theory 45(7), 2225–2238 (1999). Scholar
  3. 3.
    Nasri, M., Nezamabadi-pour, H.: Image denoising in the wavelet domain using a new adaptive thresholding function. Neurocomputing 72(4–6), 1012–1025 (2009). Scholar
  4. 4.
    Parfieniuk, M., Petrovsky, A.: Inherently lossless structures for eight- and six-channel linear-phase paraunitary filter banks based on quaternion multipliers. Signal Process. 90, 1755–1767 (2010). Scholar
  5. 5.
    Petrovsky, N.A., Rybenkov, E.V.: 2-D non-separable integer implementation of paraunitary filter bank based on the quaternionic multiplier block-lifting structure. In: 2019 27th European Signal Processing Conference (EUSIPCO). IEEE, September 2019Google Scholar
  6. 6.
    Petrovsky, N.A., Rybenkov, E.V., Petrovsky, A.A.: Two-dimensional non-separable quaternionic paraunitary filter banks. In: 2018 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA). IEEE, September 2018.
  7. 7.
    Sattar, F., Floreby, L., Salomonsson, G., Lovstrom, B.: Image enhancement based on a nonlinear multiscale method. IEEE Trans. Image Process. 6(6), 888–895 (1997). Scholar
  8. 8.
    Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice Hall, Englewood Cliffs (1992)zbMATHGoogle Scholar
  9. 9.
    Yu, H., Zhao, L., Wang, H.: Image denoising using trivariate shrinkage filter in the wavelet domain and joint bilateral filter in the spatial domain. IEEE Trans. Image Process. 18(10), 2364–2369 (2009). Scholar
  10. 10.
    Zhang, X.P.: Thresholding neural network for adaptive noise reduction. IEEE Trans. Neural Netw. 12(3), 567–584 (2001). Scholar
  11. 11.
    Zhang, X.P., Desai, M.: Adaptive denoising based on SURE risk. IEEE Signal Process. Lett. 5(10), 265–267 (1998). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computer Engineering DepartmentBelarusian State University of Informatics and RadioelectronicsMinskBelarus

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