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On the Design of Two-Dimensional Quincunx Filterbanks with Directional Vanishing Moment Based on Eigenfilter Approach

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Abstract

This paper presents a two-dimensional (2-D) eigenfilter technique to design 2-D perfect reconstruction (PR) filterbanks with directional vanishing moment (DVM). In this paper, we first introduce the DVM constraint for 2-D directional filterbank design. The proposed DVM constraint is imposed in 2-D eigenfilter formulation to obtain maximally flat 2-D low-pass analysis filter. Then, we use this designed analysis filter in 2-D time-domain formulation of PR condition to obtain complementary low-pass synthesis filters. The PR and DVM constraints are imposed to obtain 2-D low-pass synthesis filter. It is shown that the proposed 2-D filters satisfy the PR criteria with prescribed DVM. The performance of 2-D PR filters is evaluated in image denoising application. The performance of designed filterbank is compared with well-known existing methods in terms of peak signal-to-noise ratio to validate the results.

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References

  1. R. Ansari, A. Cetin, S.H. Lee, Sub-band coding of images using nonrectangular filter banks, in Proceedings SPIE Applications of Digital Image Processing, vol. 0974 (1988), p. 0974 – 0974 – 9

  2. R.H. Bamberger, M.J.T. Smith, A filter bank for the directional decomposition of images: theory and design. IEEE Trans. Signal Process. 40(4), 882–893 (1992)

    Article  Google Scholar 

  3. A.E. Cetin, O.N. Gerek, Y. Yardimci, Equiripple FIR filter design by the FFT algorithm. IEEE Signal Process. Mag. 14(2), 60–64 (1997)

    Article  Google Scholar 

  4. Y. Chen, M.D. Adams, W.S. Lu, Design of optimal quincunx filter banks for image coding via sequential quadratic programming, in IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP ’07, vol. 3 (2007), pp. III–897–III–900

  5. C. Cruz, A. Foi, V. Katkovnik, K. Egiazarian, Nonlocality-reinforced convolutional neural networks for image denoising. IEEE Signal Process. Lett. 25(8), 1216–1220 (2018)

    Article  Google Scholar 

  6. A.L. da Cunha, M.N. Do, On two-channel filter banks with directional vanishing moments. IEEE Trans. Image Process. 16(5), 1207–1219 (2007)

    Article  MathSciNet  Google Scholar 

  7. A. Danielyan, V. Katkovnik, K. Egiazarian, BM3D frames and variational image deblurring. IEEE Trans. Image Process. 21(4), 1715–1728 (2012)

    Article  MathSciNet  Google Scholar 

  8. M.N. Do, M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14(12), 2091–2106 (2005)

    Article  Google Scholar 

  9. R. Eslami, H. Radha, Translation-invariant contourlet transform and its application to image denoising. IEEE Trans. Image Process. 15(11), 3362–3374 (2006)

    Article  Google Scholar 

  10. L. Fan, X. Li, H. Fan, Y. Feng, C. Zhang, Adaptive texture-preserving denoising method using gradient histogram and nonlocal self-similarity priors. IEEE Trans. Circuits Syst. Video Technol. 29(11), 3222–3235 (2019)

    Article  Google Scholar 

  11. C. Guillemot, A.E. Cetin, R. Ansari, M-channel nonrectangular wavelet representation for 2-D signals: basis for quincunx sampled signals, in ICASSP 91: International Conference on Acoustics, Speech, and Signal Processing, vol. 4, (1991), pp. 2813–2816

  12. J. Kim, J.K. Lee, K.M. Lee, Accurate image super-resolution using very deep convolutional networks, in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016), pp. 1646–1654

  13. J. Kovacevic, M. Vetterli, Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases of \({R}^{n}\). IEEE Trans. Inf. Theory 38(2), 533–555 (1992)

    Article  Google Scholar 

  14. X. Li, Y. Hu, X. Gao, D. Tao, B. Ning, A multi-frame image super-resolution method. Sig. Process. 90(2), 405–414 (2010)

    Article  Google Scholar 

  15. R. Mersereau, W. Mecklenbrauker, T. Quatieri, McClellan transformation for 2D filtering : I-design. IEEE Trans. Circuits Syst. 23(7), 405–414 (1976)

    Article  Google Scholar 

  16. M.B. Nagare, B.D. Patil, R.S. Holambe, Design of two-dimensional quincunx FIR filter banks using eigen filter approach, in International Conference on Signal and Information Processing (IConSIP) (2016), pp. 1–5

  17. M.B. Nagare, B.D. Patil, R.S. Holambe, A multi directional perfect reconstruction filter bank designed with 2-D eigenfilter approach: application to ultrasound speckle reduction. J. Med. Syst. 41(2), 31 (2016b)

    Article  Google Scholar 

  18. M.B. Nagare, , B.D. Patil, R.S. Holambe, On the design of biorthogonal halfband filterbanks with almost tight rational coefficients. IEEE Trans. Circuits Syst. II: Express Briefs 1-11 (2019)

  19. S. Nah, T.H. Kim, K.M. Lee, Deep multi-scale convolutional neural network for dynamic scene deblurring, in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2017), pp. 257–265

  20. A.K. Naik, R.S. Holambe, New approach to the design of low complexity 9/7 tap wavelet filters with maximum vanishing moments. IEEE Trans. Image Process. 23(12), 5722–5732 (2014)

    Article  MathSciNet  Google Scholar 

  21. B.D. Patil, P.G. Patwardhan, V.M. Gadre, Eigenfilter approach to the design of one-dimensional and multidimensional two-channel linear-phase fir perfect reconstruction filter banks. IEEE Trans. Circuits Syst. I Regul. Pap. 55(11), 3542–3551 (2008)

    Article  MathSciNet  Google Scholar 

  22. S.-C. Pei, J.-J. Shyu, Design of 2D FIR digital filters by McClellan transformation and least squares eigencontour mapping. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 40(9), 546–555 (1993)

    Article  Google Scholar 

  23. S.-C. Pei, C.-C. Tseng, W.-S. Yang, FIR filter designs with linear constraints using the eigenfilter approach. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 45(2), 232–237 (1998)

    Article  Google Scholar 

  24. E. Psarakis, G. Moustakides, Design of two-dimensional zero-phase FIR filters via the generalized McClellan transform. IEEE Trans. Circuits Syst. 38(11), 1355–1363 (1991)

    Article  Google Scholar 

  25. A.D. Rahulkar, R.S. Holambe, Iris Image Recognition- Wavelet Filter-banks Based Iris Feature Extraction Schemes. SpringerBriefs in Signal Processing (2014)

  26. Standard test images. https://www.ece.rice.edu/~wakin/images/

  27. A. Tkacenko, P.P. Vaidyanathan, T. Nguyen, On the eigenfilter design method and its applications: a tutorial. IEEE Trans. Circuits Syst. 50, 497–517 (2003)

    Article  Google Scholar 

  28. K. Zhang, W. Zuo, L. Zhang, FFDNet: toward a fast and flexible solution for CNN-based image denoising. IEEE Trans. Image Process. 27(9), 4608–4622 (2018)

    Article  MathSciNet  Google Scholar 

  29. L. Zhang, P. Bao, W. Xiaolin, Multiscale lmmse-based image denoising with optimal wavelet selection. IEEE Trans. Circuits Syst. Video Technol. 15(4), 469–481 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Instrumentation Engineering, Ramrao Adik Institute of Technology, Mumbai, India

    Mukund B. Nagare

  2. Philips Healthcare Innovation Center, Pune, India

    Bhushan D. Patil

  3. Department of Instrumentation Engineering, SGGS Institute of Engineering and Technology, Nanded, India

    Mukund B. Nagare & Raghunath S. Holambe

Authors
  1. Mukund B. Nagare
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  2. Bhushan D. Patil
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  3. Raghunath S. Holambe
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Correspondence to Bhushan D. Patil.

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Nagare, M.B., Patil, B.D. & Holambe, R.S. On the Design of Two-Dimensional Quincunx Filterbanks with Directional Vanishing Moment Based on Eigenfilter Approach. Circuits Syst Signal Process 39, 4482–4498 (2020). https://doi.org/10.1007/s00034-020-01379-w

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  • DOI: https://doi.org/10.1007/s00034-020-01379-w

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