Advertisement

Quantization Noise of Multilevel Discrete Wavelet Transform Filters in Image Processing

  • N. I. Chervyakov
  • P. A. Lyakhov
  • N. N. NagornovEmail author
Analysis and Synthesis of Signals and Images
  • 3 Downloads

Abstract

The effect of the quantization noise of the coefficients of discrete wavelet transform (DWT) filters on the image processing result is analyzed. A multilevel DWT method is proposed for determining the effective bit-width of DWT filter coefficients at which quantization noise has little effect on the image processing result. The dependence of the peak signal-to-noise ratio (PSNR) in DWT of images on the wavelet used, the effective bit-width of the coefficients, and the number of processing levels is revealed. Formulas are derived for determining the minimum bit-width of the coefficients that provide high quality of the processed image (PSNR ≥ 40 dB) depending on the wavelet used and the number of processing levels. Experimental modeling of a multilevel DWT image confirmed the results obtained. In the proposed method, all data are represented in fixed-point format, making possible its hardwareefficient implementation on modern devices (FPGA, ASIC, etc.).

Keywords

discrete wavelet transform digital image processing quantization noise bit-width fixedpoint format 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. C. Gonzalez and R. E. Woods, Digital Image Processing. Upper Saddle River (Prentice Hall, 2007).Google Scholar
  2. 2.
    A. Bovik, Handbook of Image and Video Processing (Academic Press, New Jersey, 2005).zbMATHGoogle Scholar
  3. 3.
    F. U. Shih, Image Processing and Pattern Recognition: Fundamentals and Techniques (John Wiley & Sons, IEEE Press, New Jersey, 2010).CrossRefGoogle Scholar
  4. 4.
    Yu. E. Voskoboinikov, “Evaluation of Optimal Parameters of the Multiplicative Algorithm Wavelet Filtering of Images,” Avtometriya 53 (4), 112–119 (2017) [Optoelectron., Instrum. Data Process. 53 (4), 402–407 (2017)].Google Scholar
  5. 5.
    M. Vetterli, J. Kovacevic, and V. K. Goyal, Foundations of Signal Processing (Cambridge University Press, Cambridge, 2014).CrossRefGoogle Scholar
  6. 6.
    I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, 1992).CrossRefzbMATHGoogle Scholar
  7. 7.
    S. Mallat, A Wavelet Tour of Signal Process the Sparse Way. Burlington (Academic Press, Elsevier, 2009).zbMATHGoogle Scholar
  8. 8.
    L. Tan and J. Jiang, Digital Signal Processing: Fundamentals and Applications (Elsevier, Academic Press, Amsterdam–Boston, 2013).CrossRefGoogle Scholar
  9. 9.
    D. G. Bailey, Design for Embedded Image Processing on FPGAs (John Wiley & Sons, IEEE Press, Singapore, 2011).CrossRefGoogle Scholar
  10. 10.
    Y. Liu and E. M.-K. Lai, “Design and Implementation of an RNS-Based 2-D DWT Processor,” IEEE Trans. Consum. Electron. 50 (1), 376–385 (2004).CrossRefGoogle Scholar
  11. 11.
    C.-C. Cheng, C.-T. Huang, C.-Y. Chen, et al., “On-Chip Memory Optimization Scheme for VLSI Implementation of Line-Based Two-Dimentional Discrete Wavelet Transform,” IEEE Trans. Circuits and Syst. for Video Technol. 17 (7), 814–822 (2007).CrossRefGoogle Scholar
  12. 12.
    P. K. Meher, B. K. Mohanty, and J. C. Patra, “Hardware-Efficient Systolic-Like Modular Design for Two-Dimensional Discrete Wavelet Transform,” IEEE Trans. Circuits and Syst. II: Express Briefs. 55 (2), 151–155 (2008).CrossRefGoogle Scholar
  13. 13.
    W. J. Laan, A. C. Jalba, and J. B. T. M. Roerdink, “Accelerating Wavelet Lifting on Graphics Hardware using CUDA,” IEEE Trans. Parallel and Distributed Syst. 22 (1), 132–146 (2011).CrossRefGoogle Scholar
  14. 14.
    A. Safari, C. V. Niras, and Y. Kong, “Power-Performance Enhancement of Two-Dimensional RNS-Based DWT Image Processor using Static Voltage Scaling,” Integration, the VLSI J. 53 (C), 145–156 (2016).CrossRefGoogle Scholar
  15. 15.
    D. Schlichthärle, Digital Filters: Basics and Design (Springer-Verlag, Berlin–Heidelberg, 2011).CrossRefzbMATHGoogle Scholar
  16. 16.
    A. Mehrnia and A. N. Willson, “A Lower Bound for the Hardware Complexity of FIR Filters,” IEEE Circuits and Syst. Magazine 18 (1), 10–28 (2017).CrossRefGoogle Scholar
  17. 17.
    K. R. Rao and P. C. Yip, The Transform and Data Compression Handbook (CRC Press, Boca Raton, 2001).zbMATHGoogle Scholar
  18. 18.
    A. Basso, D. Cavagnino, V. Pomponui, and A. Vernone, “Blind Watermarking of Color Images using Karhunen— Loève Transform Keying,” The Computer J. 54 (7), 1076–1090 (2011).CrossRefGoogle Scholar
  19. 19.
    N. K. Smolentsev, Fundamentals of the Theory of Wavelets. Wavelets in MATLAB (DMK Press, Moscow, 2005) [in Russian].Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • N. I. Chervyakov
    • 1
  • P. A. Lyakhov
    • 1
  • N. N. Nagornov
    • 1
    Email author
  1. 1.North-Caucasus Federal UniversityStavropolRussia

Personalised recommendations