Non-Linear Polynomial Filters: Overview, Evolution and Proposed Mathematical Formulation

  • Vikrant BhatejaEmail author
  • Mukul Misra
  • Shabana Urooj
Part of the Studies in Computational Intelligence book series (SCI, volume 861)


Last few decades have marked growing interest towards developments in signal processing techniques on account of the diverse spread in multimedia applications (which includes image and video processing).


  1. H.H. Chang, C.L. Nikias, A.N. Venetsanopoulos, Efficient implementations of quadratic filters. IEEE Trans. Acoust. Speech Signal Process. 34, 1511–1528 (1986)Google Scholar
  2. T. Koh, E. Powers, Second-order Volterra filtering and its application to nonlinear system identification. IEEE Trans. Acoust. Speech Signal Process. 33(6), 1445–1455 (1985)Google Scholar
  3. Y. Lou, C.L. Nikias, A.N. Venetsanopoulos, Efficient VLSI array processing structures for adaptive quadratic digital filters. Circuits Syst. Signal Process. 7(2), 253–273 (1988)CrossRefGoogle Scholar
  4. V.J. Mathews, Adaptive polynomial filters. IEEE Signal Process. Mag. 8(3), 10–26 (1991)CrossRefGoogle Scholar
  5. V.J. Mathews, G.L. Sicuranza, Polynomial Signal Processing, vol. 27 (Wiley, New York, 2000)Google Scholar
  6. B.G. Mertzios, G.L. Sicuranza, A.N. Venetsanopoulos, Efficient realizations of two-dimensional quadratic digital filters. IEEE Trans. Acoust. Speech Signal Process. 37(5), 765–768 (1989)CrossRefGoogle Scholar
  7. S.K. Mitra, H. Li, I. Li, T.-H. Yu, A new class of non-linear filters for image enhancement, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP-1991), Toronto, Canada, April 1991, pp. 2525–2528Google Scholar
  8. A.V. Oppenheim, R.W. Schafer, Discrete Time Signal Processing, 5th edn. (Prentice Hall of India, New Delhi, 1998)Google Scholar
  9. I. Pitas, A.N. Venetsanopoulos, Morphological shape decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 12(1), 38–45 (1990)CrossRefGoogle Scholar
  10. I. Pitas, A.N. Venetsanopoulos, Order statistics in digital image processing. Proc. IEEE 80(12), 1893–1921 (1992)CrossRefGoogle Scholar
  11. G. Ramponi, Bi-impulse response design of isotropic quadratic filters. Proc. IEEE 78(4), 665–667 (1990)CrossRefGoogle Scholar
  12. G. Ramponi, G.L. Sicuranza, Quadratic digital filters for image processing. IEEE Trans. Acoust. Speech Signal Process. 36(6), 937–939 (1988)CrossRefGoogle Scholar
  13. G.L. Sicuranza, Quadratic filters for signal processing. Proc. IEEE 80(8), 1263–1285 (1992)CrossRefGoogle Scholar
  14. D.J. Struik, A Source Book in Mathematics 1200–1800 (Princeton University Press, 2014)Google Scholar
  15. S. Thurnhofer, S.K. Mitra, A general framework for quadratic Volterra filters for edge enhancement. IEEE Trans. Image Process. 5(6), 950–963 (1996)CrossRefGoogle Scholar
  16. J.H. Yoon, Y.M. Ro, Enhancement of the contrast in mammographic images using the homomorphic filter method. IEICE Trans. Inf. Syst. 85(1), 298–303 (2002)Google Scholar
  17. Y. Zhou, K.A. Panetta, S.S. Agaian, Mammogram enhancement using alpha weighted quadratic filter, in Proceedings of Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Minneapolis, Minnesota, September 2009, pp. 3681–3684Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringShri Ramswaroop Memorial Group of Professional Colleges (SRMGPC)LucknowIndia
  2. 2.Dr. A.P.J. Abdul Kalam Technical UniversityLucknowIndia
  3. 3.Faculty of Electronics and Communication EngineeringShri Ramswaroop Memorial University (SRMU)BarabankiIndia
  4. 4.Department of Electrical Engineering, College of EngineeringPrincess Nourah Bint Abdulrahman UniversityRiyadhKingdom of Saudi Arabia

Personalised recommendations