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Applied Optics

Applied Optics


  • Vol. 42, Iss. 20 — Jul. 10, 2003
  • pp: 4166–4175

Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling

L. Yaroslavsky  »View Author Affiliations

Applied Optics, Vol. 42, Issue 20, pp. 4166-4175 (2003)

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The problem of digital signal and image resampling with discrete sinc interpolation is addressed. Discrete sinc interpolation is theoretically the best one among the digital convolution-based signal resampling methods because it does not distort the signal as defined by its samples and is completely reversible. However, sinc interpolation is frequently not considered in applications because it suffers from boundary effects, tends to produce signal oscillations at the image edges, and has relatively high computational complexity when irregular signal resampling is required. A solution that enables the elimination of these limitations of the discrete sinc interpolation is suggested. Two flexible and computationally efficient algorithms for boundary effects free and adaptive discrete sinc interpolation are presented: frame-wise (global) sinc interpolation in the discrete cosine transform (DCT) domain and local adaptive sinc interpolation in the DCT domain of a sliding window. The latter offers options not available with other interpolation methods: interpolation with simultaneous signal restoration/enhancement and adaptive interpolation with super resolution.

© 2003 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(110.6980) Imaging systems : Transforms

Original Manuscript: April 8, 2003
Published: July 10, 2003

L. Yaroslavsky, "Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling," Appl. Opt. 42, 4166-4175 (2003)

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  1. L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  2. D. Fraser, “Interpolation by the FFT Revisited—An Experimental Investigation,” IEEE Trans. Acoust. Speech Signal Process. ASSP-37, 665–675 (1989). [CrossRef]
  3. T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. ASSP-38, 1512–1517 (1990). [CrossRef]
  4. L. Yaroslavsky, “Efficient algorithm for discrete sinc interpolation,” Appl. Opt. 36, 460–463 (1997). [CrossRef] [PubMed]
  5. M. Unser, P. Thevenaz, L. Yaroslavsky, “Convolution-based interpolation for fast, high-quality rotation of images,” IEEE Trans. Image Process. 4, 1371–1382 (1995). [CrossRef] [PubMed]
  6. L. Yaroslavsky, Digital Picture Processing: An Introduction (Springer-Verlag, Berlin, 1985). [CrossRef]
  7. L. Yaroslavsky, M. Eden, Fundamentals of Digital Optics (Birkhäuser, Boston, 1996). [CrossRef]
  8. Z. Wang, “Fast algorithms for the discrete W transform and for the discrete Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 803–816 (1984). [CrossRef]
  9. H. S. Hou, “A fast recursive algorithm for computing the discrete cosine transform,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 1455–1461 (1987).
  10. Z. Wang, “A simple structured algorithm for the DCT,” in Proc. 3rd Ann. Conf. Signal Process. Xi’an, China, Nov 1988, pp. 28–31 (in Chinese).
  11. A. Gupta, K. R. Rao, “A fast recursive algorithm for the discrete sine transform,” IEEE Trans. Acoust. Speech Signal Process. ASSP-38, 553–557 (1990). [CrossRef]
  12. Z. Wang, “Pruning the Fast Discrete Cosine Transform,” IEEE Trans. Commun. 39, 640–643 (1991). [CrossRef]
  13. Z. Cvetkovic, M. V. Popovic, “New fast recursive algorithms for the computation of discrete cosine and sine transforms,” IEEE Trans. Signal Process. 40, 2083–2086 (1992). [CrossRef]
  14. J. Ch. Yao, Ch-Y. Hsu, “Further results on “New fast recursive algorithms for the discrete cosine and sine transforms,” IEEE Trans. Signal Process. 42, 3254–3255 (1994). [CrossRef]
  15. L. Yaroslavsky, A. Happonen, Y. Katyi, “Signal discrete sinc-interpolation in DCT domain: fast algorithms,” SMMSP 2002, Second International Workshop on Spectral Methods and Multirate Signal Processing, Toulouse (France), 07.09.2002–08.09.2002.
  16. M. Unser, “Splines: A perfect fit for signal and image processing,” IEEE Trans. Signal Process. 16, 22–38 (1999). [CrossRef]
  17. Ph. Thevenaz, Th. Blu, M. Unser, “Interpolation Revisited,” IEEE Trans. Med. Imaging MI-19, 739–758 (2000). [CrossRef]
  18. L. Yaroslavsky, “Image restoration, enhancement, and target location with local adaptive filters,” in International Trends in Optics and Photonics, ICOIV, T. Asakura, ed., (Springer-Verlag, Berlin, 1999), pp. 111–127. [CrossRef]
  19. L. P. Yaroslavsky, K. O. Egiazarian, J. T. Astola, “Transform domain image restoration methods: review, comparison, and interpretation,” in Photonics West 2001: Electronic Imaging Nonlinear Processing and Pattern Analysis, Proc. SPIE4304, 155–170 (2001).
  20. R. Yu. Vitkus, L. P. Yaroslavsky, “Recursive Algorithms for Local Adaptive Linear Filtration,” in Mathematical Research, Computer Analysis of Images and Patterns, L. P. Yaroslavsky, A. Rosenfeld, W. Wilhelmi, eds. Band 40, (Academie Verlag, Berlin, 1987), pp. 34–39.
  21. N. Rama Murthy, N. S. Swamy, “On computation of running discrete cosine and sine transform,” IEEE Trans. Signal Process. 40, 1430–1437 (1992). [CrossRef]
  22. K. J. R. Liu, C. T. Chiu, R. K. Kolagotla, J. F. Jaja, “Optimal unified architectures for the real-time computation of time-recursive discrete sinusoidal transforms,” IEEE Trans. Circuits and Systems for Video Technology, Vol. 4, No. 2, April1994.
  23. J. A. R. Macias, A. Exposito, “Recursive Formulation of Short-Time Discrete Trigonometric Transforms,” IEEE Transactions Circuits Syst. II Analog and Digital Signal Processing, 45, 525–527 (1998). [CrossRef]
  24. V. Kober, G. Cristobal, “Fast recursive algorithms for short-time discrete cosine transform,” Electron. Lett. 35, 1236–1238 (1999). [CrossRef]
  25. J. Xi, J. F. Chicharo, “Computing running DCT’s and DST’s based on their second order shift properties,” IEEE Trans. Circuits Syst. - I, Fundamental Theory and Applications, 47, 779–783 (2000). [CrossRef]

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