Symmetric convolution of asymmetric multidimensional sequences using discrete trigonometric transforms

IEEE Transactions on Image Processing

Volumn 8, Issue 5, 1999, Pages 640-651

  Foltz, Thomas M ^a,d   Welsh, Byron M ^b,c,d  

^a Maxwell Gunter AFB   (United States)

^b Mission Research Corporation   (United States)

^c AIR FORCE INSTITUTE OF TECHNOLOGY   (United States)

^d IEEE

Author keywords

[No Author keywords available]

Indexed keywords

COSINE TRANSFORMS; EIGENVALUES AND EIGENFUNCTIONS; FIR FILTERS; FOURIER TRANSFORMS; MATRIX ALGEBRA; VECTORS;

DISCRETE TRIGONOMETRIC TRANSFORMS; MULTIDIMENSIONAL DIGITAL FILTERS; SYMMETRIC CONVOLUTION;

IMAGE CODING;

EID: 0032675612     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.760312     Document Type: Article

References (21)

1. A. K. Jain, Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
2. K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications. New York: Academic, 1990.
3. H. S. Malvar, Signal Processing with Lapped Transforms. Norwood, MA: Artech House, 1992.
4. S. A. Martucci, "Symmetric convolution and the discrete sine and cosine transforms," IEEE Trans. Signal Processing, vol. 42, pp. 1038-1051, May 1994.
5. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
6. B. R. Hunt, "A matrix theory proof of the discrete convolution theorem," IEEE Trans. Audio Electroacoust., vol. AU-19, pp. 285-288, Dec. 1971.
7. B. R. Hunt, "The application of constrained least squares estimation to image restoration by digital computer," IEEE Trans. Comput., vol. C-22, pp. 805-812, Sept. 1973.
8. V. Sánchez et al., "Diagonalizing properties of the discrete cosine transforms," IEEE Trans. Signal Processing, vol. 43, pp. 2631-2641, Nov. 1995.
9. V. Sánchez et al., "Generating matrices for the discrete sine transforms," IEEE Trans. Signal Processing, vol. 44, pp. 2644-2646, Oct. 1996.
10. Z. Wang, "Fast algorithms for the discrete W transform and for the discrete Fourier transform," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 803-816, Aug. 1984.
11. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1991.
12. J. L. Vernet, "Real signals fast Fourier transform: Storage capacity and step number reduction by means of an odd discrete Fourier transform," Proc. IEEE, vol. 59, pp. 1531-1532, Oct. 1971.
13. A. Graham, Kronecker Products and Matrix Calculus with Applications. New York: Wiley, 1981.
14. P. J. Davis, Circulant Matrices. New York: Wiley, 1979.
15. S. L. Hahn, "Multidimensional complex signals with single-orthant spectra," Proc. IEEE, vol. 80, pp. 1287-1300, Aug. 1992.
16. M. C. Roggemann and B. Welsh, Imaging Through Turbulence. Boca Raton, FL: CRC, 1996.
17. J. W. Goodman, Fourier Optics. New York: McGraw-Hill, 1968.
18. J. Louthain, "Atmospheric turbulence scintillation effects on wavefront tilt estimation," M.S. thesis, AFIT/GE/ENG/97D-11, Air Force Inst. Technol., Wright-Patterson AFB, OH, 1997.
19. S. A. Martucci, "Digital filtering of images using the discrete sine and cosine transforms," Opt. Eng., vol. 35, pp. 119-127, Jan. 1996.
20. W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun., vol. COMM-25, pp. 1004-1009, Sept. 1977.
21. A. K. Jain, "A sinusoidal family of unitary transforms," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, pp. 356-365, Oct. 1979.