Monogenic wavelet frames

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7446, Issue , 2009, Pages

  Held, Stefan ^a   Storath, Martin ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Analytical signal; Clifford algebra; Contrast enhancement; Descreening; Hilbert transform; Monogenic signal; Phase; Phase direction; Riesz transform; Steerable filters; Wavelet

Indexed keywords

ANALYTICAL SIGNAL; CLIFFORD ALGEBRA; CONTRAST ENHANCEMENT; DESCREENING; HILBERT TRANSFORM; MONOGENIC SIGNAL; PHASE; PHASE DIRECTION; RIESZ TRANSFORM; STEERABLE FILTERS; WAVELET;

ALGEBRA; MATHEMATICAL TRANSFORMATIONS; SIGNAL PROCESSING;

WAVELET DECOMPOSITION;

EID: 70449468324     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.826026     Document Type: Conference Paper

References (24)

1. Stein, E. M., [Singular Integrals and Differentiability Properties of Functions], Princeton University Press (1970).
2. Mallat, S., [A wavelet tour of signal processing], Academic Press (1998).
3. Selesnick, I. W., Baraniuk, R. G., and Kingsbury, N. G., "The dual-tree complex wavelet transform, " IEEE Signal Processing Magazine (November 2005).
4. Bülow, T., Hypercomplex Spectral Signal Representations for Image Processing and Analysis, PhD thesis, University of Kiel (1999).
5. Held, S., Storath, M., Forster, B., and Massopust, P., "Steerable wavelet transforms based on the riesz transform, " excepted for IEEE Transactions on Image Processing.
6. Calderón, A. and Zygmund, A., "On the existence of certain singular integrals, " Acta Mathematica (1952).
7. Forster, B., Blu, T., Van de Ville, D., and Unser, M., "Shift-invariant spaces from rotation-covariant functions, " Applied and Computational Harmonic Analysis 25(2), 240-265 (2008).
8. Van de Ville, D. and Unser, M., "Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid, " IEEE Transactions on Image Processing 17(11) (2008).
9. Felsberg, M., Low-Level Image Processing with the Structure Multivector, PhD thesis, Christian-Albrechts- Universität Kiel (2002).
10. Olhede, S. and Metikas, G., "Multiple multidimensional morse wavelets, " IEEE Transactions on Image Processing 55(3) (2007).
11. Unser, M., Balać, K., and Van de Ville, D., "The monogenic Riesz-Laplace wavelet transform, " To appear in Proceedings of the Sixteenth European Signal Processing Conference (EUSIPCO'08), Lausanne VD, Switzerland, August 25-29, 2008.
12. Unser, M., Sage, D., and Van de Ville, D., "Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform, " IEEE Transactions on Image Processing (To Appear).
13. Chan, W. L., Choi, H., and Baraniuk, R., "Directional hypercomplex wavelets for multidimensional signal analysis and processing, " in [IEEE International Conference on Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04).], (2004).
14. Freeman, W. T. and Adelson, E. H., "The design and use of steerable filters, " IEEE Trans. Patt. Anal. and Machine Intell. 13 (Sept. 1991).
15. Stein, E. and Weiss, G., [Introduction to Fourier analysis on Euclidean spaces], Princeton University Press (1971).
16. Brackx, F., Delanghe, R., and Sommen, F., [Clifford Analysis], PitmanBooks Limited (1982).
17. d), ".
18. d): the analysis of the analysis operator, " Journal of functional analysis 148 (1997).
19. Romero, J., Alexander, S., Baid, S., Jain, S., and Papadakis, M., "The geometry and the analytic properties of isotropic multiresolution analysis, " Advances in Computational Mathematics 31(1-3), 283-328 (2009).
20. Rasband, W., "ImageJ, " http://rsbweb.nih.gov/ij/.
21. Storath, M. and Held, S., "MonogenicWavelet Toolbox, " http://www.mamebia.de/Software/monogenicwavelets.html.
22. Jain, A. K., [Fundamentals of Digital Image Processing], Prentice Hall (1989).
23. Felsberg, M., "Optical flow estimation from monogenic phase, " in [Complex Motion], 3417/2007 (2007).
24. Adelson, E., "Checkershadow illusion, " http://web.mit.edu/ persci/people/adelson/checkershadowillusion.html.