A fast computation method for time scale signal denoising

Signal, Image and Video Processing

Volumn 3, Issue 1, 2009, Pages 63-83

  Bruni, Vittoria ^a   Piccoli, Benedetto ^a   Vitulano, Domenico ^a  

^a CNR   (Italy)

Author keywords

Image and signal denoising; Modulus maxima representation; Time frequency atoms; Time scale trajectories; Wavelet transform

Indexed keywords

COMPUTING TIME; FAST COMPUTATION; FILTERING OPERATIONS; IMAGE AND SIGNAL DENOISING; LEAST SQUARE; LOCAL EXTREMUM; MODULUS MAXIMA REPRESENTATION; NUMERICAL SOLUTION; PROJECTION SPACE; SIGNAL DENOISING; SPEED-UPS; TIME FREQUENCY ATOMS; TIME SCALE TRAJECTORIES; TIME-SCALES; VISUAL QUALITIES; WAVELET COEFFICIENTS; WAVELET DOMAIN;

ATOMS; DIFFERENTIAL EQUATIONS; SIGNAL PROCESSING; SIGNAL TO NOISE RATIO; TIME MEASUREMENT; WAVELET TRANSFORMS;

DIFFERENCE EQUATIONS;

EID: 68249140854     PISSN: 18631703     EISSN: 18631711     Source Type: Journal    
DOI: 10.1007/s11760-008-0060-9     Document Type: Article

References (42)

1. Balster, E.J., Zheng, Y.F., Ewing, R.L.: Feature-based wavelet shrinkage algorithm for image denoising. IEEE Trans. Image Process. vol. 14, No. 12 (2005).
2. Bruni, V., Vitulano, D.: Wavelet based signal denoising via simple singularities approximation. Signal Processing, vol. 86, pp. 859-876. Elsevier Science, Amsterdam (2006).
3. Bruni, V., Piccoli, B., Vitulano, D.: Scale space atoms for signals and image de-noising. In: IAC Report (2006).
4. Chang S.G., Bin Yu, Vetterli M.: Spatially adaptive thresholding with context modeling for image denoising. IEEE Trans. Image Process. 9(9), 1522-1530 (2000).
5. Choi, H., Baraniuk, R.: Analysis of wavelet-domain wiener filters. In: Proceedings of the IEEE-SP International Symposium on Time-frequency and Time-scale Analysis, October (1998).
6. Crouse M.S., Nowak R.D., Baraniuk R.G.: Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. Signal Process. 46(4), 886-902 (1998).
7. Donoho D.L., Johnstone I.M.: Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425-455 (1994).
8. Donoho D.L.: Denoising by soft thresholding. IEEE Trans. Inform. Theory 41(3), 613-627 (1995).
9. Dragotti, P.L., Vetterli, M.: Footprints and edgeprints for image denoising and compression. In: Proceedings of IEEE International Conference on Image Processing (ICIP), Thessaloniki, Greece, October (2001).
10. Dragotti P.L., Vetterli M.: Wavelet footprints: theory, algorithms and applications. IEEE Trans. Signal Process. 51(5), 1306-1323 (2003).
11. Fan G., Xia X.: Image denoising using a local contextual hidden Markov model in the wavelet domain. IEEE Signal Process. Lett. 8(5), 125-128 (2001).
12. Gilboa G., Sochen N., Zeevi Y.Y.: Image enhancement and denoising by complex diffusion processes. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1020-1036 (2004).
13. Kazubek M.: Wavelet domain image denoising by thresholding and wiener filtering. IEEE Signal Process. Lett. 10(11), 324-326 (2003).
14. Kervrann, C., Boulanger, J.: Unsupervised patch-based image regularization and representation. In: Proceedings of European Conf. Comp. Vision (ECCV'06), Graz, Austria, May (2006).
15. Koenderink J.: The structure of images. Biol. Cybern. 50, 363-370 (1984).
16. Jaffard, S., Meyer, Y., Ryan, R.D.: Wavelets: Tools for Science and Technology. SIAM, Philadelphia (2001).
17. Lin, X., Orchard, M.T.: Spatially adaptive image denoising under overcomplete expansion. In: Proceedings of IEEE International Conference on Image Processing, September (2000), pp. 300-303.
18. Mallat, S., Hwang, W.L.: Singularity detection and processing with wavelets. IEEE Trans. Inform. Theory, vol. 38, No. 2, March (1992).
19. Mallat S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1998).
20. Mallat S., Zhong S.: Characterization of signals from multiscale edges. IEEE Trans. Pattern Anal. Mach. Intell. 14, 710-732 (1992).
21. Mihcak M.K., Kozintsev I., Ramchandran K., Moulin P.: Low-complexity image denoising based on statistical modeling of wavelet coefficients. IEEE Signal Process. Lett. 6(12), 300-303 (1999).
22. Perona P., Malik J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629-639 (1990).
23. Petrovic, A., Escoda, O.D., Vandergheynst, P.: Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations. IEEE Trans. Image Process., vol. 13, No. 8, August (2004).
24. Pizurica, A., Philips, W., Lemanhieu, I., Acheroy, M.: A joint inter- and intrascale statistical model for bayesian wavelet based image denoising. IEEE Trans. Image Process., vol. 11, No. 5, May 2002.
25. Portilla J., Strela V., Wainwright M., Simoncelli E.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338-1351 (2003).
26. Shih A.C., Liao H.M., Lu C.: A new iterated two-band diffusion equation: theory and its application. IEEE Trans. Image Process. 12(4), 466-476 (2003).
27. Rosenfeld, A., Thurston, M.: Edge and curve detection for visual scene analysis. IEEE Transactions on Comput., vol. C-20, May 1971, pp. 562-569.
28. Sendur, L., Selesnick, I.W.: Bivariate shrinkage with local variance estimation. IEEE Signal Process. Lett., vol. 9, No. 12, December (2002).
29. Shui P.L.: Image denosing algorithm via doubly local wiener filtering with directional windows in wavelet domain. IEEE Signal Process. Lett. 12(10), 681-684 (2005).
30. Teboul S., Blanc-Feraud L., Aubert G., Barlaud M.: Variational approach for edge-preserving regularization using coupled PDE's. IEEE Trans. Image Process. 7(3), 387-397 (1998).
31. Mrazek P., Weickert J., Steidl G.: Diffusion-inspired shrinkage functions and stability results for wavelet denoising. Int. J. Comput. Vis. 64(2/3), 171-186 (2005).
32. Witkin, A.: Scale-space filtering. In: Proceedings of the International Joint Conf. Artificial Intelligence, Karlsruhe, West Germany, pp. 1019-1021 (1983).
33. Zhang, H., Nosratinia, A., Wells, R.O.: Image denoising via wavelet-domain spatially adaptive FIR wiener filtering. In: Proceedings of IEEE International Conf. on Acoustic Speech and Signal Processing 2000, vol. 5, Istanbul, Turkey, June 2000, pp. 2179-2182.
34. Voloshynovskiy, S., Koval, O., Pun, T.: Image denoising based on the edge-process model. Signal Processing, Elsevier Science, Amsterdam (2006).
35. Wei J.: Lebesgue Anisotropic Image Denoising. Wiley Periodicals Inc., London (2005).
36. Pizurica, A., Philips, W.: Estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising. IEEE Trans. Image Process. (2007).
37. Charest, M.R., Elad, M., Milanfar, P.: A general iterative regularization framework for image denosing. In: Proceedings of the 40th Conference on Information Sciences and Systems, Princeton, NJ, March (2006).
38. Luisier, F., Blu, T., Unser, M.: A new SURE approach to image denoising: interscale orthonormal wavelet thresholding. IEEE Trans. Image Process., vol. 16, No. 3, March (2007).
39. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms with a new one. Multiscale Model. Simul., vol. 4, No. 2, Society for industrial and Applied Mathematics, pp. 490-530 (2005).
40. Elad, M., Aharon, M.: Image denoising via learned dictionaries and sparse representation. In: Proceedings of IEEE CVPR'06 (2006).
41. Foi, A., Katkovnik, V., Egiazarian, K.: Pointwise shape adaptive DCT for high quality denoising and deblocking og grayscale and color images. IEEE Trans. Image Process., vol. 16, No. 5, May (2007).
42. Bruni, V., Piccoli, B., Vitulano, D.: Wavelet time-scale dependencies for signal and image compression. In: Proceedings of IEEE International Conference ISPA 2005, Zagreb, pp. 105-110 (2005).