The pairing of a wavelet basis with a mildly redundant analysis via subband regression

IEEE Transactions on Image Processing

Volumn 17, Issue 11, 2008, Pages 2040-2052

  Unser, Michael ^a   Van De Ville, Dimitri ^a  

^a EPFL   (Switzerland)

Author keywords

Denoising; Feature detection; Fractals; Frames; Isotropy; Mexican hat filter; Pyramid; Wavelets

Indexed keywords

CURVE FITTING; KETONES; WAVE FILTERS; WAVELET ANALYSIS;

DENOISING; FEATURE DETECTION; FRAMES; ISOTROPY; MEXICAN-HAT FILTER; PYRAMID; WAVELETS;

WAVELET TRANSFORMS;

ALGORITHM; ARTICLE; ARTIFACT; COMPUTER ASSISTED DIAGNOSIS; FRACTAL ANALYSIS; IMAGE ENHANCEMENT; METHODOLOGY; REGRESSION ANALYSIS; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; VIDEORECORDING;

ALGORITHMS; ARTIFACTS; FRACTALS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; REGRESSION ANALYSIS; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; VIDEO RECORDING;

EID: 54949124883     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2008.2004607     Document Type: Article

References (42)

1. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, "Image coding using wavelet transform," i IEEE Trans. Image Process., vol. 1, no. 2, pp. 205-220, Apr. 1992.
2. C. Christopoulos, A. Skodras, and T. Ebrahimi, "The JPEG2000 still image coding system: An overview," IEEE Trans. Consum. Electron., vol. 16, no. 4, pp. 1103-1127, Apr. 2000.
3. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
4. S.G. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1522-1531, Sep. 2000.
5. L. Sendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency," IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2744-2756, Nov. 2002.
6. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, "Image denoising using scale mixtures of gaussians in the wavelet domain," IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338-1351, Nov. 2003.
7. M.A.T. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 906-916, Aug. 2003.
8. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol. 57, pp. 1413-1457, 2004.
9. S. Mallat and W. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 617-643, Feb. 1992.
10. G. W. Wornell, "Wavelet-based representations for the 1/f family of fractal processes," Proc. IEEE, vol. 81, no. 10, pp. 1428-1450, Oct. 1993.
11. S. G. Mallat, "A theory of multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 11, no. 7, pp. 6744593, Jul. 1989.
12. O. Rioul, "A discrete-time multiresolution theory," IEEE Trans. Signal Process., vol. 41, no. 8, pp. 2591-2606, Aug. 1993.
13. R. R. Coifman and D. L. Donoho, Wavelets and Statistics. Berlin, Germany: Springer-Verlag, 1995, ch. Translation-Invariant De-noising, pp. 125-150.
14. P. Dutilleux, Wavelets: Time-Frequency Methods and Phase Space. New York: Springer-Verlag, 1989, ch. An Implementation of the Algorithme à trous to Compute the Wavelet Transform, pp. 298-304.
15. M.J. Shensa, "The discrete wavelet transform: Wedding the à trous and Mallat algorithms," IEEE Trans. Signal Process., vol. 40, no. 10, pp. 2464-2482, Oct. 1992.
16. M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells Jr., "Noise reduction using an undecimated discrete wavelet transform," IEEE Signal Process. Lett., vol. 3, no. 1, pp. 10-12, Jan. 1996.
17. M. Unser, "Texture classification and segmentation using wavelet frames," IEEE Trans. Image Process., vol. 4, no. 11, pp. 1549-1560, Nov. 1995.
18. N. G. Kingsbury, "Complex wavelets for shift invariant analysis and filtering of signals," J. Appl. Comput. Harmon. Anal., vol. 10, no. 3, pp. 234-253, May 2001.
19. I. W. Selesnick, R. G. Baraniuk, and N. C. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, Jun. 2005.
20. E. P. Simoncelli and W. T. Freeman, "The steerable pyramid: A flexible architecture for multi-scale derivative computation," in Proc. Int. Conf. Image Processing, 1995, vol. 3, pp. 444-447.
21. B. Yang and Z. Jing, "A simple method to build oversampled filter banks and tight frames," IEEE Trans. Image Process., vol. 16, no. 11, pp. 2682-2687, Nov. 2007.
22. M. Unser, "An improved least squares Laplacian pyramid for image compression," Signal Process., vol. 27, no. 2, pp. 187-203, May 1992.
23. E. Viscito and J. P. Allebach, "The analysis and design of multidimensional fir perfect reconstruction filter banks for arbitrary sampling lattices," IEEE Trans. Circuits Syst., vol. 38, no. 1, pp. 29-42, Jan. 1991.
24. S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA: Academic, 1998.
25. n," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 533-555, Mar. 1992.
26. D. Van De Ville, T. Blu, and M. Unser, "Isotropic polyharmonic b-splines: Scaling functions and wavelets," IEEE Trans. Image Process., vol. 14, no. 11, pp. 1798-1813, Nov. 2005.
27. F. Luisier, T. Blu, and M. Unser, "A new SURE approach to image denoising: Interscale orthonormal wavelet thresholding," IEEE Trans. Image Process., vol. 16, no. 3, pp. 593-606, Mar. 2007.
28. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, Dec. 1995.
29. S. Ramani, T. Blu, and M. Unser, "Monte-Carlo SURE: A black-box optimization of regularization parameters for general denoising algorithm," IEEE Trans. Image Process, vol. 17, no. 9, pp. 1540-1554, Sep. 2008.
30. C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, "The colored revolution of bioimaging," IEEE Signal Process. Mag., vol. 23, no. 3, pp. 20-31, May 2006.
31. M. Unser and A. Aldroubi, "A review of wavelets in biomedical applications," Proc. IEEE, vol. 84, no. 4, pp. 626-638, Apr. 1996.
32. R. Strickland and H. I. Hahn, "Wavelet transform methods for object detection and recovery," IEEE Trans. Image Process., vol. 6, no. 5, pp. 724-735, May 1997.
33. A. Laine, S. Schuler, J. Fan, and W. Huda, "Mammographic feature enhancement by multiscale analysis," IEEE Trans. Med. Imag., vol. 13, no. 4, pp. 725-740, Apr. 1994.
34. R. Strickland and H. I. Hahn, "Wavelet transforms for detecting microcalcifications in mammograms," IEEE Trans. Med. Imag., vol. 15, no. 2, pp. 218-229, Apr. 1996.
35. J.-C. Olivo-Marin, "Extraction of spots in biological images using multiscale products," Pattern Recognit., vol. 35, no. 9, pp. 1989-1996, 2002.
36. A. Genovesio, T. Liedl, V. Emiliam, W. Parak, M. Coppey-Moisan, and J.-C. Olivo-Marin, "Multiple particle tracking in 3 - d + t microscopy: Method and application to the tracking of endocytosed quantum dots," IEEE Trans. Image Process., vol. 15, no. 5, pp. 1062-1070, May 2006.
37. J. Kybic, T. Blu, and M. Unser, "Generalized sampling: A variational approach - Part I: Theory," IEEE Trans. Signal Process., vol. 50, no. 8, pp. 1965-1976, Aug. 2002.
38. B. Pesquet-Popescu and J. L. Véhel, "Stochastic fractal models for image processing," IEEE Signal Process. Mag., vol. 19, no. 5, pp. 48-62, 2002.
39. S. Tirosh, D. Van De Ville, and M. Unser, "Polyharmonic smoothing splines and the multidimensional Wiener filtering of fractal-like signals," IEEE Trans. Image Process., vol. 15, no. 9, pp. 2616-2630, Sep. 2006.
40. W. B. Richardson Jr., "Applying wavelets to mammograms," IEEE Eng. Med. Biol. Mag., vol. 14, no. 5, pp. 551-560, May 1995.
41. D. Sage, F. Neumann, F. Hediger, S. Gasser, and M. Unser, "Automatic tracking of individual fluorescence particles: Application to the study of chromosome dynamics," IEEE Trans. Image Process., vol. 14, no. 9, pp. 1372-1383, Sep. 2005.
42. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multiscale transforms," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 587-607, Feb. 1992.