Mathematical concepts of multiscale smoothing

Applied and Computational Harmonic Analysis

Volumn 19, Issue 2, 2005, Pages 141-161

  Bredies, Kristian ^a   Lorenz, Dirk A ^a   Maass, Peter ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Evolution equations; Image smoothing; Multiscale methods; Wavelet transform

Indexed keywords

DIFFERENTIAL EQUATIONS; FOURIER TRANSFORMS; LINEAR EQUATIONS; WAVELET TRANSFORMS;

CONVOLUTION FILTERING; EVOLUTION EQUATION; IMAGE SMOOTHING; MULTISCALE METHODS;

IMAGE PROCESSING;

EID: 24044447221     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.acha.2005.02.007     Document Type: Article

References (28)

1. L. Alvarez, F. Guichard, P.-L. Lions, and J.-M. Morel Axioms and fundamental equations in image processing Arch. Rat. Mech. Anal. 123 1993 199 257
2. A. Antoniadis, and J. Fan Regularization of wavelet approximations J. Amer. Statist. Assoc. 96 455 2001 939 967
3. H. Brezis Opérateurs maximaux monotones et semi-groups de contractions dans les espaces de Hilbert North-Holland Mathematics Studies vol. 5 1973 North-Holland
4. B. Burgeth, and J. Weickert An explanation for the logarithmic connection between linear and morphological systems L.D. Griffin M. Lillholm Scale Space Methods in Computer Vision Lecture Notes in Computer Science vol. 2695 2003 Springer 325 339
5. A. Chambolle, R.A. DeVore, N. Lee, and B.J. Lucier Nonlinear wavelet image processing: Variational problems, compression and noise removal through wavelet shrinkage IEEE Trans. Image Process. 7 1998 319 335
6. A. Chambolle, and B.J. Lucier Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space IEEE Trans. Image Process. 10 2001 993 1000
7. R.R. Coifman, and D.L. Donoho Translation-invariant de-noising A. Antoniadis G. Oppenheim Wavelets and Statistics Springer Lecture Notes in Statistics vol. 103 1995 Springer-Verlag 125 150
8. L. Şendur, and I.W. Selesnick Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency IEEE Trans. Signal Process. 50 11 2002 2744 2756
9. D.L. Donoho Denoising via soft thresholding IEEE Trans. Inform. Theory 41 3 1995 613 627
10. D.L. Donoho, and I.M. Johnstone Minimax estimation via wavelet shrinkage Ann. Statist. 26 3 1998 879 921
11. D.L. Donoho, I.M. Johnstone, Minimax estimation via wavelet shrinkage, Technical report 402, Department of Statistics, Stanford University, 1992
12. D.L. Donoho, I.M. Johnstone, G. Kerkyacharian, D. Picard, Density estimation by wavelet thresholding, Technical report, Department of Statistics, Stanford University, 1993
13. D.L. Donoho, I.M. Johnstone, G. Kerkyacharian, and D. Picard Density estimation by wavelet thresholding Ann. Statist. 24 2 1996
14. R. Duits, L. Florack, J. de Graaf, and B.M. ter Haar Romeny On the axioms of scale space theory J. Math. Imaging Vision 20 2004 267 298
15. I. Ekeland, and R. Temam Convex Analysis and Variational Problems 1976 North-Holland Amsterdam
16. M.A.T. Figueiredo, and R.D. Nowak Wavelet-based image estimation: An empirical Bayes approach using Jefferey's noninformative prior IEEE Trans. Image Process. 10 9 2001 1322 1331
17. H.-Y. Gao Wavelet shrinkage denoising using the non-negative garrote J. Comput. Graph. Statist. 7 4 1998 469 488
18. H.-Y. Gao, A.G. Bruce. WaveShrink with semisoft shrinkage, Technical report, StatSci Division of MathSoft, Inc., 1995
19. A. Hyvärinen, P. Hoyer, and E. Oja Image denoising by sparse code shrinkage S. Haykin B. Kosko Intelligent Signal Processing 2001 IEEE Press
20. A. Hyvärinen, P. Hoyer, and E. Oja Sparse code shrinkage: Denoising by nonlinear maximum likelihood estimation Adv. Neural Inform. Process. Syst. 11 1999 473 479
21. D.A. Lorenz, Methoden der Multiskalenglättung, Ms. thesis, Universität Bremen, 2002
22. P. Moulin, and J. Liu Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors IEEE Trans. Inform. Theory 45 3 1999 909 919
23. P. Perona, and J. Malik Scale-space and edge detection using anisotropic diffusion IEEE Trans. Pattern Anal. Mach. Intelligence 12 7 1990 629 639
24. L.I. Rudin, S.J. Osher, and E. Fatemi Nonlinear total variation based noise removal algorithms Physica D 60 1992 259 268
25. G. Steidl, J. Weickert, T. Brox, P. Mrazek, and M. Welk On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization and SIDEs SIAM J. Numer. Anal. 42 2 2004 658 686
26. J.B. Weaver, Y. Xu, D.M. Healy, and L.D. Cromwell Filtering noise from images with wavelet transforms Magn. Reson. Medicine 21 1991 288 295
27. J. Weickert Anisotropic Diffusion in Image Processing 1998 Teubner Stuttgart
28. E. Wilczok New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform Doc. Math. 5 2000 201 226