The WaveD transform in R: Performs fast translation-invariant wavelet deconvolution

Journal of Statistical Software

Volumn 21, Issue 2, 2007, Pages 1-28

  Raimondo, Marc ^a   Stewart, Michael ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Deconvolution; Meyer wavelet; Vaguelettes; WaveD; Wavelets

Indexed keywords

EID: 35349011019     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v021.i02     Document Type: Article

References (27)

1. Abramovich F, Silverman BW (1998). "Wavelet Decomposition Approaches to Statistical Inverse Problems." Biometrika, 85(1), 115-129.
2. Aldrich E (2007). wavelets: A Package of Funtions for Computing Wavelet Filters, Wavelet Transforms and Multiresolution Analyses. R package version 0.2-2, URL http://www.atmos.Washington.edu/~ealdrich/wavelets/.
3. Bertero M, Boccacci P (1998). Introduction to Inverse Problems in Imaging. Institute of Physics, Bristol and Philadelphia.
4. Buckheit JB, Donoho D, Johnstone IM, Sargle JD (1995). WaveLab Reference Manual. Stanford University, Stanford, USA. URL http://www-stat.stanford.edu/~wavelab/.
5. Cavalier L, Koo JY (2002). "Poisson Intensity Estimation for Tomographic Data Using a Wavelet Shrinkage Approach." IEEE Transactions on Information Theory, 48, 2794-2802.
6. Cavalier L, Raimondo M (2006). "On Choosing Wavelet Resolution in Image Deblurring." In E Banissi, M Sarfraz, M Hunag, Q Wu (eds.), "Computer Graphics, Imaging and Visualisation 2006, Proceedings," pp. 177-181. IEEE Computer Society. ISBN 0-7695-2606-3.
7. Cavalier L, Raimondo M (2007). "Wavelet Deconvolution With Noisy Eigen-Values." IEEE Transactions on Signal Processing, 55(6), 2414-2424.
8. Donoho D (1995). "Nonlinear Solution of Linear Inverse Problems by Wavelet-Vaguelette Decomposition." Applied Computational and Harmonic Analysis, 2, 101-126.
9. Donoho D, Johnstone IM, Kerkyacharian G, Picard D (1995). "Wavelet Shrinkage: Asymptopia?" Journal of the Royal Statistical Society B, 57, 301-369. With discussion.
10. Donoho D, Raimondo M (2004). "Translation Invariant Deconvolution in a Periodic Setting." The International Journal of Wavelets, Multiresolution and Information Processing, 14(1), 415-423.
11. Donoho D, Raimondo M (2005). "A Fast Wavelet Algorithm for Image Deblurring." The Australian & New Zealand Industrial and Applied Mathematics Journal, 46, C29-C46. URL http://anziamj.austms.org.au/ V46/CTAC2004/Dono.
12. Fan J, Koo JK (2002). "Wavelet Deconvolution." IEEE Transactions on Information Theory, 48(3), 734-747.
13. Johnstone IM (1999). "Wavelet Shrinkage for Correlated Data and Inverse Problems: Adaptivity Results." Statistica Sinica, 9(1), 51-83.
14. Johnstone IM, Kerkyacharian G, Picard D, Raimondo M (2004). "Wavelet Deconvolution in a Periodic Setting." Journal of the Royal Statistical Society B, 66(3), 547-573. With discussion.
15. Johnstone IM, Raimondo M (2004). "Periodic Boxcar Deconvolution and Diophantine Approximation." The Annals of Statistics, 32(5), 1781-1804.
16. Kalifa J, Mallat S (2003). "Thresholding Estimators for Linear Inverse Problems and Deconvolutions." The Annals of Statistics, 31, 58-109.
17. Kerkyacharian G, Picard D, Raimondo M (2007). "Adaptive Boxcar Deconvolution on Full Lebesgue Measure Sets." Statistica Sinica, 17, 317-340.
18. Kolaczyk ED (1994). "Wavelet Methods for the Inversion of Certain Homogeneous Linear Operators in the Presence of Noisy Data." PhD dissertation. Department of Statistics, Stanford University, Stanford.
19. Mallat S (1998). A Wavelet Tour of Signal Processing. Academic Press Inc., San Diego, CA, 2nd edition. ISBN 0-12-466605-1.
20. Nason G, Kovac A, Mächler M (2006). wavethresh: Software to Perform Wavelet Statistics and Transforms. R package version 2.2-9.
21. O'Sullivan F (1986). "A Statistical Perspective on Ill-posed Inverse Problems." Statistical Science, 1, 502-527.
22. Pensky M, Vidakovic B (1999). "Adaptive Wavelet Estimator for Nonparametric Density Deconvolution." The Annals of Statistics, 27, 2033-2053.
23. Raimondo M, Stewart M (2006). waved: Software to Perform Wavelet Deconvolution. R package version 1.0, URL http://www.maths.usyd.edu. au/~marcr/.
24. Raimondo M, Tajvidi N (2004). "A Peaks Over Threshold Model for Change-Points Detection by Wavelets." Statistica Sinica, 14(1), 395-412.
25. R Development Core Team (2007). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/.
26. Walter GG, Shen X (1999). "Deconvolution Using the Meyer Wavelet." Journal of Integral Equations and Applications, 11, 515-534.
27. Whitcher B (2006). waveslim: Basic Wavelet Routines for One, Two and Three-Dimensional Signal Processing. R package version 1.6, URL http://www.image.ucar.edu/~whitcher/.