Dicussion on the meeting on 'Statistical approaches to inverse problems'

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 66, Issue 3, 2004, Pages 627-652

  Nason, Guy ^a   Moulines, Eric ^b   Robert, Christian P ^c   Andrieu, Christophe ^a   Stoffelen, Ad ^d   Paul, Debashis ^e   Abramovich, Felix ^f   Aykroyd, Robert G ^g   West, Robert M ^g   Meng, Sha ^g   Butucea, Cristina ^h   Cavalier, Laurent ⁱ   Cressie, Noel ^j   Davy, Manuel ^k   De Canditiis, Daniela ^l   Pensky, Marianna ^m   Golubev, Yu ⁱ   Hoffman, Ross N ⁿ   Khabie Zeitoune, Eliot ^o   Munk, A ^p   Ruymgaart, F H ^q   Olhede, S C ^r   Tsybakov, A ^s   Wahba, Grace ^t   Johnstone, Iain M ^u   Kerkyacharian, Gérard ^u   Picard, Dominique ^u   Raimondo, Marc ^u   Wolfe, Patrick J ^u   Godsill, Simon J ^u   Ng, Wee Jing ^u   Haario, H ^u   Laine, M ^u   Lehtinen, M ^u   Saksman, E ^u   Tamminen, J ^u   Cornford, Dan ^u   Csató, Lehel ^u   Evans, David J ^u   Opper, Manfred ^u   more..

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b TELECOM PARISTECH   (France)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

^d ROYAL NETHERLANDS METEOROLOGICAL INSTITUTE KNMI   (Netherlands)

^e STANFORD UNIVERSITY   (United States)

^f TEL AVIV UNIVERSITY   (Israel)

^g UNIVERSITY OF LEEDS   (United Kingdom)

^h UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

ⁱ AIX MARSEILLE UNIVERSITY   (France)

^j OHIO STATE UNIVERSITY   (United States)

^k Automat Syst Thermiques UMR C   (France)

^l CNR   (Italy)

^m UNIVERSITY OF CENTRAL FLORIDA   (United States)

ⁿ Atmospheric Environment Research Inc   (United States)

^o Computer Contract Consultants ^*  (United Kingdom)

^p UNIVERSITY OF GÖTTINGEN   (Germany)

^q TEXAS TECH UNIVERSITY   (United States)

^r IMPERIAL COLLEGE LONDON   (United Kingdom)

^s SORBONNE UNIVERSITÉ   (France)

^t UNIVERSITY OF WISCONSIN MADISON   (United States)

^u NONE

more..

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3543029866     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2004.2060d.x     Document Type: Conference Paper

References (75)

1. Abramovich, F., Benjamini, Y., Donoho, D. and Johnstone, I. (2000) Adapting to unknown sparsity by controlling false discovery rate. Technical Report 2000‐19. Department of Statistics, Stanford University, Stanford.
2. Abramovich, F. and Silverman, B. (1998) Wavelet decomposition approaches to statistical inverse problems. Biometrika, 85, 115–129.
3. Aghdasi, F. and Ward, R. (1996) Reduction of boundary artifacts in image restoration. IEEE Trans. Image Process., 5, 611–618.
4. Andrieu, C. and Moulines, E. (2002) On the ergodicity properties of some adaptive MCMC algorithms. Technical Report. University of Bristol, Bristol.
5. Andrieu, C. and Robert, C. P. (2001) Controlled MCMC for optimal sampling. Preprint.
6. Barber, S. and Nason, G. (2004) Real nonparametric regression using complex wavelets. J. R. Statist. Soc. B, to be published.
7. Bertero, M. and Boccacci, P. (1998) Introduction to Inverse Problems in Imaging. Philadelphia: Institute of Physics.
8. Bullen, R. J., Cornford, D. and Nabney, I. T. (2003) Outlier detection in scatterometer data: neural network approaches. Neur. Netwrks, 16, 419–426.
9. Butucea, C. (2004) Quadratic functional estimation and testing from noisy data. Preprint. Université Paris 6, Paris.
10. Butucea, C. and Tribouley, K. (2003) Nonparametric homogeneity tests. Preprint PMA‐871. Université Paris 6, Paris.
11. Candès, E. J. and Donoho, D. L. (2004) New tight frames of curvelets and optimal representations of objects with piecewise C 2 singularities. Communs Pure Appl. Math., 57, 219–266.
12. Cappé, O., Guillin, A., Marin, J. M. and Robert, C. P. (2004) Population Monte Carlo. J. Comput. Graph. Statist., to be published.
13. Casey, S. D. and Walnut, D. F. (1994) Systems of convolution equations, deconvolution, Shannon sampling, and the wavelet and Gabor transforms. SIAM Rev., 36, 537–577.
14. Cavalier, L. and Hengartner, N. W. (2003) Adaptive estimation for inverse problems with noisy operators. Manuscript.
15. Cavalier, L. and Tsybakov, A. (2001) Penalized blockwise Stein's method, monotone oracles and sharp adaptive estimation. Math. Meth. Statist., 10, 247–282.
16. Cavalier, L. and Tsybakov, A. (2002) Sharp adaptation for inverse problems with random noise. Probab. Theory Reltd Flds, 123, 323–354.
17. Choi, H. and Baraniuk, R. G. (2001) Multiscale image segmentation, using wavelet‐domain hidden markov models. IEEE Trans. Image Process., 10, 1309–1321.
18. Crouse, M. S., Nowak, R. D. and Baraniuk, R. G. (1998) Wavelet‐based statistical signal processing using hidden Markov models. IEEE Trans. Signal Process., 46, 886–902.
19. Csató, L., Opper, M. and Winther, O. (2002) TAP Gibbs free energy, belief propagation and sparsity. In Advan‐ ces in Neural Information Processing Systems, vol. 14 (eds T. G. Dietterich, S. Becker and Z. Ghahramani). Cambridge: MIT Press.
20. Dahlhaus, R. (1997) Fitting time series models to nonstationary processes. Ann. Statist., 25, 1–37.
21. Daubechies, I. (1995) Ten Lectures on Wavelets. Philadelphia: Society for Industrial and Applied Mathematics.
22. Davy, M. and Godsill, S. J. (2003) Bayesian harmonic models for musical signal analysis (with discussion). In Bayesian Statistics 7 (eds J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West). Oxford: Oxford University Press.
23. Diebolt, J. and Robert, C. P. (1994) Estimation of finite mixture distributions through Bayesian sampling. J. R. Statist. Soc. B, 56, 363–375.
24. Donoho, D. (1995) Nonlinear solution of linear inverse problems by wavelet‐vaguelette decomposition. Appl. Comput. Harm. Anal., 2, 101–126.
25. Donoho, D. and Raimondo, M. (2004) Translation invariant deconvolution in a periodic setting. Int. J. Wavlts Multiresoln Inform. Process., to be published.
26. Dörfler, M. (2001) Time‐frequency analysis for music signals: a mathematical approach. J. New Mus. Res., 30, 3–12.
27. Doucet, A., de Freitas, N. and Gordon, N. (2001) Sequential Monte Carlo Methods in Practice. New York: Springer.
28. Draper, D. W. and Long, D. G. (2002) An assessment of seawinds on QuikSCAT wind retrieval. J. Geophys. Res., 107.
29. Efromovich, S. and Koltchinskii, V. (2001) On inverse problems with unknown operators. IEEE Trans. Inform. Theory, 47, 2876–2893.
30. Geman, D. (1988) Random fields and inverse problems in imaging. Lect. Notes Math., 1427.
31. Gribonval, R. and Bacry, E. (2003) Harmonic decomposition of audio signals with matching pursuit. IEEE Trans. Signal Process., 51, 101–111.
32. Groetsch, C. W. (1977) Generalized Inverses of Linear Operators: Representation and Approximation. New York: Dekker.
33. Haario, H., Laine, M., Mira, A. and Saksman, E. (2003) DRAM: efficient adaptive MCMC. Report 374. University of Helsinki, Helsinki.
34. Haario, H., Saksman, E. and Tamminen, J. (1999) Adaptive proposal distribution for random walk Metropolis algorithm. Comput. Statist., 14, 375–395.
35. Haario, H., Saksman, E. and Tamminen, J. (2001) An adaptive Metropolis algorithm. Bernoulli, 7, 223–242.
36. Hall, P., Paige, R. and Ruymgaart, F. H. (2003) Using wavelet methods to solve noisy Abel‐type equations with discontinuous inputs. J. Multiv. Anal., 86, 72–96.
37. Hall, P., Ruymgaart, F., van Gaans, O. and van Rooij, A. (2001) Inverting noisy integral equations using wavelet expansions: a class of irregular convolutions. In State of the Art in Probability and Statistics (eds M. de Gunst, Ch. Klaassen and A. van der Vaart), pp. 533–546. Beachwood: Institute of Mathematics and Statistics.
38. Henderson, J. M., Hoffman, R. N., Leidner, S. M., Ardizzone, J. V., Atlas, R. and Brin, E. (2003) A comparison of a two‐dimensional variational analysis method and a median filter for NSCAT ambiguity removal. J. Geophys. Res., 108, 3176.
39. Hoffman, R. N. (1984) SASS wind ambiguity removal by direct minimization, II: Use of smoothness and dynamical constraints. Mnthly Weath. Rev., 112, 1829–1852.
40. Hoffman, R. N., Leidner, S. M., Henderson, J. M., Atlas, R., Ardizzone, J. V. and Bloom, S. C. (2003) A two‐dimensional variational analysis method for NSCAT ambiguity removal: methodology, sensitivity, and tuning. J. Atmos. Ocean. Technol., 20, 585–605.
41. Hopegood, R. J. and Rayner, J. W. (1999) Bayesian single channel blind deconvolution using parametric signal and channel models. IEEE Wrkshp Applications of Signal Processing, New York, Oct. 17th–20th.
42. Householder, A. S. (1964) The Theory of Matrices in Numerical Analysis. New York: Dover Publications.
43. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.‐C., Tung, C. C. and Liu, H. H. (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non‐stationary time series analysis. Proc. R. Soc. Lond. A, 454, 903–995.
44. Johnstone, I. M. and Paul, D. (2004) Rate adaptive estimation in linear inverse problems through penalized least squares procedure. Technical Report. Stanford University, Stanford.
45. Johnstone, I. M. and Raimondo, M. (2004) Periodic boxcar deconvolution and diophantine approximation. Ann. Statist., 32, no. 5, in the press.
46. Jones, R. H. and Vecchia, A. V. (1993) Fitting continuous ARMA models to unequally spaced spatial data. J. Am. Statist. Ass., 88, 947–954.
47. Kerkyacharian, G. and Picard, D. (2000) Thresholding algorithms and well‐concentrated bases. Test, 9, 283–344.
48. Kerkyacharian, G., Picard, D. and Raimondo, M. (2004) Adaptive boxcar deconvolution on full Lebesgue measure sets. Manuscript.
49. Khabie‐Zeitoune, E. (1982) Prediction in continuous time. In Time Series Analysis: Theory and Practice 2 (ed. O. D. Anderson), pp. 7–24. Amsterdam: North‐Holland.
50. Khinchin, A. Y. (1997) Continued Fractions. New York: Dover Publications.
51. Leidner, S. M., Isaksen, L. and Hoffman, R. N. (2003) Impact of NSCAT winds on tropical cyclones in the ECMWF 4D‐Var assimilation system. Mnthly Weath. Rev., 131, 3–26.
52. Lorenc, A. C. (1986) Analysis methods for NWP. Q. J. R. Meteorol. Soc., 112, 1177–1194.
53. Malfait, M. and Roose, D. (1997) Wavelet‐based image denoising using a Markov random field a priori model. IEEE Trans. Image Process., 6, 549–565.
54. Marron, J. S., Adka, S., Johnstone, I. M., Neumann, M. H. and Patil, P. (1998) Exact risk analysis of wavelet regression. J. Comput. Graph. Statist., 7, 278–309.
55. Nason, G. P., von Sachs, R. and Kroisandt, G. (2000) Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. J. R. Statist. Soc. B, 62, 271–292.
56. Neelamani, R., Choi, H. and Baraniuk, R. (2004) Fourier‐wavelet regularized deconvolution for ill‐conditioned systems. IEEE Trans. Signal Process., 52, 418–433.
57. Ng, W.‐J. (2000) Noise reduction for audio signals using the Gabor expansion. MPhil Thesis. University of Cambridge, Cambridge.
58. Pensky, M. and Zayed, A. I. (2002) Density deconvolution of different conditional distributions. Ann. Inst. Statist. Math., 54, 701–712.
59. Portilla, J., Strela, V., Wainwright, M. and Simoncelli, E. (2003) Image denoising using scale mixtures of gaussians in the wavelet domain. IEEE Trans. Image Process., 12, 1338–1351.
60. Robert, C. P. and Casella, G. (2004) Monte Carlo Statistical Methods, 2nd edn. New York: Springer.
61. Robinson, E. A. (1967) Multichannel Time Series Analysis with Digital Computer Programs. San Francisco: Holden‐Day.
62. Royle, J., Berliner, L., Wikle, C. and Milliff, R. (1998) A hierarchical spatial model for constructing wind fields from scatterometer data in the Labrador sea. In Case Studies in Bayesian Statistics IV, pp. 367–382. New York: Springer.
63. Sardy, S. (2000) Minimax thresholds for denoising complex signals with waveshrink. IEEE Trans. Signal Process., 48, 1023–1028.
64. Schultz, H. (1990) A circular median filter approach for resolving directional ambiguities in wind fields retrieved from spaceborne scatterometer data. J. Geophys. Res., 95, 5291–5304 ; erratum, 9783.
65. Shaffer, S. J., Dunbar, R. S., Hsiao, S. V. and Long, D. G. (1991) A median‐filter‐based ambiguity removal algorithm for NSCAT. IEEE Trans. Geosci. Remote Sens., 29, 167–174.
66. Stoffelen, A. and Anderson, D. (1997) Ambiguity removal and assimilation of scatterometer data. Q. J. R. Meteorol. Soc., 123, 491–518.
67. Tamminen, J. (2004) Validation of nonlinear inverse algorithms with Markov chain Monte Carlo method. To be published.
68. Thépaut, J.‐N., Hoffman, R. N. and Courtier, P. (1993) Interactions of dynamics and observations in a four‐dimensional variational assimilation. Mnthly Weath. Rev., 121, 3393–3414.
69. de Vries, J. C. W. and Stoffelen, A. C. M. (2000) 2D variational ambiguity removal. Technical Report 226. Royal Netherlands Meteorological Institute, De Bilt.
70. Wahba, G. and Wang, Y. (1990) When is the optimal regularization parameter insensitive to the choice of the loss function ? Communs Statist. Theory Meth., 19, 1685–1700.
71. Wainwright, M., Simoncelli, E. and Willsky, A. (2001) Random cascades on wavelet trees and their use in analyzing and modeling natural images. Appl. Comput. Harm. Anal., 11, 89–123.
72. West, R. M., Aykroyd, R. G., Meng, S. and Williams, R. A. (2004) MCMC techniques and spatial temporal modelling for medical EIT. Physiol. Measmnts, 25, 181–194.
73. West, R. M., Meng, S., Aykroyd, R. G. and Williams, R. A. (2003) Spatial‐temporal modelling for electrical impedance imaging of a mixing process. In Proc. 3rd Wrld Congr. Industrial Process Tomography, Banff, pp. 226–232.
74. Wolfe, P. J. and Godsill, S. J. (2003) Bayesian estimation of time‐frequency coefficients for audio signal enhancement. In Advances in Neural Information Processing Systems, vol. 15 (eds S. Becker, S. Thrun and K. Obermayer). Cambridge: MIT Press.
75. Zemanian, A. H. (1987) Generalized Integral Transformations. New York: Dover Publications.