Superresolution rates in Prokhorov metric

Canadian Journal of Mathematics

Volumn 48, Issue 2, 1996, Pages 316-329

  Doukhan, P ^a,b   Gamboa, F ^a,b,c  

^a CNRS   (France)

^b Bât 425   (France)

^c UNIVERSITÉ PARIS 13   (France)

Author keywords

Generalized moments; Prokhorov metric; Superresolution; T systems

Indexed keywords

EID: 0030508129     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1996-017-9     Document Type: Article

References (20)

1. F. Altomare and M. Campiti, Korovkin-type approximation theory and its applications, Walter de Gruyter-Berlin, 1994.
2. 2}, Constr. Approx, 3(1987), 257-263.
3. _, Weak convergence and the Prokhorov radius, J. Math. Anal. Appl. 163(1992), 541-558.
4. R. De Vore R and G. G. Lorentz, Constructive Approximation, Springer Verlag, New York, 1993.
5. D. Donoho, Superresolution via sparsity constraints, SIAM J. Math. Anal. 5(1992), 1309-1331.
6. D. Donoho and E. Gassiat, Superresolution via positivity constraints, 1992, preprint.
7. D. Donoho, I. Johnstone, J. Hoch and Stern, Maximum entropy and the nearly black object, J. Roy. Statist. Soc. Ser. B 54(1992), 41-82.
8. F. Gamboa and E. Gassiat, The maximum entropy method on the mean: Applications to linear programming and Superresolution, Math. Programming, Series A 66(1994), 103-122.
9. _, Bayesian methods for ill posed problems, Ann. Statist. (1996), to appear.
10. _, Sets of Superresolution and the maximum entropy method on the mean, SIAM J. Math. Anal., 1996, to appear.
11. E. Gassiat, Problème sommatoire par maximum d'entropie, C. R. Acad. Sci. Paris Sér. I 303(1986), 675-680.
12. _, Problème des moments et concentration de mesure, C. R. Acad. Sci. Paris Sér. I 310(1990), 41-44.
13. P. A. Jansson, Deconvolution, With Applications in Spectroscopy, New York, Academic Press, 1984.
14. S. Karlin and W. J. Studden, Tchebycheff Systems: With Applications in Analysis and Statistics, John Wiley and Sons, 1966.
15. M. G. Krein and A. A. Nudel'man, The Markov moment problem and extremal problems, Amer. Math. Soc., 1977.
16. A. S. Lewis, Consistency of moment systems, J. Math. Anal. Appl. (1996), to appear.
17. _, Superresolution in the Markov moment problem, 1993, preprint.
18. J. Milnor, Morse theory, Princeton Univ. Press, 1963.
19. J. Navaza, Use of non local constraints in maximum entropy electron reconstruction, Acta Cryst. Sect. A 42(1986), 212-222.
20. Y. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1(1956), 157-214.