Resolution enhancement of spectra using differentiation

Inverse Problems

Volumn 21, Issue 3, 2005, Pages 915-934

  Hegland, Markus ^a   Anderssen, Robert S ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; ERROR ANALYSIS; ESTIMATION; INFRARED SPECTROSCOPY; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; PROBABILITY; PROBLEM SOLVING; STATISTICAL METHODS;

HILBERT SPACE FRAMEWORK; NONLINEAR FITTING METHOD; SPECTRAL LINES; TAYLOR SERIES;

SPECTRUM ANALYSIS;

EID: 18744364427     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/3/008     Document Type: Article

References (18)

1. Allen L, Gladney H and Glarum S 1964 Resolution enhancement for spectra of chemical and physical interest J. Chem. Phys. 40 3135-41
2. Anderssen B, de Hoog F and Hegland M 1998 A stable finite difference ansatz for higher order differentiation of non-exact data Bull. Austral. Math. Soc. 58 223-32
3. Fearn T, Osborne B G and Hindle P H 1993 Practical NIR Spectroscopy (Harlow: Longman)
4. Björck Åke 1996 Numerical Methods for Least Squares Problems (Philadelphia, PA: SIAM)
5. Pappin D J C, Hojrup P and Bleasby A J 1993 Rapid identification of proteins by peptide-mass fingerprinting Curr. Biol. 3 327-32
6. ak(x, s)dg(s) Combining double low line u(x) Sov. Math. Dokl. 11 901-3
7. Hegland M 1995 Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization Appl. Anal. 59 207-23
8. Hollas J M 1992 Modern Spectroscopy 2nd edn (New York: Wiley)
9. Kahn M H, Mackisack M S, Osborne M R and Smyth G K 1992 On the consistency of Prony's method and related algorithms J. Comput. Graph. Statist. 1 329-49
10. Krein S G and Petunin Yu I 1966 Scales of Banach spaces Russ. Math. Surv. 21 85-159
11. Maddams W F 1980 The scope and limitations of curve fitting Appl. Spectrosc. 34 245-67
12. Micchelli C A and Rivlin T J 1977 A survey of optimal recovery Optimal Estimation in Approximation Theory (Proc. Int. Symp. (Freudenstadt 1976)) (New York: Plenum) pp 1-54
13. Milanfar P and Shakouri A 2002 A statistical analysis of diffraction-limited imaging Proc. 2002 Int. Conf. on Image Processing (Piscataway, NJ: IEEE) pp I-864-I-867
14. Tautenhahn U 1996 Error estimates for regularization methods in Hilbert scales SIAM J. Numer. Anal. 33 2120-30
15. Tihonov A N, Goncharsky A V, Stepanov V V and Yagola A G 1995 Numerical Methods for the Solution of Ill-Posed Problems (Dordrecht: Kluwer)
16. Wahba G 1990 Spline Models for Observational Data CBMS vol 59 (Philadelphi, PA: SIAM)
17. Wand M P and Jones M C 1995 Kernel Smoothing (Monographs on Statistics and Applied Robability vol 60) (London: Chapman and Hall)
18. Warren K E 2004 Nmr spectroscopy and pediatric brain tumors The Oncologist 9 312-8