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DOI: 10.1039/A608255F (Paper) Reference Section for: Analyst, 1997, 122, 645-652

Wavelet Denoising of Infrared Spectra

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Bjørn K. Alsberg, Andrew M. Woodward, Michael K. Winson, Jem Rowland and Douglas B. Kell

Abstract

The application of wavelet denoising to infrared spectra was investigated. Six different wavelet denoising methods (SURE, VISU, HYBRID, MINMAX, MAD and WAVELET PACKETS) were applied to pure infrared spectra with various added levels of homo- and heteroscedastic noise. The performances of the wavelet denoising methods were compared with the standard Fourier and moving mean filtering in terms of root mean square errors between the pure and denoised spectra and visual quality of the denoised spectrum. The use of predictive ability as a possible objective criterion for denoising performance was also investigated. The main conclusion is that for very low signal-to-noise ratios (S/N) the standard denoising methods (Fourier and moving mean) are comparable to the more sophisticated methods. At higher S/N levels the wavelet denoising methods, in particular the HYBRID and VISU methods, are better. Wavelet methods are also better in restoring the visual quality of the denoised infrared spectra.

References

  1. P. B. Stark, M. M. Herron and A. Matteson, Applied Spectrosc., 1993, 47, 1820 Search PubMed.
  2. B. Walczak, B. van den Bogaert and D. L. Massart, Anal. Chem., 1996, 68, 1742 CrossRef CAS.
  3. J. Berger, R. R. Coifman and M. J. Goldberg, J. Audio-Eng. Soc., 1994, 42, 808 Search PubMed.
  4. R. R. Coifman and M. V. Wickerhauser, Opt. Eng., 1994, 33, 2170.
  5. D. L. Donoho and I. M. Johnstone, C.R. Acad. Sci., Ser. I., 1994, 319, 1317 Search PubMed.
  6. D. M. Healy, J. Lu and J. B. Weaver, Ann. Biomed. Eng., 1995, 23, 637.
  7. X. Paternot, Signal Processing via Wavelet and Identification, Massachusetts Institute of Technology Laboratory for Information and Decision Systems, Cambridge, MA, 1996 Search PubMed.
  8. Wavelet Transform Applications to Data, Signal, Image, and Video Processing: September 11–15, 1995, Engineering 867.121, University of California Los Angeles University Extension Department of Engineering Information Systems and Technical Management Short Course Program, Los Angeles, CA, 1995 Search PubMed.
  9. Wavelet Applications in Signal and Image Processing II: 27–29 July 1994, San Diego, California, SPIE, Bellingham, WA, 1994 Search PubMed.
  10. R. K. Young, Wavelet Theory and its Applications, Kluwer, Boston, 1993 Search PubMed.
  11. I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992 Search PubMed.
  12. I. Daubechies and A. Grossmann, Commun. Pure Appl. Math., 1988, 41, 151 Search PubMed.
  13. A. Teolis and J. J. Benedetto, Signal Process., 1995, 45, 369 CrossRef.
  14. M. Cartwright, Fourier Methods for Mathematicians, Scientists and Engineers, Ellis Horwood, New York, 1990 Search PubMed.
  15. S. Mallat, IEEE Trans. Pattern Anal. Machine Intell., 1989, 11, 674 CrossRef.
  16. S. Mallat, Trans. Am. Math. Soc., 1989, 315, 69 and 18 215 Search PubMed.
  17. G. Davis, S. Mallat and Z. F. Zhang, Opt. Eng., 1994, 33, 2183.
  18. M. A. Cody, Dr. Dobbs J., 1994, 19, 44 Search PubMed.
  19. J. Berger, R. R. Coifman and M. J. Goldberg, J. Audio-Eng. Soc., 1994, 42, 808 Search PubMed.
  20. C. H. H. Chu, Opt. Eng., 1994, 33, 2136.
  21. C. K. Chui and C. Li, SIAM J. Math. Anal., 1993, 24, 712 Search PubMed.
  22. D. L. Donoho, in Different Perspectives on Wavelets, ed. Daubechies, I., American Mathematical Society, Providence, RI, 1993, pp. 173–205 Search PubMed.
  23. B. Jawerth and W. Sweldens, SIAM Rev., 1994, 36, 377 Search PubMed.
  24. A. Laine and J. Fan, IEEE Trans. Pattern Anal. Machine Intell., 1993, 15, 1186 CrossRef.
  25. C. V. Lambrecht and M. Karrakchou, Signal Process., 1995, 47, 135 CrossRef.
  26. R. E. Learned and A. S. Willsky, Appl. Comput. Harmonic Anal., 1995, 2, 265 Search PubMed.
  27. D. Park and M. H. Lee, IEEE Trans. Consumer Electron., 1994, 40, 527 CrossRef.
  28. M. V. Wickerhauser, in Different Perspectives on Wavelets, ed. Daubechies, I., American Mathematical Society, Providence, RI, 1993, pp. 155–171 Search PubMed.
  29. N.-C. Yen, J. Am. Stat. Assoc., 1994, 95, 889.
  30. H. Yoshida, K. Doi, R. M. Nishikawa and M. L. Giger, Radiology, 1995, 197, 393 Search PubMed.
  31. J. Buckheit, S. Chen, J. Crutchfield, D. Donoho, H. Gao, I. Johnstone, E. Kolaczyk, J. Scargle, K. Young and T. Yu, http://playfair.Stanford.EDU:80/~wavelab/, 1966.
  32. D. L. Donoho and I. M. Johnstone, Biometrika, 1994, 81, 425 Search PubMed.
  33. D. L. Donoho and I. M. Johnstone, C.R. Acad. Sci., Seri. I, 1994, 319, 1317 Search PubMed.
  34. D. L. Donoho and I. M. Johnstone, J. Am. Stat. Assoc., 1995, 90, 1200.
  35. D. L. Donoho, IEEE Trans. Inf. Theory, 1995, 41, 613 CrossRef.
  36. D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, R. Stat. Soc., Ser. B, 1995, 57, 301 Search PubMed.
  37. D. L. Donoho and I. M. Johnstone, J. Am. Stat. Assoc., 1995, 90, 1200.
  38. R. R. Coifman and M. V. Wickerhauser, IEEE Trans. Inf. Theory, 1992, 38, 713 CrossRef.
  39. J. Toft and O. M. Kvalheim, Chemom. Intell. Lab. Syst., 1993, 19, 65 CrossRef CAS.
  40. A. J. Iversen and T. Palm, Appl. Spectrosc., 1985, 39, 641 CAS.
  41. T. Isaksson and T. Næs, Appl. Spectrosc., 1988, 42, 1273 CAS.
  42. J. Sorvaniemi, A. Kinnunen, A. Tsados and Y. Malkki, Food Sci. Technol. Lebensm.-Wiss. Technol., 1993, 26, 251 Search PubMed.
  43. T. Isaksson and B. Kowalski, Appl. Spectrosc., 1993, 47, 702 CAS.
  44. A. E. Carlsson and K. L. R. Janne, Appl. Spectrosc., 1995, 49, 1037 CAS.
  45. I. S. Helland, T. Næs and T. Isaksson, Chemom. Intell. Lab. Syst., 1995, 29, 233 CrossRef CAS.
  46. R. D. Snee, Technometrics, 1977, 19, 415.
  47. H. R. Keller, D. L. Massart, Y. Z. Liang and O. M. Kvalheim, Anal. Chim. Acta, 1992, 263, 29 CrossRef CAS.
  48. O. M. Kvalheim, F. Brakstad and Y. Z. Liang, Anal. Chem., 1994, 66, 43 CrossRef CAS.
  49. C. Ritter, J. A. Gilliard, J. Cumps and B. Tilquin, Anal. Chim. Acta, 1996, 318, 125 CrossRef CAS.
  50. S. Clementi, S. Alunni, M. L. Bisani, d. Bonelli, D. Chiocchini, G. Cruciani, G. Giulietti, E. Johansson and S. Wold, Chim. Ind. (Milan), 1988, 70, 78 Search PubMed.
  51. S. DeJong, J. Chemom., 1993, 7, 551 CAS.
  52. I. E. Frank, Chemom. Intell. Lab. Syst., 1990, 8, 109 CrossRef CAS.
  53. P. Geladi, Chemom. Intell. Lab. Syst., 1987, 2, 257 CrossRef.
  54. P. Geladi, Chemom. Intell. Lab. Syst., 1992, 15, R7 CrossRef.
  55. T. R. Holcomb and M. Morari, Comput. Chem. Eng., 1992, 16, 393 CrossRef CAS.
  56. I. N. Wakeling and H. J. H. Macfie, J. Chemom., 1992, 6, 189 CAS.
  57. S. Wold, H. Martens and H. Wold, Lect. Notes Math., 1983, 973, 286 Search PubMed.
  58. S. Wold, A. Ruhe, H. Wold and W. J. Dunn, SIAM J. Sci. Stat. Comput., 1984, 5, 735 Search PubMed.
  59. S. Wold, Technometrics, 1993, 35, 136.
  60. E. Y. Zhu and R. M. Barnes, J. Chemom., 1995, 9, 363 CAS.
  61. A. B. Bulsari, Neural Networks for Chemical Engineers, Elsevier, Amsterdam, 1995 Search PubMed.
  62. C. M. Bishop, Neural Networks for Pattern Recognition, Clarendon Press, Oxford, 1995 Search PubMed.
  63. B. Cheng and D. M. Titterington, Stat. Sci., 1994, 9, 2 Search PubMed.
  64. S. Haykin, Neural Networks, Macmillan, New York, 1994 Search PubMed.
  65. R. Goodacre, M. J. Neal and D. B. Kell, Zbl. Bakteriol., 1996, 284, 516 Search PubMed.
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