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Wavelet denoising of powder diffraction patterns

Published online by Cambridge University Press:  10 January 2013

Ľubomír Smrčok ,
Marián Ďurík  and
Vladimír Jorík
Ľubomír Smrčok*
Affiliation:
Institute of Inorganic Chemistry, Slovak Academy of Sciences, SK-842 36 Bratislava, Slovak Republic
Marián Ďurík
Affiliation:
Institute of Inorganic Chemistry, Slovak Academy of Sciences, SK-842 36 Bratislava, Slovak Republic
Vladimír Jorík
Affiliation:
Department of Inorganic Chemistry, Slovak Technical University, SK-812 37 Bratislava, Slovak Republic
*
a)Corresponding author, electronic mail: uachsmrk@savba.sk
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Abstract

Four powder diffraction patterns taken under different experimental conditions were denoised by a new method, i.e., thresholding of wavelet coefficients. The patterns were transformed by discrete wavelet transform applying Coiflet4 wavelet function. WLS refinements of peaks’ positions, FWHM, and intensity showed that wavelet denoising, in contrast to previously used polynomial smoothing, did not shift the maxima and preserved peak and integrated intensities. This method may therefore represent an useful alternative to polynomial filters or filters based on Fourier transform.

Type
Research Article
Information
Powder Diffraction , Volume 14 , Issue 4 , December 1999 , pp. 300 - 304
Copyright
Copyright © Cambridge University Press 1999

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References

Barclay, V. J., Bonner, R. F., and Hamilton, I. P. (1997). “Application of wavelet transform to experimental spectra: Smoothing, denoising, and data set compression,” Anal. Chem. 69, 78–90.CrossRefGoogle Scholar
Buckheit, J., Chen, S., Donoho, D., Johnstone, I., and Scargle, J. (1995). “WaveLab 0.700.” http://playfair.stanford.edu/ ~wavelab.Google Scholar
Chui, C. K. (1991). Introduction to Wavelets, 1st ed. (Academic, Boston).Google Scholar
Daubechies, I. (1988). “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math. 41, 909–996.CrossRefGoogle Scholar
Depczynski, U., Jetter, K., Molt, K., and Niemöller, A. (1997). “The fast wavelet transform on compact intervals as a tool in chemometrics. I. Mathematical background,” Chemom. Intell. Lab. Syst. 39, 19–27.CrossRefGoogle Scholar
Donoho, D. L., and Johnstone, I. M. (1994). “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455.CrossRefGoogle Scholar
Gasser, T., Sroka, L., and Jennen-Steinmetz, Ch. (1986). “Residual variance and residual pattern in nonlinear regression,” Biometrika 73, 625–633.CrossRefGoogle Scholar
Mallat, S. (1989). “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern. Anal. Mach. Intell. 11, 674–693.CrossRefGoogle Scholar
Mallory, Ch. L., and Snyder, R. L. (1979). “The Alfred University X-ray powder diffraction automation system,” Technical paper No. 144, Alfred University, Alfred, New York.Google Scholar
Mittermayr, C. R., Nikolov, S. G., Hutter, H., and Grasserbauer, M. (1996). “Wavelet denoising of Gaussian peaks: A comparative study,” Chemom. Intell. Lab. Syst. 34, 187–202.CrossRefGoogle Scholar
Savitzky, A., and Golay, M. J. E. (1964). “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639.CrossRefGoogle Scholar
Smrčok, Ľ. (1999). “Rietveld refinement with wavelet compressed data.” Z. Kristallogr. (in press).CrossRefGoogle Scholar
Steiner, J., Termonia, Y., and Deltour, J. (1972). “Comments on smoothing and differentiation of data by simplified least squares procedure,” Anal. Chem. 44, 1906–1909.CrossRefGoogle Scholar
Visual X POW. (1994). STOE & CIE, GmbH.Google Scholar
Walczak, B., and Massart, D. L. (1997). “Noise suppression and signal compression using the wavelet packet transform,” Chemom. Intell. Lab. Syst. 36, 81–94.CrossRefGoogle Scholar