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Application of the HLSVD Technique to the Filtering of X-Ray Diffraction Data
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 039575 (2007)
Abstract
A filter based on the Hankel-Lanczos singular value decomposition (HLSVD) technique is presented and applied for the first time to X-ray diffraction (XRD) data. Synthetic and real powder XRD intensity profiles of nanocrystals are used to study the filter performances with different noise levels. Results show the robustness of the HLSVD filter and its capability to extract easily and effciently the useful crystallographic information. These characteristics make the filter an interesting and user-friendly tool for processing of XRD data.
References
Mierzwa B, Pielaszek J: Smoothing of low-intensity noisy X-ray diffraction data by Fourier filtering: application to supported metal catalyst studies. Journal of Applied Crystallography 1997,30(5):544-546. 10.1107/S0021889897000198
Hieke A, Dörfler H-D: Methodical developments for X-ray diffraction measurements and data analysis on lyotropic liquid crystals applied to K-soap/glycerol systems. Colloid and Polymer Science 1999,277(8):762-776. 10.1007/s003960050450
Schmidt M, Rajagopal S, Ren Z, Moffat K: Application of singular value decomposition to the analysis of time-resolved macromolecular X-ray data. Biophysical Journal 2003,84(3):2112-2129. 10.1016/S0006-3495(03)75018-8
Rajagopal S, Schmidt M, Anderson S, Ihee H, Moffat K: Analysis of experimental time-resolved crystallographic data by singular value decomposition. Acta Crystallographica Section D 2004,60(5):860-871.
Aubanel EE, Oldham KB: Fourier smoothing without the fast Fourier transform. Byte 1985,10(2):207-222.
Wooff C: Smoothing of data by least squares fitting. Computer Physics Communications 1986,42(2):249-251. 10.1016/0010-4655(86)90040-8
Barkhuijsen H, de Beer R, van Ormondt D: Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals. Journal of Magnetic Resonance 1987,73(3):553-557.
Laudadio T, Mastronardi N, Vanhamme L, van Hecke P, van Huffel S: Improved Lanczos algorithms for blackbox MRS data quantitation. Journal of Magnetic Resonance 2002,157(2):292-297. 10.1006/jmre.2002.2593
Wales DJ: Structure, dynamics, and thermodynamics of clusters: tales from topographic potential surfaces. Science 1996,271(5251):925-929. 10.1126/science.271.5251.925
Siegel RW, Hu E, Cox DM, et al.: Nanostructure Science and Technolgy. A Worldwide Study. The Interagency Working Group on NanoScience, Engineering and Technolgy, https://doi.org/www.wtec.org/loyola/nano/
Zanchet D, Hall MBD, Ugarte D: Structure population in thioi-passivated gold nanoparticles. Journal of Physical Chemistry B 2000,104(47):11013-11018.
Golub GH, Reinsch C: Singular value decomposition and least squares solutions. Numerische Mathematik 1970,14(5):403-420. 10.1007/BF02163027
Anderson E, Bai Z, Bischof C, et al.: LAPACK Users' Guide. SIAM, Philadelphia, Pa, USA; 1995.
Young RA: The Rietvel Method. Oxford University Press, New York, NY, USA; 1993.
Cervellino A, Giannini C, Guagliardi A: Determination of nanoparticle structure type, size and strain distribution from X-ray data for monatomic f.c.c.-derived non-crystallographic nanoclusters. Journal of Applied Crystallography 2003,36(5):1148-1158. 10.1107/S0021889803013542
Taylor JR: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Scientific Books, Sausalito, Calif, USA; 1997.
Stoica P, Moses R: Introduction to Spectral Analysis. Prentice-Hall, Upper Saddle River, NJ, USA; 1997.
Simon HD: The Lanczos algorithm with partial reorthogonalization. Mathematics of Computation 1984,42(165):115-142. 10.1090/S0025-5718-1984-0725988-X
Marple SL: Digital Spectral Analysis with Applications. Prentice-Hall, Englewood Cliffs, NJ, USA; 1987.
Golub G, Pereyra V: Separable nonlinear least squares: the variable projection method and its applications. Inverse Problems 2003,19(2):R1-R26. 10.1088/0266-5611/19/2/201
Baxter BJC, Iserles A: On approximation by exponentials. Annals of Numerical Mathematics 1997, 4: 39–54. The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin, hskip 1em plus 0.5em minus 0.4em
Beylkin G, Monzón L: On approximation of functions by exponential sums. Applied and Computational Harmonic Analysis 2005,19(1):17-48. 10.1016/j.acha.2005.01.003
Bjoirck A: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, Pa, USA; 1996.
Kung SY, Arun KS, Bhaskar Rao DV: State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem. Journal of the Optical Society of America 1983,73(12):1799-1811. 10.1364/JOSA.73.001799
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Ladisa, M., Lamura, A., Laudadio, T. et al. Application of the HLSVD Technique to the Filtering of X-Ray Diffraction Data. EURASIP J. Adv. Signal Process. 2007, 039575 (2007). https://doi.org/10.1155/2007/39575
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DOI: https://doi.org/10.1155/2007/39575