Application of the HLSVD Technique to the Filtering of X-Ray Diffraction Data
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Research Article Application of the HLSVD Technique to the Filtering of X-Ray Diffraction Data M. Ladisa,1 A. Lamura,2 T. Laudadio,3 and G. Nico2 1 Istituto
di Cristallografia (IC), Consiglio Nazionale delle Ricerche (CNR), Via Amendola 122/O, 70126 Bari, Italy Applicazioni del Calcolo Mauro Picone (IAC), Consiglio Nazionale delle Ricerche (CNR), Via Amendola 122/D, 70126 Bari, Italy 3 SISTA, SCD Division, Department of Electrical Engineering (ESAT), Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, 3001 Leuven-Heverlee, Belgium 2 Istituto
Received 6 February 2006; Revised 21 December 2006; Accepted 2 February 2007 Recommended by Jacques G. Verly 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. Copyright © 2007 M. Ladisa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. INTRODUCTION In many applications of X-ray diffraction (XRD) techniques to the study of crystal properties, a key step in the data processing chain is an effective and adaptive noise filtering [1– 4]. A correct noise removal can facilitate the separation of the useful crystallographic information from the background signal, and the estimation of crystal structure and domain size. Important issues of XRD data filtering are performances in noise suppression, capability to preserve the peak position, computational cost, and finally, the possibility of being used as a blackbox tool. Different digital filters have been applied to XRD data, in spatial and frequency domains. Simple procedures are based on polynomial filtering (and fitting) in the spatial domain [1]. A standard practice when working in frequency domain is to use Fourier smoothing. It consists in removing the high-frequency components of the spectrum [5]. Since the truncation of high-frequency components can be problematic in the case of high-level noise, a different approach based on the Wiener-Fourier (WF) filter has been proposed to clean XRD data [6]. A different approach, which makes use of the singular value decomposition (SVD), has been successfully applied to time-resolved XRD data to reduce noise level [3, 4]. In this work, we describe an application of the HankelLanczos singular value decomposition (HLSVD) algorithm
to filter XRD intensity data. The proposed filter is based on a subspace-based parameter estimation method, called Hankel singular value decomposition (HSVD) [7], which is currently applied to nuclear magnetic r
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