Enhancing the Signal-to-Noise Ratio of X-ray Diffraction Profiles by Smoothed Principal Component Analysis

Abstract

X-ray diffraction is one of the most widely applied methodologies for the in situ analysis of kinetic processes involving crystalline solids. However, due to its relatively high detection limit, it has only limited application in the context of crystallizations from liquids. Methods that can improve the detection limit of X-ray diffraction are therefore highly desirable. Signal processing approaches such as Savitzky-Golay, maximum likelihood, stochastic resonance, and wavelet transforms have been used previously to preprocess X-ray diffraction data. Since all these methods only utilize the frequency information contained in the single X-ray diffraction profile being processed to discriminate between the signals and the noise, they may not successfully identify very weak but important peaks especially when these weak signals are masked by severe noise. Smoothed principal component analysis (SPCA), which takes advantage of both the frequency information and the common variation within a set of profiles, is proposed as a methodology for the preprocessing of the X-ray diffraction data. Two X-ray diffraction data sets are used to demonstrate the effectiveness of the proposed approach. The first was obtained from mannitol-methanol suspensions, and the second data set was generated from slurries of L-glutamic acid (GA) in methanol. The results showed that SPCA can significantly improve the signal-to-noise ratio and hence lower the detection limits (approximately 0.389% g/mL for mannitol-methanol suspensions and 0.4 wt % for beta-form GA in GA-methanol slurries comprising mixtures of both alpha- and beta-forms of GA) thereby providing an important contribution to crystallization process performance monitoring.

Data mining density of states spectra for crystal structure classification: An inverse problem approach

“…PCA, described in17–21, defines latent variables or PC that are defined to capture the maximum variance in a dataset and are comprised of a combination of properties to capture this variance. PCA is used in this work to quantitatively analyze the DOS to classify materials based on crystal structure.…”

Polymorphic transformation of l-glutamic acid monitored using combined on-line video microscopy and X-ray diffraction

“…3. Treatment of the recorded XRD profiles consisted of data smoothing using a Smooth Process Component Analysis (SPCA) algorithm [21] to smooth the profiles by reducing the noise component of the signals, followed by background subtraction to remove the diffraction component due to solvent scattering, peak searching and peak fitting using Bede [28] Polycrystal V1.00 software to determine peak areas.…”

“…Previous independent studies monitoring L-glutamic acid (LGA) using on-line video microscopy [17][18][19][20] and on-line XRD [11,[21][22][23] have shown the potential of using these techniques to detect and monitor polymorphs during the early stages of crystallisation. For the first time, the two on-line techniques have been coupled to simultaneously observe the solution mediated phase transformation of LGA [24][25][26][27].…”

Smoothing of X-ray diffraction data andKα2elimination using penalized likelihood and the composite link model

“…Other methods use wavelets or Fourier transforms, which are both reviewed by Artursson et al (2000). Chen et al (2005) used smooth principal components to exploit the shared variation in a set of different patterns. This can be valuable in some cases but also limits the applicability of the method, because often only a single scan is obtained.…”