Accounting for Poisson noise in the multivariate analysis of ToF‐SIMS spectrum images

Self Cite

Full-spectrum imaging is fast becoming a tool of choice for characterizing heterogeneous materials. Spectral images, which consist of a complete spectrum at each point in a spatial array, can be acquired from a wide variety of surface and microanalytical spectroscopic techniques. It is not uncommon that such spectral image data sets comprise tens of thousands of individual spectra, or more. Given the vast quantities of raw spectral data, factor analysis methods have proved indispensable for extracting the chemical information from these high-dimensional data sets into a limited number of factors that represent the spectral and spatial characteristics of the sample's composition. It is well known that factor models suffer a 'rotational ambiguity', that is, there are an infinite number of factor models that will fit the data equally well. Thus, physically inspired constraints are often employed to derive relatively unique models that make the individual factors more easily interpreted by the practicing analyst. In the present work, we note that many samples undergoing spectral image analysis are 'simple' in the sense that only one or a few of the sample's constituents are present at any particular location. When this situation prevails, simplicity in the spatial domain can be exploited to make the resulting factor models more realistic. In particular, orthogonal rotation of the spatial-domain vectors arising from singular value decomposition (SVD) of the spectral data matrix will be shown to be an effective method for making physically acceptable and easily interpretable estimates of the pure-component spectra and abundances.

Section: Methodsmentioning

confidence: 99%

“…Additional details about the MCR-ALS calculation are presented in the Appendix. After completion of the various matrix factorizations, the derived components were inversely scaled [30,32] to return them to the physical domain for interpretation.…”

Section: Methodsmentioning

confidence: 99%

Exploiting spatial‐domain simplicity in spectral image analysis

Keenan

2009

Self Cite

“…The raw data were scaled to account for Poisson statistics (noise in most ToF-SIMS studies is approximately Poisson-distributed), which affords maximum discrimination of chemical information from noise and allows small spectral features to be detected that would be otherwise overlooked. [26] SVD was used to reduce the dimension of the scaled data. The data analysis protocols discussed in this paper then represent, essentially, four different approaches to postprocessing the reduced-dimension factors with the goal of deriving factors that are more easily interpreted in terms of the sample's chemistry.…”

Section: Multivariate Statistical Analysis Methodologymentioning

confidence: 99%

A comparison of multivariate statistical analysis protocols for ToF‐SIMS spectral images

Smentkowski

Ostrowski

Keenan

2008

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) instruments produce raw data sets with a tremendous quantity of data. Multivariate statistical analysis (MVA) tools are being used to reduce the massive amount of chemical information into a smaller set of components that are easier to interpret and understand as a result of species association. Standard principal component analysis (PCA) is the most heavily used MVA algorithm in the ToF-SIMS community, and is frequently computed using the singular value decomposition (SVD). Other algorithms such as multivariate curve resolution (MCR) have also gained popularity over the past few years. In this work, we compare the as-measured ToF-SIMS spectrum and ion images with four MVA data analysis protocols: standard PCA, image-rotated SVD, spectra-rotated SVD, and a PCA-based MCR procedure. Imagerotated SVD and spectra-rotated SVD are closely connected to PCA and involve abstract rotations of the singular vectors that naturally arise during computation of the principal components via SVD. These rotations are designed to enhance either spatial contrast or spectral contrast in the components, respectively. We will show that the four MVA protocols provide essentially the same information, but accentuate different aspects of the sample's composition and lateral distribution, and that taken together these methods provide a more complete understanding of the sample. We will demonstrate that the component spectra estimated by MVA protocols assist the analyst in discovering minor constituents and understanding species correlation that would have been difficult, if not impossible, using univariate analysis protocols. For the data set described here, MVA tools identified unexpected species, which were not obvious in the as-measured data.

“…Two methods have been used to redistribute Poisson noise throughout the data set, square root scaling [17] and optimal scaling. Keenan and Kotula [18,19] reported the use of optimal scaling for TOF-SIMS data, on the basis of a procedure developed by Cochran and Horne, [20] which proved to be superior in identifying low-intensity components. A recent review on the application of MVA techniques to TOF-SIMS analysis recommended the use of optimal scaling prior to the use of both PCA and MCR.…”

Section: Introductionmentioning

confidence: 99%

Data scaling for quantitative imaging XPS

Walton¹,

Fairley²

2009

XPS spectrum image data sets acquired on laboratory instruments have inherently poor signal/noise, and require the use of multivariate analytical techniques to avoid prohibitively long acquisition times. However, when procedures that order the data by variance are used, the data set must be scaled beforehand, since it has a Poisson distribution. Different scaling methods may be used, but their effectiveness in allowing a separation of the chemical information from the noise is critical if loss of information is to be avoided. The performance of three methods, square root, root mean square and optimal scaling, has been compared, and their effectiveness for quantitative photoelectron spectromicroscopy is discussed.