Principle Component Analysis
Principle component analysis (PCA) assumes that any dataset can be described by a linear combination of one or more pure components.  As described in the paper by Walton [1] multiplying the data matrix by its transpose, a covariance matrix is formed which can then be decomposed into an orthogonal dataset, using singular value decomposition (SVD) sort.  From this the maximum variation in the data is partitioned into abstract components with the largest eigenvalues.  The abstract factors without any obvious features can be attributed to noise.  If the original dataset is reconstructed from only those abstract factors containing significant information, the result is a new dataset where the influence of the noise is reduced in magnitude.  One limitation of the PCA approach to noise reduction is the significant computation time required although substantial decreases can be achieved by operating on a subset of each images at a time.  In the example shown to the right the dataset of 256 images is processed in groups of 16 images such that the SVD is applied to adjacent images and then stepped through the dataset instead of being applied to the entire dataset at once.  The result is to move the vector containing the most information to the top

Summary
The SMA allows high energy and spatial resolution images to be acquired very rapidly.  With the use of a pulse counting delay-line detector genuine quantitative images are acquired to characterise surface distribution of elemental or chemical state species.  Acquiring a set of images incremented in energy over photoemission peaks a large 3-dimensional dataset can be generated easily.  The use of multivariate statistical analysis to extract the information content of the multi-spectral dataset and as a tool for noise reduction in images or spectra has been demonstrated.

An A4 pdf version of the poster can be downloaded directly from the 'downloads>General Reference' section of the Members Area or by contacting the Applications Specialists at Kratos Analytical Ltd, Manchester.