Abstract: X-ray radiographic images of paintings often show little or no contrast. In order to increase the contrast in radiographic images we measured the X-ray spectrum of a low power X-ray tube, after passing through the painting, with a high energy-resolution SDD detector. To obtain images, the detector is collimated with a 400 mu m diameter pinhole and the painting was moved through the beam in the x and y-direction using a dwell time of a few seconds per pixel. The data obtained consists of a data cube of, typically, 200 x 200 pixels and a 512-channel X-ray spectrum for each pixel, spanning the energy range from 0 to 40 keV. Having the absorbance spectrum available for each pixel, we are able, a posteriori, to produce images by edge subtraction for any given element. In this way high contrast, element-specific, images can be obtained. Because of the high energy-resolution a much simpler edge subtraction algorithm can be applied. We also used principal-component imaging to obtain, in a more automated way, images with high contrast. Some of these images can easily be attributed to specific elements. It turns out that preprocessing of the spectral data is crucial for the success of the multivariate image processing.

Abstract: A new method to estimate case specific prediction uncertainty for univariate trilinear partial least squares (tri-PLS1) regression is introduced. This method is, from a theoretical point of view, the most exact finite sample approximation to true prediction uncertainty that has been reported up till now. Using the new method, different error sources can be propagated, which is an advantage that cannot be offered by data driven approaches such as the bootstrap. In a concise example, it is illustrated how the method can be applied. In the Appendix, efficient algorithms are presented to compute the estimates required.