On Adaptive Time-Constrained Macro X-Ray Fluorescence Scanning and Analysis of Works of Art

Chopp, Henry Hayashi

doi:https://doi.org/10.21985/n2-m4fe-5d12

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On Adaptive Time-Constrained Macro X-Ray Fluorescence Scanning and Analysis of Works of Art

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In the late 2000’s, scientific studies in cultural heritage saw a great advancement in macro X-ray fluorescence (XRF) imaging of paintings. These images are used to generate elemental distribution maps, which aid in identifying chemical elements and paint pig- ments as well as their locations throughout the layers of the paintings. However, since this technique uses a scanning probe that operates pixel by pixel, it often requires many hours, or even days, to collect high quality image data.We introduce novel image processing techniques to reduce the acquisition time of the image data regardless of the XRF hardware. We investigate two image denoising techniques: XRF volume denoising, which merges dictionary learning with a Poisson noise model, and elemental map denoising, which incorporates a novel Poissonian regularizer. These denoising methods allow for fast, noisy scans without losing image quality. Additionally, we detail a pair of sampling algorithms to collect the most informative data. In one method, an initial fast raster scan is conducted, which is then followed by a pixel-wise dwell time-varying scan designed to minimize the expected error. Our second approach builds upon the first, whereby we predict the initial scanning pattern using only a handful of samples. Knowing that artists paint with a finite number of paints (and therefore XRF responses), these initial samples are strategically chosen via a color image of the painting. To find these sampling patterns, we detail novel optimization schema that allow users to include strict time constraints. One method, called the Constrained Average, Variance, and Extrema (CAVE) function, is a differentiable function meant to impose strict global mean, range, and/or variance constraints on the output. CAVE is designed for gradient descent-based optimization algorithms, including applications in neural networks. Our other solver is non-differentiable, but is quick to converge upon the exact solution and even allows for additional time constraints to be imposed on the pixel level. We demonstrate that by combining the denoising and adaptive sampling techniques, we have a powerful framework that can reduce XRF acquisition times to hours or even minutes.

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