Accelerating MA-XRF Data Acquisition by Exploiting Local Spatial and Spectral Relations within a Hyperspectral Datacube

An Approach through Wavelet Denoising

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Macro X-ray fluorescence (MA-XRF) is a recently developed technology allowing to obtain elemental information from cultural heritage objects. This information can, for example, be used to identify pigments used in a painting. Yet, the extended period of time it takes to scan an object is a major issue within MA-XRf. For instance, it took about 60 days to scan the Ghent Altarpiece. The long scanning time is a consequence of the necessary dwell time per pixel to create a robustly interpretable spectrum: the higher the dwell time, the higher the signalto-noise ratio (SNR), hence, the easier to detect elements. This thesis explores a possible solution for this problem using a denoising algorithm that increases the signal-to-noise ratio post-acquisition by exploiting the similarity between neighbouring pixels and spectra. To this end, a customized method of wavelet filter bank denoising is proposed. Current thresholding methods used in wavelet filter bank denoising are not suitable for filtering MA-XRF data, therefore, a novel thresholding method is introduced. Here, the widely used universal thresholding method is used as a basis, for which the formula for calculating the standard deviation of the detail coefficients of a channel is altered. Several design parameters of wavelet filter bank denoising were evaluated using a synthetic dataset, for which the performance quality indicators root mean square error (RMSE), mean absolute error (MAE) and SNR were determined. The parameters for which we optimized were the mother wavelet, the number of decomposition levels, and the number of neighbouring channels used for determining the standard deviation σ for thresholding. Good performance was obtained with the haar, db2, and coif1 wavelets, all at 3 levels of decomposition. A suitable number of neighbouring channels depended on the decomposition level and was determined to be 3 (on each side of the channel). Herewith, the signal-to-noise ratio was improved for both the average pixel spectra and the sum spectrum. The filtered synthetic dataset simulated to have a dwell time of 0.5 seconds had a SNR approximately equal to the raw synthetic dataset simulated to have a dwell time of 0.75 seconds. Hence, the algorithm succeeded in lowering the necessary dwell time. A case study of a daguerreotype was used to test the proposed denoising algorithm.