Spectral deconvolution and spatial super-resolution for 3D datacubes collected from old master paintings with macro x-ray fluorescence scanning
Creators: name: Yan, Su
Publisher: name: Imperial College London
Year: 2022

description: Easel painting has been one of the most influential and important forms of art since the 13th century. To avoid invasive procedures such as sample removal, various non-destructive analytical imaging techniques are increasingly being used to investigate paintings and obtain valuable information about their composition, creation, history, and to inform their future preservation. For this reason, there is a growing interest in developing new image and signal processing methods to process the large and often multimodal datasets, produced by these imaging methods. In this thesis, we focused on the three-dimensional datacubes collected on Old Master paintings with Macro X-ray Fluorescence (MA-XRF) scanning, a technique that can be used for non-invasive elemental analysis of paintings. Two tasks in processing MA-XRF datacubes have been addressed in this thesis: MA-XRF spectral deconvolution and MA-XRF spatial super-resolution. The aim of MA-XRF spectral deconvolution is to identify the chemical elements that are present in a painting and produce their distribution maps. The task of MA-XRF spatial super-resolution is to enhance the spatial resolution of the collected MA-XRF datacubes. Firstly, we present an automatic method based on the finite rate of innovation (FRI) sampling theory to deconvolute the MA-XRF datacubes (AFRID method). By applying the FRI sampling theory, we can automatically retrieve the locations and amplitudes of the spectral pulses from the spectra. The detected pulses are then used to estimate the presence of chemical elements. We demonstrate that our AFRID method can not only detect chemical elements with weak intensities from the noisy datacube, but also separate overlapping spectral signals and assign them to the correct chemical elements, without the requirement of additional user intervention. Then, we further develop a fast and automatic deconvolution (FAD) method for MA-XRF spectral deconvolution. By applying our AFRID method on the average and maximum spectrum of the datacube for the first detection, we can create a pulse shape matrix and the MA-XRF datacube can be modelled as a multiplication of the pulse shape matrix and the desired amplitude matrix. In this way, MA-XRF spectral deconvolution is converted into a matrix factorisation problem, which is solved by two fast optimisation approaches: one is based on the inner-loop-free alternating direction method of multipliers (ILF-ADMM) algorithm and the other one is inspired by the fast iterative shrinkage-thresholding algorithm (FISTA). The results show that our FAD method can produce element maps with better visual quality and less noise, while the processing time is significantly reduced. Finally, we present a coupled dictionary learning based approach for MA-XRF spatial super-resolution, leveraging the high-resolution (HR) RGB image of the painting. In particular, we propose to divide the RGB image and MA-XRF datacube into common and unique parts and the high-resolution information shared between the common parts is transferred from the HR RGB image to the HR reconstructed MA-XRF datacube. We demonstrate that our method can produce high-quality reconstructions and avoid introducing unnecessary artificial features, which outperforms the state-of-the-art SR methods.