Abstract: Advances in multi-spectral detectors are causing a paradigm shift in x-ray computed tomography (CT). Spectral information acquired from these detectors can be used to extract volumetric material composition maps of the object of interest. If the materials and their spectral responses are known a priori, the image reconstruction step is rather straightforward. If they are not known, however, the maps as well as the responses need to be estimated jointly. A conventional workflow in spectral CT involves performing volume reconstruction followed by material decomposition, or vice versa. However, these methods inherently suffer from the ill-posedness of the joint reconstruction problem. To resolve this issue, we propose 'A Dictionary-based Joint reconstruction and Unmixing method for Spectral Tomography' (ADJUST). Our formulation relies on forming a dictionary of spectral signatures of materials common in CT and prior knowledge of the number of materials present in an object. In particular, we decompose the spectral volume linearly in terms of spatial material maps, a spectral dictionary, and the indicator of materials for the dictionary elements. We propose a memory-efficient accelerated alternating proximal gradient method to find an approximate solution to the resulting bi-convex problem. From numerical demonstrations on several synthetic phantoms, we observe that ADJUST performs exceedingly well compared to other state-of-the-art methods. Additionally, we address the robustness of ADJUST against limited and noisy measurement patterns. The demonstration of the proposed approach on a spectral micro-CT dataset shows its potential for real-world applications. Code is available at https://github.com/mzeegers/ADJUST.

Abstract: Morphological characterization of nanoparticle assemblies and hybrid nanomaterials is critical in determining their structure-property relationships as well as in the development of structures with desired properties. Electron tomography has become a widely utilized technique for the three-dimensional characterization of nanoparticle assemblies. However, the extraction of quantitative morphological parameters from the reconstructed volume can be a complex and labor-intensive task. In this study, we aim to overcome this challenge by automating the volumetric segmentation process applied to three-dimensional reconstructions of nanoparticle assemblies. The key to enabling automated characterization is to assess the performance of different volumetric segmentation methods in accurately extracting predefined quantitative descriptors for morphological characterization. In our methodology, we compare the quantitative descriptors obtained through manual segmentation with those obtained through automated segmentation methods, to evaluate their accuracy and effectiveness. To show generality, our study focuses on the characterization of assemblies of CdSe/CdS quantum dots, gold nanospheres and CdSe/CdS encapsulated in polymeric micelles, and silica-coated gold nanorods decorated with both CdSe/CdS or PbS quantum dots. We use two unsupervised segmentation algorithms: the watershed transform and the spherical Hough transform. Our results demonstrate that the choice of automated segmentation method is crucial for accurately extracting the predefined quantitative descriptors. Specifically, the spherical Hough transform exhibits superior performance in accurately extracting quantitative descriptors, such as particle size and interparticle distance, thereby allowing for an objective, efficient, and reliable volumetric segmentation of complex nanoparticle assemblies.