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: A detailed 3D investigation of nanoparticles at a local scale is of great importance to connect their structure and composition to their properties. Electron tomography has therefore become an important tool for the 3D characterization of nanomaterials. 3D investigations typically comprise multiple steps, including acquisition, reconstruction, and analysis/quantification. Usually, the latter two steps are performed offline, at a dedicated workstation. This sequential workflow prevents on-the-fly control of experimental parameters to improve the quality of the 3D reconstruction, to select a relevant nanoparticle for further characterization or to steer an in-situ tomography experiment. Here, we present an efficient approach to overcome these limitations, based on the real-time reconstruction of arbitrary 2D reconstructed slices through a 3D object. Implementation of this method may lead to generalized implementation of electron tomography for routine nanoparticle characterization in 3D.