Improving reconstructions in nanotomography via mathematical optimization
In collaboration with colleagues from the Department of Data Science, IMN researchers developed a new compressed sensing method that uses mathematical optimization to improve the quality of 3D reconstructions in nanotomography of homogeneous materials. The work was performed in the framework of the DFG-funded Collaborative Research Center CRC 1411 “Design of particulate products” and recently appeared in Nanoscale Advances (https://doi.org/10.1039/D3NA01089A).
Compressed sensing is an image reconstruction technique to achieve high-quality results from a limited amount of data. To achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. In this work, we include additional problem-specific knowledge for image reconstruction in nanotomography and propose further classes of algebraic inequalities that are added to the compressed sensing model.
The first consists of a valid upper bound on the pixel brightness. It only exploits general information about the projections and is thus applicable to a broad range of reconstruction problems. The second class is applicable whenever the sample material is of roughly homogeneous composition. The model favors a constant density and penalizes deviations from it. The resulting mathematical optimization models are algorithmically tractable and can be solved to global optimality by state-of-the-art available implementations of interior point methods.
To evaluate the novel models, obtained results are compared to existing image reconstruction methods, and tested on simulated and experimental data sets. The experimental data comprise one 360° electron tomography tilt series of a macroporous zeolite particle (from project B01 of CRC 1411) and one absorption contrast nano X-ray computed tomography (nano-CT) data set of a copper microlattice structure, which was thankfully provided by our colleagues from Max-Planck-Institut für Eisenforschung GmbH (see https://arxiv.org/abs/2311.14018 for more information).
The enriched models are optimized quickly and show improved reconstruction quality, outperforming the existing models. Promisingly, our approach yields superior reconstruction results, particularly when only a few tilt angles are available.
The study was recently published in Nanoscale Advances:
Kreuz, B. Apeleo Zubiri, S. Englisch, M. Buwen, S.-G. Kang, R. Ramachandramoorthy, E. Spiecker, F. Liers, J. Rolfes, Improving reconstructions in nanotomography for homogeneous materials via mathematical optimization, Nanoscale Advances 2024, Advance Article, https://doi.org/10.1039/D3NA01089A