Joint Image Reconstruction and Segmentation Using the Potts Model

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data

Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

ToScA North America (6 – 8 June 2017, The University of Texas, Austin, TX) Program

ToScA North America will address key areas of science, including Multi-modal Imaging, Geosciences, Forensics, Increasing Contrast, Educational Outreach, Data, Materials Science and Medical and Biological Science.University of Texas High-Resolution X-ray CT Facility (UTCT); Jackson School of Geosciences, The University of Texas at Austin; Natural History Museum (London); Royal Microscopical Society (Oxford, UK)Geological Science

Assessment of glued timber integrity by limited-angle microfocus X-ray computed tomography

Glued timber products have an extensive range of applications in construction. In this work a Microfocus X-ray Computed Tomography method was developed to inspect gluing defects in timber samples and was applied successfully on experimental data. The bonding plane was segmented into glued and non-glued regions and imaged with 5mm resolution. Moreover, the gap topology between timber lamellas was precisely characterised. Alimited-angle reconstruction with anisotropic frame binning together with a specific glue line readout method efficiently filters out undesired wood structure highlighting the information of the adhesive joint. This method imposes limitations on the size of the specimen in only one dimension. The presence and absence of glue could be detected for glue line thicknesses over 50μm and air gaps larger than 150μm could be characterised. Several information reduction approaches were combined in the reconstruction process to implement the assessment of a 100×100mm2 bonding plane in less than 40

EDS tomographic reconstruction regularized by total nuclear variation joined with HAADF-STEM tomography

Energy-dispersive X-ray spectroscopy (EDS) tomography is an advanced technique to characterize compositional information for nanostructures in three dimensions (3D). However, the application is hindered by the poor image quality caused by the low signal-to-noise ratios and the limited number of tilts, which are fundamentally limited by the insufficient number of X-ray counts. In this paper, we explore how to make accurate EDS reconstructions from such data. We propose to augment EDS tomography by joining with it a more accurate high-angle annular dark-field STEM (HAADF-STEM) tomographic reconstruction, for which usually a larger number of tilt images are feasible. This augmentation is realized through total nuclear variation (TNV) regularization, which encourages the joint EDS and HAADF reconstructions to have not only sparse gradients but also common edges and parallel (or antiparallel) gradients. Our experiments show that reconstruction images are more accurate compared to the non-regularized and the total variation regularized reconstructions, even when the number of tilts is small or the X-ray counts are low