Detection of unwanted (‘foreign’) objects within products is a common procedure in many branches of industry for maintaining production quality. X-ray imaging is a fast, non-invasive and widely applicable method for foreign object detection. Deep learning has recently emerged as a powerful approach for recognizing patterns in radiographs (i.e., X-ray images), enabling automated X-ray based foreign object detection. However, these methods require a large number of training examples and manual annotation of these examples is a subjective and laborious task. In this work, we propose a Computed Tomography (CT) based method for producing training data for supervised learning of foreign object detection, with minimal labor requirements. In our approach, a few representative objects are CT scanned and reconstructed in 3D. The radiographs that are acquired as part of the CT-scan data serve as input for the machine learning method. High-quality ground truth locations of the foreign objects are obtained through accurate 3D reconstructions and segmentations. Using these segmented volumes, corresponding 2D segmentations are obtained by creating virtual projections. We outline the benefits of objectively and reproducibly generating training data in this way. In addition, we show how the accuracy depends on the number of objects used for the CT reconstructions. The results show that in this workflow generally only a relatively small number of representative objects (i.e., fewer than 10) are needed to achieve adequate detection performance in an industrial setting.

We present a new hyper graph-based method, the medium-grain method, for solving the sparse matrix partitioning problem. This problem arises when distributing data for parallel sparse matrix-vector multiplication. In the medium-grain method, each matrix nonzero is assigned to either a row group or a column group, and these groups are represented by vertices of the hyper graph. For an m×n sparse matrix, the resulting hyper graph has m+n vertices and m+n hyper edges. Furthermore, we present an iterative refinement procedure for improvement of a given partitioning, based on the medium-grain method, which can be applied as a cheap but effective post processing step after any partitioning method. The medium-grain method is able to produce fully two-dimensional bipartitionings, but its computational complexity equals that of one-dimensional methods. Experimental results for a large set of sparse test matrices show that the medium-grain method with iterative refinement produces bipartitionings with lower communication volume compared to current state-of-the-art methods, and is faster at producing them.

Filtered backprojection, one of the most widely used reconstruction methods in tomography, requires a large number of low-noise projections to yield accurate reconstructions. In many applications of tomography, complete projection data of high quality cannot be obtained, because of practical considerations. Algebraic methods tend to handle such problems better, but are computationally more expensive. In this paper, we introduce a new method that improves the filtered backprojection method by using a custom data-dependent filter that minimizes the projection error of the resulting reconstruction. We show that the computational cost of the new method is significantly lower than that of algebraic methods. Experiments on both simulation and experimental data show that the method is able to produce more accurate reconstructions than filtered backprojection based on popular static filters when presented with data with a limited number of projections or statistical noise present. Furthermore, the results show that the method produces reconstructions with similar accuracy to algebraic methods, but is faster at producing them. Finally, we show that the method can be extended to exploit certain forms of prior knowledge, improving reconstruction accuracy in specific cases.

Image reconstruction from a small number of projections is a challenging problem in tomography. Advanced algorithms that incorporate prior knowledge can sometimes produce accurate reconstructions, but they typically require long computation times. Furthermore, the required prior knowledge can be very specific, limiting the type of images that can be reconstructed. Here, we present a reconstruction method that automatically learns prior knowledge using an artificial neural network. We show that this method can be viewed as a combination of filtered backprojection steps, and, therefore, has a relatively low computational cost. Results for two different cases show that the new method is able to use the learned information to produce high quality reconstructions in a short time, even when presented with a small number of projections.