5 research outputs found
Spectral X-ray CT for fast NDT using discrete tomography
We present progress in fast, high-resolution imaging, material classification, and fault detection using
hyperspectral X-ray measurements. Classical X-ray CT approaches rely on data from many projection
angles, resulting in long acquisition and reconstruction times. Additionally, conventional CT cannot
distinguish between materials with similar densities. However, in additive manufacturing, the majority of
materials used are known a priori. This knowledge allows to vastly reduce the data collected and increase
the accuracy of fault detection. In this context, we propose an imaging method for non-destructive testing
of materials based on the combination of spectral X-ray CT and discrete tomography. We explore the
use of spectral X-ray attenuation models and measurements to recover the characteristic functions of
materials in heterogeneous media with piece-wise uniform composition. We show by means of numerical
simulation that using spectral measurements from a small number of angles, our approach can alleviate
the typical deterioration of spatial resolution and the appearance of streaking artifacts.Mechanical Engineerin
A sketched finite element method for elliptic models
We consider a sketched implementation of the finite element method for
elliptic partial differential equations on high-dimensional models. Motivated
by applications in real-time simulation and prediction we propose an algorithm
that involves projecting the finite element solution onto a low-dimensional
subspace and sketching the reduced equations using randomised sampling. We show
that a sampling distribution based on the leverage scores of a tall matrix
associated with the discrete Laplacian operator, can achieve nearly optimal
performance and a significant speedup. We derive an expression of the
complexity of the algorithm in terms of the number of samples that are
necessary to meet an error tolerance specification with high probability, and
an upper bound for the distance between the sketched and the high-dimensional
solutions. Our analysis shows that the projection not only reduces the
dimension of the problem but also regularises the reduced system against
sketching error. Our numerical simulations suggest speed improvements of two
orders of magnitude in exchange for a small loss in the accuracy of the
prediction