Tatiana A. Bubba — Page 2

arXiv2016

Tomographic X-ray data of a lotus root filled with attenuating objects

This is the documentation of the tomographic X-ray data of a lotus root, filled with four different attenuating objects, of different sizes. Data are available at www.fips.fi/dataset.php, and can be freely used for scientific purposes with appropriate references to them, and to this document in http://arxiv.org/arXiv. The data set consists of (1) the X-ray sinogram of a single 2D slice of the lotus root with two different resolutions and (2) the corresponding measurement matrices modeling the linear operation of the X-ray transform. Each of these sinograms was obtained from a measured 360-projection fan-beam sinogram by down-sampling and taking logarithms. The original (measured) sinogram is also provided in its original form and resolution.

physics.data-an↗

arXiv2016

Numerical assessment of shearlet-based regularization in ROI tomography

When it comes to computed tomography (CT), the possibility to reconstruct a small region-of-interest (ROI) using truncated projection data is particularly appealing due to its potential to lower radiation exposure and reduce the scanning time. However, ROI reconstruction from truncated projections is an ill-posed inverse problem, with the ill-posedness becoming more severe when the ROI size is getting smaller. To address this problem, both ad hoc analytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI CT reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection (SGP) method and is tested in the context of fan beam CT. Our results show that this approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.

math.NA↗