Search

X-ray tensor tomography (XTT) is a novel imaging modality for the three-dimensional reconstruction of X-ray scattering tensors from dark-field images obtained in a grating interferometry setup. The two-dimensional dark-field images measured in XTT are degraded by noise effects, such as detector readout noise and insufficient photon statistics, and consequently, the three-dimensional volumes reconstructed from this data exhibit noise artifacts. In this paper, we investigate the best way to incorporate a denoising technique into the XTT reconstruction pipeline, i.e., the popular total variation denoising technique. We propose two different schemes of including denoising in the reconstruction process, one using a column block-parallel iterative scheme and one using a whole-system approach. In addition, we compare the results when using a simple denoising approach applied either before or after reconstruction. The effectiveness is evaluated qualitatively and quantitatively based on datasets from an industrial sample and a clinical sample. The results clearly demonstrate the superiority of including denoising in the reconstruction process, along with slight advantages of the whole-system approach.

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

The x-ray dark-field signal measured in grating interferometers is anisotropic, depending on both the beam direction and the grating orientation with respect to the sample. We present a novel general closed-form, continuous forward model of the anisotropic dark-field signal. Furthermore, we derive a discretization using spherical harmonics, leading to a large-scale linear inverse problem. We present first experimental results of a wooden sample, demonstrating marked advantages over previous results, in particular, the resolution of multiple scattering directions in one volume element.

X-ray Tensor Tomography (XTT) is a recently developed imaging modality that provides reconstruction of X-ray scattering tensors from dark-field projections obtained in a grating interferometry setup. In this work we present a novel component-based total variation (TV) regularized reconstruction technique for XTT data. First results show promising qualitative improvements of the reconstructed tensors as well as reduced noise and reduced streak artifacts.