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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.

Purpose: Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography. Methods: In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization. Results: Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method’s strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection. Conclusions: The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directionalmore » features.« less

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.

Attenuation based X-ray micro computed tomography (XCT) provides three-dimensional images with micrometer resolution. However, there is a trade-off between the smallest size of the structures that can be resolved and the measurable sample size. In this letter, we present an imaging method using a compact laboratory setup that reveals information about micrometer-sized structures within samples that are several orders of magnitudes larger. We combine the anisotropic dark-field signal obtained in a grating interferometer and advanced tomographic reconstruction methods to reconstruct a six dimensional scattering tensor at every spatial location in three dimensions. The scattering tensor, thus obtained, encodes information about the orientation of micron-sized structures such as fibres in composite materials or dentinal tubules in human teeth. The sparse acquisition schemes presented in this letter enable the measurement of the full scattering tensor at every spatial location and can be easily incorporated in a practical, commercially feasible laboratory setup using conventional X-ray tubes, thus allowing for widespread industrial applications.

Quite recently, a method has been presented to reconstruct X-ray scattering tensors from projections obtained in a grating interferometry setup. The original publications present a rather specialised approach, for instance by suggesting a single SART-based solver. In this work, we propose a novel approach to solving the inverse problem, allowing the use of other algorithms than SART (like conjugate gradient), a faster tensor recovery, and an intuitive visualisation. Furthermore, we introduce constraint enforcement for X-ray tensor tomography (cXTT) and demonstrate that this yields visually smoother results in comparison to the state-of-art approach, similar to regularisation.