Robust artefact reduction in tomography using Student’s t data fitting

Algebraic methods are popular for tomographic image reconstruction from limited data. These methods typically minimize the Euclidean norm of the residual of the corresponding linear equation system. The underlying assumption of this approach is that the noise has a Gaussian distribution. However, in cases where large outliers are present in the projection data, e.g., due to defective camera pixels, photon starvation from metal implants etc., the equation system is not consistent and the reconstruction will be fitted to these outliers, resulting in artefacts in the reconstruction. In this paper we use a penalty function for the residual that is based on the maximum likelihood estimate from the Student’s t distribution, which assigns a smaller penalty to outliers. No preprocessing is required to locate the outliers. We demonstrate the effectiveness of this approach on a 3D cone-beam simulated dataset for a series of perturbations in the projection data. Our results suggest that artefacts due to metal objects, de

A parametric level-set method for partially discrete tomography

This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the background reconstruction we impose smoothness through Tikhonov regularization. The bi-level optimization problem is solved in an alternating fashion; in each iteration we first reconstruct the background and consequently update the level-set function. We test our method on numerical phantoms and show that we can successfully reconstruct the geometry of the anomaly, even from limited data. On these phantoms, our method outperforms Total Variation reconstruction, DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry for Computer Imager

Development in Aspergillus

AbstractThe genus Aspergillus represents a diverse group of fungi that are among the most abundant fungi in the world. Germination of a spore can lead to a vegetative mycelium that colonizes a substrate. The hyphae within the mycelium are highly heterogeneous with respect to gene expression, growth, and secretion. Aspergilli can reproduce both asexually and sexually. To this end, conidiophores and ascocarps are produced that form conidia and ascospores, respectively. This review describes the molecular mechanisms underlying growth and development of Aspergillus

On the (not so) constant proportional trade-off in TTO

Abstract. Purpose: The linear and power QALY models require that people in Time Trade-off (TTO) exercises sacrifice the same proportion of lifetime to obtain a health improvement, irrespective of the absolute amount. However, evidence on these constant proportional trade-offs (CPTOs) is mixed, indicating that these versions of the QALY model do not represent preferences. Still, it may be the case that a more general version of the QALY model represents preferences. This version has the property that people want to sacrifice the same proportion of utilities of lifetime for a health improvement, irrespective of the amount of this lifetime. Methods: We use a new method to correct TTO scores for utility of life duration and test whether decision makers trade off utility of duration and quality at the same rate irrespective of duration. Results: We find a robust violation of CPTO for both uncorrected and corrected TTO scores. Remarkably, we find higher values for longer durations, contrary to most previous studies. This represents the only study correcting for utility of life duration to find such a violation. Conclusions: It seems that the trade-off of life years is indeed not so constantly proportional and, therefore, that health state valuations depend on durations

Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

Mathematical scripting languages are commonly used to develop new tomographic reconstruction algorithms. For large experimental datasets, high performance parallel (GPU) implementations are essential, requiring a re-implementation of the algorithm using a language that is closer to the computing hardware. In this paper, we introduce a new Matlab interface to the ASTRA toolbox, a high performance toolbox for building tomographic reconstruction algorithms. By exposing the ASTRA linear tomography operators through a standard Matlab matrix syntax, existing and new reconstruction algorithms implemented in Matlab can now be applied directly to large experimental datasets. This is achieved by using the Spot toolbox, which wraps external code for linear operations into Matlab objects that can be used as matrices. We provide a series of examples that demonstrate how this Spot operator can be used in combination with existing algorithms implemented in Matlab and how it can be used for rapid development of new algorithms, resulting in direct applicability to large-scale experimental datasets

A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

Regularized iterative reconstruction methods in computed tomography can be effective when reconstructing from mildly inaccurate undersampled measurements. These approaches will fail, however, when more prominent data errors, or outliers, are present. These outliers are associated with various inaccuracies of the acquisition process: defective pixels or miscalibrated camera sensors, scattering, missing angles, etc. To account for such large outliers, robust data misfit functions, such as the generalized Huber function, have been applied successfully in the past. In conjunction with regularization techniques, these methods can overcome problems with both limited data and outliers. This paper proposes a novel reconstruction approach using a robust data fitting term which is based on the Student’s t distribution. This misfit promises to be even more robust than the Huber misfit as it assigns a smaller penalty to large outliers. We include the total variation regularization term and automatic estimation of a scaling parameter that appears in the Student’s t function. We demonstrate the effectiveness of the technique by using a realistic synthetic phantom and also apply it to a real neutron dataset

Measuring loss aversion under ambiguity: a method to make prospect theory completely observable

We propose a simple, parameter-free method that, for the first time, makes it possible to completely observe Tversky and Kahneman’s (1992) prospect theory. While methods exist to measure event weighting and the utility for gains and losses separately, there was no method to measure loss aversion under ambiguity. Our method allows this and thereby it can measure prospect theory’s entire utility function. Consequently, we can properly identify properties of utility and perform new tests of prospect theory. We implemented our method in an experiment and obtained support for prospect theory. Utility was concave for gains and convex for losses and there was substantial loss aversion. Both utility and loss aversion were the same for risk and ambiguity, as assumed by prospect theory, and sign-comonotonic trade-off consistency, the central condition of prospect theory, held

A Multi-Channel DART algorithm

Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute accurate reconstructions from highly limited projection data. For cases where the allowed intensity values in the reconstruction are known a priori, the discrete algebraic reconstruction technique (DART) has shown to yield accurate reconstructions from few projections. However, a key limitation is that the benefit of DART diminishes as the number of different materials increases. Many tomographic imaging techniques can simultaneously record tomographic data at multiple channels, each corresponding to a different weighting of the materials in the object. Whenever projection data from more than one channel is available, this additional information can potentially be exploited by the reconstruction algorithm. In this paper we present Multi-Channel DART (MC-DART), which deals effectively with multi-channel data. This class of algorithms is a generalization of DART to multiple channels and combines the information for each separate channel-reconstruction in a multi-channel segmentation step. We demonstrate that in a range of simulation experiments, MC-DART is capable of producing more accurate reconstructions compared to single-channel DART