A fast algorithm for ring artefact reduction in high-resolution micro-tomography with synchrotron radiation is presented. The new method is a generalization of the one proposed by Titarenko and collaborators, with a complete sinogram restoration prior to reconstruction with classical algorithms. The generalized algorithm can be performed in linear time and is easy to implement. Compared with the original approach, with an explicit solution, this approach is fast through the use of the conjugate gradient method. Also, low/high-resolution sinograms can be restored using higher/lower-order derivatives of the projections. Using different order for the derivative is an advantage over the classical Titarenko's approach. Several numerical results using the proposed method are provided, supporting our claims.
We describe a new approach for the inversion of the generalized attenuated radon transform in X-ray fluorescence computed tomography (XFCT). The approach consists of using the radon inverse as an approximation for the actual one, followed by an iterative refinement. Also, we analyze the problem of retrieving the attenuation map directly from the emission data, giving rise to a novel alternating method for the solution. We applied our approach to real and simulated XFCT data and compared its performance to previous inversion algorithms for the problem, showing its main advantages: better images than those obtained by other analytic methods and much faster than iterative methods in the discrete setting.
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they are closer to the Pareto optimal curve than the non-superiorized techniques. A new scaled gradient iteration is proposed and three superiorization schemes are evaluated. Theoretical analysis of the methods as well as computational experiments with both synthetic and real data are provided.
X-ray fluorescence computed tomography (XFCT) is a relatively new synchrotron-based imaging modality aiming at reconstructing the distribution of nonradiative elements within a sample irradiated with high-intensity monochromatic x-rays. In a recent paper La Rivière (2004 Phys. Med. Biol. 49 2391-405) presented an approximated inversion method based on reducing the problem to the inversion of the exponential radon transform. In this paper we compare La Rivière's results with recently derived 'exact' analytic formulae for the generalized attenuated radon transform. We present numerical experiments with real and simulated data.
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