Exact analytic reconstruction in x-ray fluorescence CT and approximated versions

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.

Iterative reconstruction in X-ray fluorescence tomography based on radon inversion

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.

A new distortion model for strong inhomogeneity problems in echo-planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).