Fast Continuous Iterative Methods in X-Rays Fluorescence Computed Tomography

Fluorescence computed tomography is a synchrotron imaging technique that reconstructs the fluorescence emission within a sample object. For a monochromatic source hitting the object, the amount of fluorescence detected is given as a linear equation. Iterative methods based on the inversion of the Radon transform were introduced. These methods were compared with the Expectation Maximization algorithm, implemented in a continuous setting. This implementation provided better quality results, but with higher computational cost. Recently, a faster OS-EM algorithm was applied in XFCT, in a discrete setting. In this manuscript we further improve on previous results by considering a relaxed version of OS-EM, in a continuous setting (faster implementation per iteration).