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The task of reconstructing an object from its projections via tomographic methods is a time-consuming process due to the vast complexity of the data. For this reason, manufacturers of equipment for medical computed tomography (CT) rely mostly on special application specified integrated circuits (ASICs) to obtain the fast reconstruction times required in clinical settings. Although modern CPUs have gained sufficient power in recent years to be competitive for two-dimensional (2D) reconstruction, this is not the case for three-dimensional (3D) reconstructions, especially not when iterative algorithms must be applied. The recent evolution of commodity PC computer graphics boards (GPUs) has the potential to change this picture in a very dramatic way. In this paper we will show how the new floating point GPUs can be exploited to perform both analytical and iterative reconstruction from X-ray and functional imaging data. For this purpose, we decompose three popular three-dimensional (3D) reconstruction algorithms (Feldkamp filtered backprojection, the simultaneous algebraic reconstruction technique, and expectation maximization) into a common set of base modules, which all can be executed on the GPU and their output linked internally. Visualization of the reconstructed object is easily achieved since the object already resides in the graphics hardware, allowing one to run a visualization module at any time to view the reconstruction results. Our implementation allows speedups of over an order of magnitude with respect to CPU implementations, at comparable image quality.