Computed tomography (CT) reconstruction includes reconstructing an axially extended reconstructed image from a measured cone beam x-ray projection data set (Pm), optionally having an off-center geometry. The reconstructing is performed for an extended volume (eFOV) comprising a reconstructable volume (rFOV) of the measured cone beam x ray data set that is extended along the axial direction. The projection data set may be weighted in the volume domain. Iterative reconstruction may be used, including initializing a constant volume and performing one or more iterations employing a first iterative update followed by one or more iterations employing a second, different iterative update. Alternatively, backprojection filtration (BPF) reconstruction may be used, including transforming the projection data set to a new geometry including finite differences between neighboring projection views and performing BPF using Hilbert filtering along a plurality of different directions and averaging the resultant reconstructed images to generate the final reconstructed image.
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