The invention provides improvements in reconstructive imaging of the type
in which a volume is reconstructed from a series of measured projection
images (or other two-dimensional representations) generated by projection
of a point x-ray source (or other radiation source), positioned at a
distinct focus, through the volume to a plane at which the respective
projection image is acquired ("detector plane"). In one aspect, the
improvements are with respect to back-projecting a two-dimensional
representation lying in the detector plane (representing, for example, a
difference between an originally-acquired measured projection image and a
subsequently-generated estimate thereof) to generate three-dimensional
representation (which can be used, for example, to update an estimate of
the volume). According to this aspect, for each of one or more slices of
the 3D representation parallel to the projection plane and for each
distinct focus at which a projection is generated, the following steps
are performed in connection with the back-projection: (i) warping the
first 2D representation to generate a second 2D representation by
applying to the first 2D representation a selected linear mapping, where
that selected linear mapping would map, in order to match dimensions of
the respective slice within the 3D representation, a region defined by
projection, at the respective focus, of corners of that slice onto the
detector plane, and (ii) incrementing values of each of one or more
voxels of the respective slice by an amount that is a function of a value
of a correspondingly indexed pixel of the second 2D representation. A
related aspect provides improvements with respect to forward-projecting,
as well as in iterative (and non-iterative) methodologies that
incorporate both back-projection and forward-projection.