A CT reconstruction is a multi-dimensional image showing the internal structure of a patient or an object.  It is prepared by taking numerous x-ray projections through the patient or object, which are then used in a computational process that calculates a structure that would have led to the collection of x-ray projections that was used. 
Various forms of x-ray projection can be used.  A single narrow beam (or “pencil beam”) can be used which will measure the attenuation of the x-ray beam along it.  This is then rotated around the patient or object so as the measure the attenuation along a series of directions.  This allows the internal structure of a single “slice” to be determined, the slice being the plane in which the beam rotated.  More commonly, a fan beam can be used, usually orienting the fan within the plane of the slice, which gives a one-dimensional projection offering more information than a single measurement.  In both cases, the patient or object (or the x-ray apparatus) are indexed perpendicularly to the slice plane in order to capture an adjacent slice and thereby build up a three-dimensional image. 
In another form of CT, known as “Cone-Beam CT” or CBCT, a cone of radiation is directed towards the patient or object and detected after attenuation by a two-dimensional flat-panel detector to yield a number of two-dimensional projection images.  The radiation source and the detector are then rotated around the patient or object to give the necessary collection of images from multiple directions.  These can then be used to reconstruct a three-dimensional volume image. 
Regardless of the type of CT scanning, the mathematical algorithms used to create the images from the projections assume that the photons which arrive at a specific location in the projection image have been attenuated along a straight-line path from a point-like source of radiation.  In practice, and especially for fan-beam and cone-beam CT, this is not the case due to scattering.  When an x-ray photon interacts with matter, it can be attenuated (i.e. absorbed), or it can be scattered.  In the latter case, the photon is re-emitted in a random direction, and therefore may be detected giving rise to an inaccurate measurement of the attenuation elsewhere in the projection image.  Fortunately, x-ray scattering is a well-characterised phenomenon and is therefore relatively predictable given knowledge of the nature of the beam and the matter that it will be interacting with.  A Monte-Carlo-type simulation can therefore be run, computing the outcome of a large number of random interactions between x-ray photons and the target to produce projection images of just the scattered radiation.  These images can then be subtracted from the actual projection images captured by the apparatus, producing a set of clean (substantially scatter-free) projection images.  These can be used to reconstruct a substantially scatter-free CT image. 
U.S. Pat.  No.  6,256,367 discloses such a scatter correction method for computed tomography images of general object geometries where the object geometry is not known a priori, by using the initial CT image (including scatter) as the basis for the Monte-Carlo simulation, which then yields an improved CT image with less scatter.  That process can be iterated if necessary until the CT images being produced start to converge; U.S. Pat.  No.  6,256,367 notes that convergence can be relatively swift.