The mathematical problem that CT image reconstruction is trying to solve is to compute the attenuation coefficients of different x-ray absorption paths (ray sum) that are obtained as a set of data (projection). There are various algorithms used in CT image reconstruction, the following are some of the more common algorithms utilized in commercially available CT today. Iterative algorithms without statistical modeling use an assumption and will compare to the assumption with its measured data, then will continue to make iterations until the two data sets are in agreement. Iterative reconstruction can also use statistical modeling to take into account optics (x-ray source, image voxels and detector), noise (photon statistics), physics (data acquisition),object (radiation attenuation), and other factors. Alternatively, a convolution method known as filtered back projection can be used; this method is widely used in CT today. Because there are many possible sub-optimal solutions to the reconstruction problem, but each have their own drawbacks (such as different imaging artifacts), it is thought to be ill-posed. 

Resolution is the measure of how far apart two objects must be before they can be seen as separate details in the image. The resolution of CT is highly dependent on the hardware being used. Current CT scanners have a spatial resolution of 0.5–0.625 mm in the z-axis, and approximately 0.5 mm in the x- to y-axes. A basic requirement for adequate multiplanar reconstruction is that the resolution is isotropic; eg, the resolution is approximately equal in all directions. To determine the fundamental limits of CT, an equation for calculating the theoretical attenuation profile optical transfer function (OTF) from the geometrical dimensions of the system can be derived. Using this OTF information in conjunction with the pixel size and data sampling frequency of the attenuation profiles, an analysis of the factors limiting the spatial resolution of each unit can be made.
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