A different, and more general, approach to tomographic reconstruction is to formulate the problem in terms of a system of linear equations [4,5]. In order to accomplish this, the image is discretized and approximated by
where the 
are basis functions given by
The projection data may now be written as
where 
is a projection operator that determines the contribution
of each pixel to projection i. Since the 
are known, the
numbers
may be calculated. This results in a matrix W, describing the contribution of each pixel to each projection as shown in Fig. 9, and since only a small number of pixels will contribute to a given projection, W will be a very sparse matrix.
The reconstruction problem is now the problem of solving the linear system of equations,
where 
is a vector containing pixel intensities 
and
is a vector containing projection values 
.
Figure 9: The sparse matrix W contains weighting factors for the
contribution of each pixel to individual projection points.
