  Variational formulations of reconstruction in computed tomography have the
notable drawback of requiring repeated evaluations of both the forward Radon
transform and either its adjoint or an approximate inverse transform which are
relatively expensive. We look at two methods for reducing the effect of this
resulting computational bottleneck via approximating the transform evaluation
with sparse matrix multiplications. The first method is applicable for general
iterative optimization algorithms. The second is applicable in error-forgetting
algorithms such as split Bregman. We demonstrate these approximations
significantly reduce the needed computational time needed for the iterative
algorithms needed to solve the reconstruction problem while still providing
good reconstructions.
