Accelerating optimization-based computed tomography via sparse matrix approximations

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.