Fast variance computation for quadratically penalized iterative reconstruction of 3D axial CT images

Finding the variance of iteratively-reconstructed 3D axial CT images is useful for statistical analysis of these images or could be useful for dynamic, on-line beam intensity adjustment. Previous methods for finding the variance are either computationally intractable or approximations that take minutes per voxel to compute. In this paper, we propose a method that can generate a variance image for an entire volume in seconds by making approximations specific to third-generation 3D axial CT geometries. We compare the computation time and error of the resulting approximate image to the empirical image formed from many simulated realizations of a reconstruction.