Tomographic image reconstruction for systems with partially-known blur

In tomographic image reconstruction, it is usually assumed that the system matrix is known exactly, although this is not usually the case in practice. We investigate the potential benefit of modeling the system matrix as the sum of a known part and an unknown random error. Using some of simplifying assumptions, we develop a penalized weighted least squares (PWLS) reconstruction algorithm for this problem. Our experiments indicate that this approach can, indeed lead to significant improvements in the reconstructed image, both visually and quantitatively.