Sinogram restoration from partially-known blur for tomographic reconstruction

The authors consider the problem of tomographic image reconstruction when the system response matrix (SRM) of the imaging process is not known exactly, a situation which arises almost universally in practice. The authors frame the problem in terms of pre-reconstruction restoration of the sinogram, and propose an iterative maximum a posteriori (MAP) algorithm for simultaneous sinogram-covariance estimation and restoration. Convergence analysis is performed to ascertain that the proposed covariance estimator converges to the optimal one in the MAP sense. The proposed algorithm is demonstrated in computer simulations, and compared with several other iterative restoration techniques. The results show the proposed method to be very robust to incorrect SRM information and noise, and to offer a significant computational advantage over other algorithms.