Iterative maximum a posteriori (MAP) restoration from partially-known blur for tomographic reconstruction

An iterative maximum a posteriori (MAP) algorithm is proposed for simultaneous signal-covariance estimation and restoration when only partial knowledge of the system response matrix (SRM) and the noisy-blurred sinogram of an image to be reconstructed are available. Convergence analysis is performed to ascertain that the proposed covariance estimator converges to the optimal one in the MAP sense. The superiority of the proposed algorithm, in comparison with the iterative linear minimum mean-squared-error (LMMSE) filter for incorrect SRM information, is experimentally verified.