MAP and regularized constrained total least-squares image restoration

In this paper the problem of restoring an image distorted by a linear space-invariant (LST) point-spread function (PSF) which is not exactly known is solved using a maximum-a posteriori (MAP) formulation. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the MAP estimate is computed in the DFT domain. The similarities between the MAP and the regularized constrained total least-squares (RCTLS) estimates are reported and their equivalence under certain conditions is discussed. A perturbation analysis of the MAP estimate is performed to obtain its mean-squared error (MSE) in a closed form, for small PSF errors. Numerical experiments for different PSF errors are performed to test the MAP estimator for this problem. Objective MSE-based and visual comparisons with the modified linear minimum mean-squared error (LMMSE) filter are presented that verify the superiority of the MAP estimator for higher PSF errors.