Regularized constrained total least-squares image restoration

In this paper the problem of restoring an image distorted by a linear space-invariant point- spread function (psf) which is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible for large images. Numerical experiments for different psf approximations are performed to check the effectiveness of the RCTLS approach for this problem. Objective and subjective comparisons are presented with the linear minimum mean-squared-error and the regularized least-squares estimates, for 2D images, that verify the superiority of the RCTLS approach.