REGULARIZED CONSTRAINED TOTAL LEAST-SQUARES IMAGE-RESTORATION

In this paper, the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (PSF) that is not exactly known is formulated as the solution of a perturbed set of linear equa tions, The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization prop erties 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 implemen tation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion, is performe d to verify its superiority over the constrained total least-squares ( CTLS) estimate. Numerical experiments for different errors in the PSF are performed to test the RCTLS estimator. Objective and visual compar isons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator. Our experiments sh ow that the RCTLS estimator reduces significantly ringing artifacts ar ound edges as compared to the two other approaches.