Regularization methods for image restoration based on autocorrelation functions

Image restoration is a procedure which is charaterized by ill-poseness, ill-conditioning and non-uniqueness of the solution in the presence of noise. Iterative numerical methods have gained much attention for solving these inverse problems. Among the methods, minimal variance or least squares approaches are widely used and often generate good results at a reasonable cost in computing time using iterative optimization of the associated cost functional. In this paper, a new regularization method obtained by minimizing the autocorrelation function of residuals is proposed. Several numerical tests using the BFGS nonlinear optimization method are reported and comparisons to the classical Tikhonov regularization method are given. The results show that this method gives competitive restoration and is not sensitive to the regularization weighting parameter. Furthermore, a comprehensive procedure of image restoration is proposed by introducing a modified version of the Mumford-Shah model, which is often used in image segmentation. This approach shows promising improvement in restoration quality.