Regularization Methods for Image Restoration Based on Autocorrelation Functions

摘要

Image restoration is a procedure which is charaterized by ill-poseness. ill-conditioning and non-uniqueness of the solution in 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 genrate good results at a reasonable cost in computing time using iterative optimization of the associated cost functional. In this paper, a new regualrization method obtained by minizing the autocorrelation function of residuals is proposed. Several numerical tests using the BFGS nonlinear optimization method are repoted and comparisons to the classical Tikhonov regularization method are given. The results show that this method gives compertiive restoration and is not sensitive to the reguarization 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 segmetation. This approach shows promising improviement in restoration quality.