Regularization and image restoration using differential equations

Linear image restoration is posted as a solution to a set of ordinary differential equations (ODE). Explicit and implicit Euler's methods are used to integrate this set of ODE's. The explicit method introduces a regularization operator to the Van Cittert's method while the implicit method leads to the Tikhonov-Miller restoration. Since both methods are simply numerical integration procedures for the same set of ODE's, the extended Van Cittert's method and the Tikhonov-Miller method are shown to be approximately equivalent in performance if a conversion formula is followed. An analysis of the difference between the restorations by the two methods is included, as well as the ramifications of this conversion formula.