Regularization and image restoration using differential equations

Linear image restoration is posted as a solution to a set of ordinary differential equations (ODEs). Explicit and implicit Euler methods are used to integrate this set of ODEs. The explicit method introduces a regularization operator in the Van Cittert method, while the implicit method leads to the Tikhonov-Miller restoration. Since both methods are simply numerical integration procedures for the same set of ODEs, the extended Van Cittert method and 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 presented and the ramifications of this conversion formula are discussed.<>