The author studies an image distorted by a nonlinear transformation $T $ and which then is restored back to the original by the inverse transformation $T^{-1}$. This cycle conversion $T^{-1}T$ of digital images can be facilitated by the combination (CSIM) using the splitting-shooting method for $T$ and $T^{-1}$, respectively. A priori error estimates and convergence rates are given which are derived for pixel greyness obtained from CSIM. The analytical results are extended to the harmonic transformation. Numerical and graphical experiments are provided to support the theoretical analysis.
Reviewer: J.Kofroň (Praha)