Advanced splitting-integrating methods with high convergence rates for restoring images and patterns

The restoration of digital images and patterns by the splitting-integrating method (SIM) proposed by Li (1993) and Liet al. (1992) is much simpler than other algorithms because no solutions of nonlinear algebraic equations are required. Let a pixel in 2D images be split intoN ² subpixels; the convergence rates areO(1/N) andO/(1/N ²) for pixel greyness under image normalization by SIM. In this paper, the advanced SIM using spline functions can raise the convergence rates to (O(1/N ³) andO(1/N ⁴). Error bounds of pixel greyness obtained are derived from numerical analysis, and numerical experiments are carried out to confirm the high convergence rates ofO(1/N ³) andO(1/N ⁴).