Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system

Abstract

The point spread function (PSF) is asymmetric in a wavefront coding (WFC) system with cubic phase mask (CPM). The image formation of the WFC system is described as the generalized Sylvester matrix equation. With Tikhonov regularization, a global generalized minimal residual method (Gl-GMRES) algorithm is used to obtain the restored sharp image. For this large-scale, linear, and discrete, ill-posed problem, we introduce a Kronecker product approximation of the blurring operator to reduce the computation consumption. To eliminate ringing effect, four boundary conditions (BCs) are considered in the image restoration: periodic BCs, zero BCs, reflective BCs, and antireflective BCs. Analysis and numerical results show that the antireflective BCs provide better results than others. The experiment results show that the Gl-GMRES algorithm with antireflective BCs is more effective than the classic Wiener filter.