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

Qin-Xiao Liu; Ting-yu Zhao; Wen-zi Zhang; Fei-hong Yu

doi:10.1117/1.3050348

1 December 2008 Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system

Qin-Xiao Liu, Ting-yu Zhao, Wen-zi Zhang, Fei-hong Yu

Author Affiliations +

Optical Engineering, Vol. 47, Issue 12, 127005 (December 2008). https://doi.org/10.1117/1.3050348

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.

©(2008) Society of Photo-Optical Instrumentation Engineers (SPIE)

Citation Download Citation

Qin-Xiao Liu, Ting-yu Zhao, Wen-zi Zhang, and Fei-hong Yu "Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system," Optical Engineering 47(12), 127005 (1 December 2008). https://doi.org/10.1117/1.3050348

Published: 1 December 2008

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