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Optical Engineering

Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system
Author(s): Qin-Xiao Liu; Ting-yu Zhao; Wen-zi Zhang; Fei-hong Yu
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Paper 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.

Paper Details

Date Published: 1 December 2008
PDF: 5 pages
Opt. Eng. 47(12) 127005 doi: 10.1117/1.3050348
Published in: Optical Engineering Volume 47, Issue 12
Show Author Affiliations
Qin-Xiao Liu, Zhejiang Univ. (China)
Ting-yu Zhao, Zhejiang Univ. (China)
Wen-zi Zhang, Zhejiang Univ. (China)
Fei-hong Yu, Zhejiang Univ. (China)

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