• Title/Summary/Keyword: fast truncated Lagrange method, image restoration

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A FAST LAGRANGE METHOD FOR LARGE-SCALE IMAGE RESTORATION PROBLEMS WITH REFLECTIVE BOUNDARY CONDITION

  • Oh, SeYoung;Kwon, SunJoo
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.2
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    • pp.367-377
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    • 2012
  • The goal of the image restoration is to find a good approximation of the original image for the degraded image, the blurring matrix, and the statistics of the noise vector given. Fast truncated Lagrange (FTL) method has been proposed by G. Landi as a image restoration method for large-scale ill-conditioned BTTB linear systems([3]). We implemented FTL method for the image restoration problem with reflective boundary condition which gives better reconstructions of the unknown, the true image.

THE FAST TRUNCATED LAGRANGE METHOD FOR IMAGE DEBLURRING WITH ANTIREFLECTIVE BOUNDARY CONDITIONS

  • Oh, SeYoung;Kwon, SunJoo
    • Journal of the Chungcheong Mathematical Society
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    • v.31 no.1
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    • pp.137-149
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    • 2018
  • In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.