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An image restoration problem with Poisson noise arises in many applications of medical imaging, astronomy, and microscopy. To overcome ill-posedness, Total Variation (TV) model is commonly used owing to edge preserving property. Since staircase artifacts are observed in restored smooth regions, higher-order TV regularization is introduced. However, sharpness of edges in the image is also attenuated. To compromise benefits of TV and higher-order TV, the weighted sum of the non-convex TV and non-convex higher order TV is used as a regularizer in the proposed variational model. The proposed model is non-convex and non-smooth, and so it is very challenging to solve the model. We propose an iterative reweighted algorithm with the proximal linearized alternating direction method of multipliers to solve the proposed model and study convergence properties of the algorithm.
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참고문헌 (24)
참고문헌 신청
M. Bertero / 2009 / Image deblurring with Poisson data: from cells to galaxies / Inverse Problems 25(12):26
S. Boyd / 2011 / Distributed optimization and statistical learning via the alternating direction method of multipliers / Foundations and Trends in Machine Learning 3:1~122
E. Bratsolis / 2001 / A spatial regularization method preserving local photometry for Richardson-Lucy restoration / Astron. Astrophys. 375:1120~1128
E. J. Cande / 2008 / Enhancing sparsity by reweighted $l_1$ minimization / J. Fourier Anal. Appl. 14(5-6):877~905
T. Chan / 2000 / High-order total variation-based image restoration / SIAM J. Sci. Comput. 22(2):503~516
S. Boyd / 2011 / Distributed optimization and statistical learning via the alternating direction method of multipliers / Foundations and Trends in Machine Learning 3:1~122
E. Bratsolis / 2001 / A spatial regularization method preserving local photometry for Richardson-Lucy restoration / Astron. Astrophys. 375:1120~1128
E. J. Cande / 2008 / Enhancing sparsity by reweighted
T. Chan / 2000 / High-order total variation-based image restoration / SIAM J. Sci. Comput. 22(2):503~516
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