J. Korean Math. Soc. 2018; 55(3): 719-734
Online first article December 6, 2017 Printed May 1, 2018
https://doi.org/10.4134/JKMS.j170432
Copyright © The Korean Mathematical Society.
Taeuk Jeong, Yoon Mo Jung, Sangwoon Yun
Yonsei University, Sungkyunkwan University, Sungkyunkwan University
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.
Keywords: iterative reweighted algorithm, proximal linearized alternating direction method of multipliers, Poisson image restoration, non-convex
MSC numbers: Primary 90C26, 49M37
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