An Iterative Support Shrinking Algorithm for Non-Lipschitz Optimization in Image Restoration

作者：Zeng, Chao^*; Jia, Rui; Wu, Chunlin

来源：Journal of Mathematical Imaging and Vision, 2019, 61(1): 122-139.

DOI：10.1007/s10851-018-0830-0

• Non-convex non-smooth optimization
• Non-Lipschitz optimization
• Lower bound theory
• Kurdyka-ojasiewicz property
• Total variation regularization
• Image restoration

We consider a class of non-Lipschitz regularization problems that include the TVp model as a special case. A lower bound theory of the non-Lipschitz regularization is obtained, which inspires us to propose an algorithm guaranteeing the non-expansiveness of the images gradient support set. After being proximally linearized, this algorithm can be easily implemented. Some standard techniques in image processing, like the fast Fourier transform, could be utilized. The global convergence is also established. Moreover, we prove that the restorations by the algorithm have edge preservation property. Numerical examples are given to show good performance of the algorithm and the rationality of the theories.

• 出版日期2019-1
• 单位南开大学