Image restoration from noisy incomplete frequency data by alternative iteration scheme

Xiaoman Liu Southeast University Jijun Liu Southeast University

Numerical Analysis and Scientific Computing mathscidoc:2103.25004

Inverse Problems and Imaging, 14, (4), 583-606, 2020.5
Consider the image restoration from incomplete noisy frequency data with total variation and sparsity regularizing penalty terms. Firstly, we establish an unconstrained optimization model with di erent smooth approximations on the regularizing terms. Then, to weaken the amount of computations for cost functional with total variation term, the alternating iterative scheme is developed to obtain the exact solution through shrinkage thresholding in inner loop, while the nonlinear Euler equation is appropriately linearized at each iteration in exterior loop, yielding a linear system with diagonal coeffi cient matrix in frequency domain. Finally the linearized iteration is proven to be convergent in generalized sense for suitable regularizing parameters, and the error between the linearized iterative solution and the one gotten from the exact nonlinear Euler equation is rigorously estimated, revealing the essence of the proposed alternative iteration scheme. Numerical tests for different confi gurations show the validity of the proposed scheme, compared with some existing algorithms.
Image restoration, alternating iteration, regularization, optimization
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@inproceedings{xiaoman2020image,
  title={Image restoration from noisy incomplete frequency data by alternative iteration scheme},
  author={Xiaoman Liu, and Jijun Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210325170458733740762},
  booktitle={Inverse Problems and Imaging},
  volume={14},
  number={4},
  pages={583-606},
  year={2020},
}
Xiaoman Liu, and Jijun Liu. Image restoration from noisy incomplete frequency data by alternative iteration scheme. 2020. Vol. 14. In Inverse Problems and Imaging. pp.583-606. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210325170458733740762.
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