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Image restoration by minimizing zero norm of wavelet frame coefficients

Chenglong Bao Department of Mathematics, National University of Singapore, 117543, Singapore Bin Dong Beijing International Center for Mathematical Research, Peking University, Beijing 100871, Peopleʼs Republic of China Likun Hou Institute of Natural Sciences, Shanghai Jiao Tong Univeristy, Shanghai 200240, Peopleʼs Republic of China Zuowei Shen Department of Mathematics, National University of Singapore, 117543, Singapore Xiaoqun Zhang Institute of Natural Sciences, Shanghai Jiao Tong Univeristy, Shanghai 200240, Peopleʼs Republic of China; School of Mathematical Sciences, Shanghai Jiao Tong Univeristy, Shanghai 200240, Peopleʼs Republic of China Xue Zhang School of Mathematical Sciences, Shanghai Jiao Tong Univeristy, Shanghai 200240, Peopleʼs Republic of China

TBD mathscidoc:2206.43008

Inverse Problems, 32, (11), 2016.9
In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the $\ell_0$-norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka–Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of $\ell_0$-norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.
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@inproceedings{chenglong2016image,
  title={Image restoration by minimizing zero norm of wavelet frame coefficients},
  author={Chenglong Bao, Bin Dong, Likun Hou, Zuowei Shen, Xiaoqun Zhang, and Xue Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220614160745082575363},
  booktitle={Inverse Problems},
  volume={32},
  number={11},
  year={2016},
}
Chenglong Bao, Bin Dong, Likun Hou, Zuowei Shen, Xiaoqun Zhang, and Xue Zhang. Image restoration by minimizing zero norm of wavelet frame coefficients. 2016. Vol. 32. In Inverse Problems. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220614160745082575363.
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