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A modified augmented lagrange multiplier algorithm for toeplitz matrix completion

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Abstract

In this paper, a modified scheme is proposed for iterative completion matrices generated by the augmented Lagrange multiplier (ALM) method based on the mean value. So that the iterative completion matrices generated by the new algorithm are of the Toeplitz structure, which decrease the computation of SVD and have better approximation to solution. Convergence is discussed. Finally, the numerical experiments and inpainted images show that the new algorithm is more effective than the accelerated proximal gradient (APG) algorithm, the singular value thresholding (SVT) algorithm and the ALM algorithm, in CPU time and accuracy.

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Authors and Affiliations

  1. Higher Education Key Laboratory of Engineering Science Computing in Shanxi Province, Taiyuan Normal University, Taiyuan, 030012, China

    Chuanlong Wang & Chao Li

  2. School of Computer Science and Technology, Beihang University, Beijing, 100191, People’s Republic of China

    Jin Wang

Authors
  1. Chuanlong Wang
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  2. Chao Li
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  3. Jin Wang
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Corresponding author

Correspondence to Chuanlong Wang.

Additional information

Communicated by: Raymond H. Chan

This work was supported by National Natural Science Foundation of China (Grant No. 11371275).

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Wang, C., Li, C. & Wang, J. A modified augmented lagrange multiplier algorithm for toeplitz matrix completion. Adv Comput Math 42, 1209–1224 (2016). https://doi.org/10.1007/s10444-016-9459-y

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  • DOI: https://doi.org/10.1007/s10444-016-9459-y

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