2022 Fiscal Year Annual Research Report
Efficient Numerical Solution for Constrained Tensor Ring Decomposition: A Theoretical Convergence Analysis and Applications
| Project/Area Number |
20K19749
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
鄭 寧 統計数理研究所, 統計的機械学習研究センター, 特任研究員 (60859122)
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | ill-posed problem / iterative method / ADMM / nonnegative constraints |
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| Outline of Annual Research Achievements |
Firstly, the linear discrete ill-posed problem with total variation Tikhonov model is considered for preserving sharp attributes in images. Meanwhile, the restored images from TV-based methods are constrained in a given dynamic range. We propose using the alternating direction method of multipliers to solve the constrained models and the constrained subproblems are solved by modulus-based iteration methods. Our numerical results show that for some images where there are many pixels with values lying on the boundary of the dynamic range, and the proposed algorithm is better than state-of-the-art unconstrained algorithms in terms of both accuracy and robustness with respect to the regularization parameter.
Secondly, we consider the gradient projection successive overrelaxation methods with randomized and Gauss-Southwell selection of update indices, for solving large sparse nonnegative constrained least squares problem, or linear complementarity problem. The unified theoretical convergence analysis is proposed, and the convergence rates are discussed. The proposed methods can be naturally extended to the block coordinate descent method with randomized or Gauss-Southwell version, and thus can be applied for solving the nonnegative matrix factorization, nonnegative constrained tensor train/ring decomposition problems. Numerical experiments on synthetic data and real application data show the efficiency of the proposed methods and further confirm the theoretical analysis.
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Research Products
(1 results)
