On the Convergence of Learning-Based Iterative Methods for Nonconvex Inverse Problems

Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is...

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Veröffentlicht in:IEEE transactions on pattern analysis and machine intelligence Jg. 42; H. 12; S. 3027 - 3039
Hauptverfasser: Liu, Risheng, Cheng, Shichao, He, Yi, Fan, Xin, Lin, Zhouchen, Luo, Zhongxuan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.12.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Acceleration
Algorithms
Convergence
convergence guarantee
Empirical analysis
image deconvolution
Inverse problems
Iterative algorithms
Iterative methods
Learning
Learning systems
learning-based iteration
Modularization
Nonconvex optimization
Numerical methods
rain streaks removal
Statistical analysis
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
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Zusammenfassung:Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis about the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. This paper moves beyond these limits and proposes Flexible Iterative Modularization Algorithm (FIMA), a generic and provable paradigm for nonconvex inverse problems. Our theoretical analysis reveals that FIMA allows us to generate globally convergent trajectories for learning-based iterative methods. Meanwhile, the devised scheduling policies on flexible modules should also be beneficial for classical numerical methods in the nonconvex scenario. Extensive experiments on real applications verify the superiority of FIMA.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2019.2920591