A study of stochastic hierarchical convex optimization algorithms and their applications to signal recovery

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06197
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Soft computing
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Ono Shunsuke 東京工業大学, 科学技術創成研究院, 助教 (60752269)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 信号復元 / 確率的最適化 / 階層型最適化 / 凸最適化 / 非凸最適化

Outline of Final Research Achievements

This study aims to establish novel signal recovery methods. The key idea of this study is twofold: stochastic optimization, which enables very efficient optimization based on randomized procedures, and hierarchical optimization, which allows optimization subject to involved hard constraints. Several main contributions are as follows. 1. signal recovery algorithms based on stochastic proximal optimization, which enables efficient signal recovery in the case where the model matrix describing observation process has no specific structure. 2. signal recovery algorithms that can deal with involved hard constraints on data-fidelity arising in signal recovery under non-Gaussian noise contamination. 3. Acceleration of hierarchical convex optimization based on fixed stepsizes. 4. Efficient algorithm to deal with a nonconvex constraint involving a group L0 norm.

Free Research Field

信号処理、画像処理、数理最適化