A study on orthogonal matrix optimization and application to blind source separation problems

正交矩阵优化及其在盲源分离问题中的应用研究

• 批准号: 15500129
• 负责人: YAMADA Isao
• 金额: $ 2.3万
• 依托单位: TOKYO INSTITUTE OF TECHNOLOGY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15500129/
• 关键词: Orthogonal matrix; Semi-orthogonal matrix; Dual-Cayley Parametrization; Reduced Rank matrix; Low-rank linear estimator; Adaptive projected subgradient method; Blind interference reduction; Stereo acoustic echo canceling; ブラインド信号分離; Stiefel manifo

In this research project, we studied the blind signal processing and its related problems including (i)orthogonal matrix optimization for blind source separations, (ii)quadratic matrix optimization over the reduced rank matrices, (iii)convex optimization over the fixed point set of quasi-nonexpansive mapping, (iv)asymptotic minimization of sequence of convex functions and its unified view for adaptive filtering problems, (v)blind multiple access interfererence reduction problem for DS/CDMA systems, (vi)stereophonic acoustic echo canceling problem.Mathematically, the above problems are callenging optimization problems which can be classified as follows. The problems on (i)and (ii)are, optimization problems over certain nonconvex constraint sets. The algorithm developed in (iii)answers the question posed by V.Vasin in 1995. The algorithm (adaptive projected subgradient method) developed in (iv)can solve a generalized optimization problem, where the cost function itself keeps changing during the whole process. The problems (v)and (vi)have been tackled by applying the adaptive projected subgradient method

在本研究项目中，我们研究了盲信号处理及其相关问题，包括(I)盲源分离的正交矩阵优化，(Ii)降阶矩阵上的二次矩阵优化，(Iii)拟非扩张映射不动点集上的凸优化，(Iv)凸函数序列的渐近最小化及其自适应滤波问题的统一观点，(V)DS/CDMA系统的盲多址干扰抑制问题，(Vi)立体声回声抵消问题。(I)和(II)中的问题是某些非凸约束集上的最优化问题。文(III)中提出的算法回答了V.Vasin在1995年提出的问题。文(4)中提出的算法(自适应投影次梯度法)可以解决代价函数在整个过程中不断变化的广义优化问题。问题(V)和(Vi)已用自适应投影次梯度法处理。

项目成果

Convex feasibility problem with prioritized hard constraints? double layered projected gradient method

具有优先硬约束的凸可行性问题？

• 发表时间: 2004
• 期刊: IEICE Transactions Fundamentals E87-A, No.4
• 作者: Nobuhiko OGURA;Isao YAMADA
• 通讯作者: Isao YAMADA

A fast blind multiple access interference reduction in DS/CDMA systems by adaptive projected subgradient method

自适应投影次梯度法快速消除DS/CDMA系统盲多址干扰

• 发表时间: 2004
• 期刊: Proceedings of 12th European Signal Processing Conference(EUSIPCO-2004),Vienna
• 作者: Renato CAVALCANTE;Isao YAMADA;Kohichi SAKANIWA
• 通讯作者: Kohichi SAKANIWA

A Non-strictly convex minimization over the bounded fixed point set of the nonexpansive mapping

非扩张映射有界不动点集上的非严格凸最小化

• 发表时间: 2003
• 期刊: Numerical Functional Analysis and Optimization, Numerical Functional Analysis and Optimization vol.24, No.1 & 2
• 作者: Nobuhiko OGURA;Isao YAMADA
• 通讯作者: Isao YAMADA

山田 功: "射影型適応アルゴリズムの新展開---射影劣こう配法による統的視点とその応用"電子情報通信学会誌. 86-8. 654-658 (2003)

Isao Yamada：“投影自适应算法的新进展——使用投影次梯度方法的系统视角及其应用”，电子信息与通信工程师学会杂志 86-8（2003）。

Adaptive Projected Subgradient Method for Asymptotic Minimization of Sequence of Nonnegative Convex Functions

• DOI: 10.1081/nfa-200045806
• 发表时间: 2005-01
• 期刊: Numerical Functional Analysis and Optimization
• 影响因子: 1.2
• 作者: I. Yamada;N. Ogura