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带边界条件约束的非相干字典学习方法及其稀疏表示

汤红忠 张小刚 陈华 程炜 唐美玲

汤红忠, 张小刚, 陈华, 程炜, 唐美玲. 带边界条件约束的非相干字典学习方法及其稀疏表示. 自动化学报, 2015, 41(2): 312-319. doi: 10.16383/j.aas.2015.c140183
引用本文: 汤红忠, 张小刚, 陈华, 程炜, 唐美玲. 带边界条件约束的非相干字典学习方法及其稀疏表示. 自动化学报, 2015, 41(2): 312-319. doi: 10.16383/j.aas.2015.c140183
TANG Hong-Zhong, ZHANG Xiao-Gang, CHEN Hua, CHENG Wei, TANG Mei-Ling. Incoherent Dictionary Learning Method with Border Condition Constrained for Sparse Representation. ACTA AUTOMATICA SINICA, 2015, 41(2): 312-319. doi: 10.16383/j.aas.2015.c140183
Citation: TANG Hong-Zhong, ZHANG Xiao-Gang, CHEN Hua, CHENG Wei, TANG Mei-Ling. Incoherent Dictionary Learning Method with Border Condition Constrained for Sparse Representation. ACTA AUTOMATICA SINICA, 2015, 41(2): 312-319. doi: 10.16383/j.aas.2015.c140183

带边界条件约束的非相干字典学习方法及其稀疏表示

doi: 10.16383/j.aas.2015.c140183
基金项目: 

国家自然科学基金(61174050,61203016),湘潭大学控制科学与工程学科建设经费资助

详细信息
    作者简介:

    汤红忠 湘潭大学信息工程学院副教授.湖南大学电气与信息工程学院博士研究生. 主要研究方向为压缩感知, 稀疏表示及其在图像处理与模式识别中的应用.E-mail: diandiant@126.com

    通讯作者:

    陈华 湖南大学信息科学与工程学院讲师. 主要研究方向为图像处理与模式识别. 本文通信作者.E-mail: anneychen@126.com

Incoherent Dictionary Learning Method with Border Condition Constrained for Sparse Representation

Funds: 

Supported by National Natural Science Foundation of China (61174050, 61203016) and Control Science and Engineering Disciplinary Construction Funds of Xiangtan University

  • 摘要: 从字典的相干性边界条件出发, 提出一种基于极分解的非相干字典学习方法(Polar decomposition based incoherent dictionary learning, PDIDL), 该方法将字典以Frobenius范数逼近由矩阵极分解获取的紧框架, 同时采用最小化所有原子对的内积平方和作为约束, 以降低字典的相干性, 并保持更新前后字典结构的整体相似特性. 采用最速梯度下降法和子空间旋转实现非相干字典的学习和优化. 最后将该方法应用于合成数据与实际语音数据的稀疏表示. 实验结果表明, 本文方法学习的字典能逼近等角紧框架(Equiangular tight-frame, ETF), 实现最大化稀疏编码, 在降低字典相干性的同时具有较低的稀疏表示误差.
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出版历程
  • 收稿日期:  2014-03-31
  • 修回日期:  2014-07-23
  • 刊出日期:  2015-02-20

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