Optimization over finite frame varieties and structured dictionary design

详细信息	查看全文 | 推荐本文 |

• 作者：Nate Strawn¹ ; ^{nathaniel.strawn@duke.edu}
• 关键词：Grassmannian frames ; Welch bound ; Mutual coherence ; Geometric optimization
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2012
• 期刊代码：119_10635203
• 类别：cp
• 出版时间：May, 2012
• 卷：32
• 期：3
• 页码：413-434
• 文件大小：399 K

摘要

A finite -frame variety consists of real or complex matrices satisfying and for all . This paper introduces an approximate geometric gradient descent procedure over these varieties, which is powered by minimization algorithms for the frame operator distance and recent characterizations of these varieties始 tangent spaces. For almost all compatible pairings , we demonstrate that minimization of the frame operator distance converges linearly under a threshold, we derive a process for constructing the orthogonal projection onto these varieties始 tangent spaces, and finally demonstrate that the approximate gradient descent procedure converges. Finally, we apply this procedure to numerically construct Grassmannian frames and Welch bound equality sequences with low mutual coherence.