对偶框架稀疏性的两个结果

李登峰, 陈书燕

数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 737-744.

PDF(461 KB)
PDF(461 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 737-744. DOI: 10.12386/A2014sxxb0068
论文

对偶框架稀疏性的两个结果

    李登峰1, 陈书燕2
作者信息 +

Two Results of Sparsity for Dual Frames

    Deng Feng LI1, Shu Yan CHEN2
Author information +
文章历史 +

摘要

利用矩阵 φ 的概念 sparkj(φ)讨论对偶框架的稀疏性. 首先,建立谱块算法框架的最佳稀疏对偶框架的稀疏值之新表示形式;其次,给出对偶框架稀疏值为最小的有限框架的充要条件.

Abstract

This paper investigates the sparsity of dual frames by using the concept sparkj(Φ) of matrix Φ. First, a new expression of sparsity of optimal sparse dual frames for spectral tetris frame is established. Second, a sufficient and necessary condition of a finite frame, whese dual frame's sparsity is minimal, is presented.

关键词

框架 / 对偶框架 / 稀疏性

Key words

frame / dual frame / sparsity

引用本文

导出引用
李登峰, 陈书燕. 对偶框架稀疏性的两个结果. 数学学报, 2014, 57(4): 737-744 https://doi.org/10.12386/A2014sxxb0068
Deng Feng LI, Shu Yan CHEN. Two Results of Sparsity for Dual Frames. Acta Mathematica Sinica, Chinese Series, 2014, 57(4): 737-744 https://doi.org/10.12386/A2014sxxb0068

参考文献

[1] Cahill J., Fickus M., Mixon D. G., et al., Constructing finite frames of a given spectrum and set of lengths, Appl. Comput. Harmon. Anal., 2013, 35(1): 52-73.

[2] Calderbank A. R., Casazza P. G., Heinecke A., et al., Sparse fusion frames: existence and construction, Adv. Comput. Math., 2011, 35(1): 1-31.

[3] Casazza P. G., The art of frame theory, Taiwanese J. Math., 2000, 4(1): 129-201.

[4] Casazza P. G., Fickus M., Heinecke A., et al., Spectral tetris fusion frame constructions, J. Fourier Anal. Appl., 2012, 18 (4): 828-851.

[5] Casazza P. G., Fickus M., Mixon D. G., et al., Constructing tight fusion frames, Appl. Comput. Harmon. Anal., 2011, 30(2): 175-187.

[6] Casazza P. G., Heinecke A., Krahmer F., et al., Optimally Sparse Frames, IEEE Trans. Inform. Theory, 2011, 57(11): 7279-7287.

[7] Casazza P. G., Heinecke A., Kornelson K., et al., Necessary and sufficient conditions to perform spectral tetris, Lin. Alg. and its Appl., 2013, 438(5): 2239-2255.

[8] Casazza P. G., Kutyniok G., Finite Frames: Theory and Applications, Boston, Birkhäuser, 2012.

[9] Christensen O., Introduction to Frames and Riesz Bases, Boston, Birkhäuser, 2003.

[10] Christensen O., Frames and Bases: An Introductory Course, Boston, Birkhäuser, 2008.

[11] Krahmer F., Kutyniok G., Lemvig J., Sparsity and spectral properties of dual frames, Lin. Alg. and its Appl., 2013, 439(4): 982-998.

[12] Li D. F., Xue M. Z., Bases and Frames in Banach Spaces (in Chinese), Science Press, Beijing, 2007.

基金

国家自然科学基金资助项目(61071189)

PDF(461 KB)

Accesses

Citation

Detail

段落导航
相关文章

/