• 论文 •

### 等距丢失模型下的框架张量积重构方法

1. 1. 电子科技大学数学科学学院, 成都 611731;
2. 肥工业大学数学学院, 合肥 230009
• 收稿日期:2018-04-11 出版日期:2020-05-15 发布日期:2020-05-15
• 基金资助:

自然基金科研项目结题后新建项目（LJT10110010115）资助.

Fan Junmin, Leng Jinsong, Li Dongwei. TENSOR PRODUCT METHOD FOR FRAMES BASED ON EQUIDISTANT ERASURES MODEL[J]. Mathematica Numerica Sinica, 2020, 42(2): 159-169.

### TENSOR PRODUCT METHOD FOR FRAMES BASED ON EQUIDISTANT ERASURES MODEL

Fan Junmin1, Leng Jinsong1, Li Dongwei2

1. 1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. School of Mathematicals, HeFei University of Technology, Hefei 230009, China
• Received:2018-04-11 Online:2020-05-15 Published:2020-05-15

Frames theory has a very common application in signal reconstruction. When equidistant erasures occur during the transmission process of the coding coefficient data, we can reduce the effect of data erasures on reconstructed signal by using the tensor product of frames to encode the signal, which is based on some properties of the tensor product of frames. In this paper, we propose a equidistant erasures model, and the tensor product of the optimal dual frame for equidistant erasures is studied based on it. And we get two sufficient and necessary conditions that the tensor product of the dual frame and the canonical dual frame are obtained as the tensor product of the optimal dual frame for equidistant erasures. Finally, numerical experiments show that the signal recovery result of the tensor product of the optimal dual frame is better than the tensor product of the general dual frame under the equidistant erasures model.

MR(2010)主题分类:

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 [1] Duffin R J, Schaeffer A C. A class of nonharmonic Fourier series[J]. Transactions of the American Mathematical Society, 1952, 72(2):341-366.[2] Casazza P G, Kovacevic J. Uniform tight frames for signal processing and communication[J]. Proceedings of SPIE - The International Society for Optical Engineering, 2001, 4478.[3] Casazza P G, Kutyniok G. Frames of subspaces[J]. Wavelets Frames & Operator Theory, 2003, 8(3):87-113.[4] Casazza P G, Kutyniok G, Li S. Fusion frames and distributed processing[J]. Applied & Computational Harmonic Analysis, 2008, 25(1):114-132.[5] Casazza P G, Kutyniok G. Robustness of Fusion Frames under Erasures of Subspaces and of Local Frame Vectors[J]. Contemporary Mathematics, 2008, 464:149-160.[6] Casazza P G, Fickus M. Minimizing Fusion Frame Potential[J]. Acta Applicandae Mathematicae, 2009, 107(1-3):7-24.[7] Casazza P G, Fickus M, Mixon D G, et al. Constructing tight fusion frames[J]. Applied & Computational Harmonic Analysis, 2011, 30(2):175-187.[8] Holmes R B, Paulsen V I. Optimal frames for erasures[J]. Linear Algebra & Its Applications, 2004, 377(1):31-51.[9] Leng J, Han D, Huang T. Probability modelled optimal frames for erasures[J]. Linear Algebra & Its Applications, 2013, 438(11):4222-4236.[10] Leng J, Han D. Orthogonal projection decomposition of matrices and construction of fusion frames[J]. Advances in Computational Mathematics, 2013, 38(2):369-381.[11] Leng J, Huang T. Construction of Fusion Frame Systems in Finite Dimensional Hilbert Spaces[J]. Abstract and Applied Analysis, 2014:1-9.[12] Li D, Leng J, Huang T, et al. Frame expansions with probabilistic erasures[J]. Digital Signal Processing, 2018, 72:75-82.[13] Lopez J, Han D. Optimal dual frames for erasures[J]. Linear Algebra & Its Applications, 2010, 432(1):471-482.[14] Harbrecht H, Schneider R, Schwab C. Multilevel frames for sparse tensor product spaces[J]. Numerische Mathematik, 2008, 110(2):199.[15] Meyer C. Matrix analysis and applied linear algebra[M]. Society for Industrial and Applied Mathematics, 2000.[16] Han D, Kornelson K, Larson D, et al. Frames for Undergraduates[J]. 2007, 40:295.[17] 王文丹, 马昌凤. 关于矩阵Kronecker积的几个范数公式[J]. 福建师大学报(自然科学版), 2015, (6):10-17.[18] 黄廷祝, 钟守铭. 矩阵理论[M]. 高等教育出版社, 2003, 37-38.
 [1] 宋丛威, 邸继征. Shearlet框架的构造和图像处理[J]. 计算数学, 2011, 33(2): 199-212. [2] 何永滔. 紧支撑的最小能量框架[J]. 计算数学, 2011, 33(2): 165-176. [3] 胡齐芽,梁国平. 区域分解界面预条件子构造的一般框架[J]. 计算数学, 1999, 21(1): 117-128.