等距丢失模型下的框架张量积重构方法  

TENSOR PRODUCT METHOD FOR FRAMES BASED ON EQUIDISTANT ERASURES MODEL

作　　者：范俊民 冷劲松[1] 李东伟 Fan Junmin;Leng Jinsong;Li Dongwei(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China;School of Mathematicals,HeFei University of Technology,Hefei 230009,China)

机构地区：[1]电子科技大学数学科学学院,成都611731 [2]合肥工业大学数学学院,合肥230009

出　　处：《计算数学》2020年第2期159-169,共11页Mathematica Numerica Sinica

基　　金：自然基金科研项目结题后新建项目(LJT10110010115)资助.

摘　　要：框架理论常应用于信号重构.当编码系数在传输过程中发生等距丢失时,基于框架张量积的一些性质,我们可以利用框架张量积对信号进行编码从而降低数据丢失对重构信号的影响.本文由此提出了一种等距丢失模型,并在此模型下,研究了数据等距丢失下的最优对偶框架张量积,得出了对偶框架和正则对偶框架的张量积是最优对偶框架张量积的两个充分必要条件.最后数值实验也说明了:在等距丢失模型下,最优对偶框架张量积比一般对偶框架张量积的信号重构结果更优.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.

关 键 词：框架 对偶框架 张量积 等距丢失 

分 类 号：O183.2[理学—数学]