期刊文献+
共找到3篇文章
< 1 >
每页显示 20 50 100
Stable recovery of signals from frame coefficients with erasures at unknown locations 被引量:1
1
作者 deguang han Fusheng Lv Wenchang Sun 《Science China Mathematics》 SCIE CSCD 2018年第1期151-172,共22页
In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy par... In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one. 展开更多
关键词 FRAMES ERASURES signal recovery almost robust frames totally robust frames
原文传递
Structural Properties of Homomorphism Dilation Systems 被引量:1
2
作者 deguang han David R.LARSON +1 位作者 Bei LIU Rui LIU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2020年第4期585-600,共16页
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras,the authors ... Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras,the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces.By introducing two natural dilation structures,namely the canonical and the universal dilation systems,they prove that every linearly minimal dilation is equivalent to a reduced homomorphism dilation of the universal dilation,and all the linearly minimal homomorphism dilations can be classified by the associated reduced subspaces contained in the kernel of synthesis operator for the universal dilation. 展开更多
关键词 Linear systems Linearly minimal homomorphism dilation systems Principle and universal dilations Equivalent dilation systems
原文传递
Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system
3
作者 Youfa Li deguang han +1 位作者 Shouzhi Yang Ganji Huang 《Science China Mathematics》 SCIE CSCD 2021年第2期351-372,共22页
The Sobolev space H^(■)(R^(d)),where■>d/2,is an important function space that has many applications in various areas of research.Attributed to the inertia of a measurement instrument,it is desirable in sampling t... The Sobolev space H^(■)(R^(d)),where■>d/2,is an important function space that has many applications in various areas of research.Attributed to the inertia of a measurement instrument,it is desirable in sampling theory to recover a function by its nonuniform sampling.In the present paper,based on dual framelet systems for the Sobolev space pair(H^(s)(R^(d)),H^(-s)(R^(d))),where d/2<s<■,we investigate the problem of constructing the approximations to all the functions in H^(■)(R^(d))by nonuniform sampling.We first establish the convergence rate of the framelet series in(H^(s)(R^(d)),H^(-s)(R^(d))),and then construct the framelet approximation operator that acts on the entire space H^(■)(R^(d)).We examine the stability property for the framelet approximation operator with respect to the perturbations of shift parameters,and obtain an estimate bound for the perturbation error.Our result shows that under the condition d/2<s<■,the approximation operator is robust to shift perturbations.Motivated by Hamm(2015)’s work on nonuniform sampling and approximation in the Sobolev space,we do not require the perturbation sequence to be in■^(α)(Z^(d)).Our results allow us to establish the approximation for every function in H^(■)(R^(d))by nonuniform sampling.In particular,the approximation error is robust to the jittering of the samples. 展开更多
关键词 Sobolev space framelet series truncation error perturbation error nonuniform sampling and approximation
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部