20 citations · 24 across the 11 of their papers we have counts for
11 papers
Frequency Analysis with Multiple Kernels and Complete Dictionary
Cuiyun Lin, Tao Qian
In signal analysis, among the effort of seeking for efficient representations of a signal into the basic ones of meaningful frequencies, to extract principal frequency components,…
Sampling Gaussian Stationary Random Fields: A Stochastic Realization Approach
Bin Zhu, Jiahao Liu, Zhengshou Lai +1
Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologi…
The sparse representation related with fractional heat equations
Pengtao Li, Tao Qian, Ieng Tak Leong +1
This study introduces pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and t…
Sparse Representations of Solutions to a class of Random Boundary Value Problems
Fang Yang, Min Chen, Jiecheng Chen +2
We introduce certain sparse representation methods, named as stochastic pre-orthogonal adaptive Fourier decomposition 1 and 2 (SPOAFD1 and SPOAFD2) to solve the Dirichlet boundary…
Reproducing kernels of some weighted Bergman spaces
Guan-Tie Deng, Yun Huang, Tao Qian
Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergma…
On Monogenic Reproducing Kernel Hilbert Spaces of the Paley-Wiener Type
Pei Dang, Weixiong Mai, Tao Qian
In the Clifford algebra setting the present study develops three reproducing kernel Hilbert spaces of the Paley-Wiener type, namely the Paley-Wiener spaces, the Hardy spaces on str…
Sparse Approximation to the Dirac-δ Distribution
Wei Qu, Tao Qian, Guan-Tie Deng
The Dirac-δ distribution may be realized through sequences of convlutions, the latter being also regarded as approximation to the identity. The present study proposes the so called…
A Sparse Representation of Random Signals
Tao Qian
Studies of sparse representation of deterministic signals have been well developed. Amongst there exists one called adaptive Fourier decomposition (AFD) established through adaptiv…
A sufficient condition for n-Best Kernel Approximation in Reproducing Kernel Hilbert Spaces
Wei Qu, Tao Qian, Guan-Tie Deng
We show that if a reproducing kernel Hilbert space consisting of functions defined on enjoys Double Boundary Vanishing Condition (DBVC) and Linear Independent Con…
Sparse Solutions for Inverse Problems in Reproducing Kernel Hilbert Spaces
Tao Qian
A linear operator in a Hilbert space defined through the form of Riesz representation naturally introduces a reproducing kernel Hilbert space structure over the range space. Such f…
The Fourier Type Expansions on Tubes
Weixiong Mai, Tao Qian
In view of recent developments of the study of reproducing kernel Hilbert spaces, in particular with the context the Hardy spaces on tubes, aspects of rational approximation for fu…