69 citations · 518 across the 94 of their papers we have counts for
4 papers · 1 filter
Convergence of the Point Integral method for the Poisson equation with Dirichlet boundary on point cloud
Zuoqiang Shi, Jian Sun
The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the…
Sparse Time Frequency Representations and Dynamical Systems
T. Y. Hou, Z. Shi, P. Tavallali
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations…
Sparse Time-Frequency decomposition by dictionary learning
Thomas Y. Hou, Zuoqiang Shi
In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optim…
Convergence of a data-driven time-frequency analysis method
Thomas Y. Hou, Zuoqiang Shi, Peyman Tavallali
In a recent paper, Hou and Shi introduced a new adaptive data analysis method to analyze nonlinear and non-stationary data. The main idea is to look for the sparsest representation…