719 citations · 1.9k across the 57 of their papers we have counts for
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Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient
Thomas Y. Hou, Pengfei Liu
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to co…
Sparse Time-Frequency decomposition for multiple signals with same frequencies
Thomas Y. Hou, Zuoqiang Shi
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of th…
Extracting a shape function for a signal with intra-wave frequency modulation
Thomas Y. Hou, Zuoqiang Shi
In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using…
On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data
Chunguang Liu, Thomas Y. Hou, Zuoqiang Shi
In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of…