高效的数据分析方法是我们理解自然现象的重要工具。在很多数据中，频率往往包涵了重要的信息，可以用来揭示和理解数据背后的物理机制。完全自适应于数据本身的时频分析方法对于理解数据及其背后隐藏的物理机制就变得非常重要。..受经验模态分解和压缩感知的启发，本项目提出发展一种数据驱动的稀疏时频分解方法。主要的想法是在一个充分大的时频字典集合里面寻找最稀疏的分解。这种分解可以通过求解一个非线性优化问题来得到。一方面，我们可以借鉴压缩感知中的算法和理论，来高效的求解这一优化问题。另一方面利用这个模型，我们也为经验模态分解提供了严格的数学模型和数学理论。

Developing effective time-frequency analysis methods is an important path through which we can understand the underlying processes of natural phenomena. So far, most time-frequency analysis methods use a pre-determined basis to process data and assume linearity or stationarity of data. Applications of these methods to nonlinear and nonstationary data tend to give many unphysical harmonic modes. To better understand the physical mechanisms hidden in the data, one needs to develop truly adaptive time-frequency ansysis methods that could handle the non-stationary and nonlinearity of the data. Such methods should be adaptive to the nature of the data, which requires the use of an adaptive basis that is derived from the data rather than determined a priori...We propose to develop a new data-driven time-frequency analysis method to study nonlinear and non-stationary data. The key idea is to look for the sparsest time-frequency representation of a signal over the largest possible dictionary using nonlinear optimization, and develop an efficient method to solve this nonlindar nonconvex optimization problem. This method shares many attractive features as those of the Empirical Mode Decomposition method, and can be used to extract physically meaningful information of the signal such as instantaneous frequency and trend. Moerover, our method has solid mathematical foundation and is stable to noise perturbation. Another objective of this proposal is to solve some challenging real work problems in structure health monitering and medical imaging.