基于EMD-CS的脉冲星周期超快速估计

面向X射线脉冲星周期估计的压缩感知（CS）中测量矩阵尺寸大，进而导致计算量大。针对这一问题，提出了一种基于经验模态分解-压缩感知（EMD-CS）的脉冲星周期超快速估计方法。将不同畸变度的脉冲轮廓进行EMD分解，得到一系列固有模态函数（IMF）。由于IMF包含了不同时间尺度的局部特征信号，脉冲轮廓畸变度这一微弱局部特征可体现在某些IMF中。采用迭代剔除法剔除冗余的IMF，剩下的IMF构成了测量矩阵。由于IMF的数量较少，采样率大幅减少。利用EMD-CS可实现X射线脉冲星周期超快速估计。通过计算复杂度分析结果可知，采样率与计算量呈正比关系。仿真结果中表明，EMD-CS的采样率为0.25%，仅为FFT-CS的1/29，因而计算量更小。

Ultra-fast estimation of pulsar period based on EMD-CS

In the Compressed Sensing (CS) for X-ray pulsar period estimation, the large size of measurement matrix leads to a large amount of calculation. To solve this problem, an ultra-fast pulsar period estimation method based on Empirical Mode Decomposition-Compressed Sensing (EMD-CS ) is proposed. The pulse profiles of multi-distortions are decomposed by EMD to obtain a series of Intrinsic Mode Functions (IMF). As the IMFs contain local characteristic signals at different time scales, the weak local features of the pulse profile distortion can be reflected in some IMFs. The iteration and elimination method is used to eliminate redundant IMFs, and the remaining IMFs form the measurement matrix. Due to the small number of IMFs, the sampling rate is greatly reduced. By using the EMD-CS method, we can realize ultra-fast period estimation of X-ray pulsars. From the results of calculation complexity analysis, we can know that the sampling rate is proportional to the amount of calculation. The simulation results show that the sampling rate of EMD-CS is 0.25%, which is only 1/29 of FFT-CS. Thus, the calculation amount of EMD-CS is smaller than that of FFT-CS.