基于压缩感知的信号重建方法及在气枪震源信号处理中的应用

Signal Reconstruction Method Based on Compressive Sensing and Its Application in Signal Processing of Air-Gun Sources

摘要:

在气枪源探测过程中，由于各种干扰因素的影响，导致部分有效信号缺失或受随机干扰严重，为了重构出连续完整的数据，依据气枪源信号在傅里叶变换域中具有稀疏性的特点，构建了一种基于压缩感知（Compressive Sensing，简称CS）的缺失信号重建方法。首先进行数值模拟，并将该方法与传统的插值方法处理效果进行对比，对重建效果进行均方根误差及信噪比（SNR）分析，结果显示：压缩感知方法重建前后信号的波形吻合度高、振幅一致性更强、同相轴清晰且连续性相同，对噪声压制较好。综上表明：该方法重建效果优于传统的三次样条插值方法。将该方法应用于实际资料，结果显示受干扰的有效信号能够得到很好的恢复重建。

Abstract:

In air-gun source detection, some effective signals are missing or seriously disturbed by random signals due to the influence of various interference factors. To reconstruct continuous and complete data, a missing signal reconstruction method based on compressive sensing is constructed according to the sparse characteristics of air-gun source signals in a Fourier transform domain. First, a numerical simulation is carried out, and the processing effect of this method is compared with that of the traditional interpolation method. The root mean square error and signal-to-noise ratio analyses of the reconstruction effect are carried out. Results show that the compressive sensing method has a high waveform coincidence, strong amplitude consistency, and clear and continuous phase axis and suppresses noise before and after reconstruction. In conclusion, the reconstruction effect of this method is better than that of the traditional cubic spline interpolation method. The method is applied to practical data, and the results show that the interfered effective signal can be well reconstructed.