基于最大相关熵准则的压缩感知地震道重建方法

Compressed sensing seismic data reconstruction based on maximum correntropy criterion

从含异常振幅噪声的缺失地震道重建问题出发,引入信息论中的最大相关熵准则,构建以最大化相关熵为目标函数的鲁棒地震道重建模型,降低异常振幅噪声在残差度量中的影响;利用最大相关熵的导数构建伪观测数据,并利用迭代阈值算法进行直接求解,进而实现异常振幅噪声干扰下的地震道鲁棒重建。结果表明,欠采样数据中的异常振幅噪声会严重影响传统压缩感知地震信号重建方法的重建精度,而最大相关熵准则可有效抑制噪声对重建过程的影响,可有效提高重建方法的精度及稳定性。

For robust reconstruction of under-sampled and noisy data,the maximum correntropy criterion(MCC),which is widely used in the field of information theoretic learning,is introduced to measure the distance between the observed data and the recovered signal,reducing the influence of erratic noise on misfit estimation.With the help of MCC-based reconstruction model,an iterative shrinkage algorithm is applied to solve the nonlinear problem and robust reconstruction in the presence of erratic noise is achieved.Several seismic examples show that erratic noise present in the under-sampled data indeed influences the reconstruction accuracy with conventional compressive sensing methods,whereas the proposed MCC-based method can effectively attenuate the influence of erratic noise and provide superior accuracy and stability.