重建误差Huber范数最小化约束的压缩感知方法

地震数据中存在异常强噪声,基于重建误差L₂范数最小化约束的压缩感知方法假设重建误差满足高斯分布。因此,上述压缩感知方法不能去除满足超高斯分布的异常噪声。为了更好地消除异常噪声并提高插值精度,提出采用Huber范数代替L₂范数对重建误差施加最小化约束,Huber范数的最小化约束实际上等价于对大重构误差(异常噪声)的L₁范数最小化约束和对小重构误差(高斯随机噪声)的L₂范数最小化约束,因此对异常噪声具有很好的鲁棒性。通过引入理论上构建的伪地震数据将Huber范数最小化问题转化为L₂范数最小化问题,可以有效地求解基于重建误差Huber范数最小化约束的压缩感知方法的Huber-L₀最优化问题。另外,还讨论了高斯随机噪声的强度、异常噪声强度和参数选取对插值精度的影响。模型数据和实际数据的处理结果表明:与基于重建误差L₂范数最小化约束的压缩感知方法相比,基于重建误差Huber范数最小化约束的压缩感知方法可以更好地消除异常噪声,并保护有效信号。

Compressive sensing method with Huber norm minimization constraint on reconstruction error

Seismic data contain strong noise outliers.The compressive sensing(CS) method based on L₂ norm minimization constraint on reconstruction error assumes that the reconstruction error satisfies Gaussian distribution.Therefore,the CS method above cannot remove super-Gaussian noise outliers.To better remove outliers and improve interpolation accuracy,Huber norm was used instead of L₂ norm to implement the minimization constraint on reconstruction error.The minimization constraint of Huber norm is equivalent to the L₁ norm minimization constraint on large reconstruction error (noise outlier) and the L₂ norm minimization constraint on small reconstruction error (Gaussian random noise).Therefore,the proposed method is robust when dealing with noise outlier.Furthermore,theoretical pseudo seismic data were introduced to convert the Huber norm minimization problem to the L₂ norm minimization problem,in order to solve the Huber-L₀ minimization problem of the proposed CS method based on Huber norm minimization constraint on construction error.Additionally,the affection of Gaussian noise intensity,noise outlier intensity and parameter selection on interpolation accuracy is tested.The processing results of synthetic and field data demonstrated that the proposed CS method based on the Huber norm minimization constraint of the construction error can better remove the noise outliers and preserve effective signals compared with the CS method based on the L₂ norm minimization constraint of the construction error.