Shearlet域自适应阈值地震数据随机噪声压制

Shearlet变换因其最优的稀疏表示和多尺度、多方向特性，对地震数据噪声有很好的压制效果。但基于Shearlet变换的传统阈值法仅考虑了信号的稀疏性在尺度上的特征，没有考虑在方向上的分布特征，不能使去噪效果达到最佳。结合Shearlet变换多尺度、多方向特性，在尺度自适应阈值基础上，研究信号在Shearlet域不同方向上的分布规律，提出一种随尺度和方向同时自适应变化的阈值。通过求取同一尺度、不同方向的L₂范数，统计有效信号的分布规律，进而在阈值计算过程中添加方向自适应项，达到随尺度和方向同时自适应的目的。理论和实际数据的试验结果表明，基于尺度和方向同时自适应的阈值相对于传统阈值能够更有效压制随机噪声，最大限度地保留有效地震信息。

Random noise suppression using adaptive threshold in Shearlet domain

Due to its optimal sparse representation and multi-scale and multi-direction characters,the Shearlet transform has a good performance for seismic noise reduction.Conventional Shearlet-based thresholding method involved the scale of sparsity,but it does not involve the direction of sparsity.It means that noise cannot be efficiently removed.We investigate the signal variation with directions in Shearlet domain and present scale and direction adaptive thresholding based on scale adaptive thresholding.The L₂ norm is calculated on a same scale in different directions to investigate the distribution of effective signals.The direction adaptive term is added to thresholding to realize scale and direction adaptive thresholding simultaneously.Model and real data tests show that this simultaneous adaptive thresholding exhibits better performance than the conventional method in random noise reduction and the utmost of signal preservation.