基于分段采样和MCA的地震数据重建

数据重建是地震资料处理中一项重要的前期工作。压缩感知(compress sensing, CS)已经在数据重建领域取得了很好的应用。CS的关键是采样的随机性,随机采样将常规欠采样引起的互相干假频转化为较低能量的不相干噪声。一方面,传统的随机采样方法缺乏对采样点的约束,导致产生过多的噪声干扰,分段随机采样可有效地控制采样点之间的距离。另一方面,单一的数学变换会导致信号的不完全稀疏表达,影响数据重建效果,形态分量分析(morphological component analysis, MCA)将信号分解成几个具有显著特征的成分以逼近数据复杂的内部结构。本文在MCA框架下找到了一个新的字典组合(Shearlet+DCT),并使用块坐标松弛(block coordinate relaxation,BCR)算法得到最优解,从而获得理想重构结果。对实际资料的实验表明,该方法在重建分段随机采样数据时具有较好效果。

Seismic data reconstruction based on segmented random sampling and MCA

Data reconstruction is a critical preliminary work in the processing of seismic data.Compressed sensing (CS) has been well applied in data reconstruction.The key to CS is random sampling,which converts the mutual coherent alias caused by regular under-sampling into lower-amplitude incoherent noise. But traditional sampling methods lack constraints on sampling points, resulting in excessive noise interference. The segmented random sampling (SRS) method can effectively control the distance between sampling points. Furthermore, a single mathematical transformation will lead to incomplete sparse representation and impact data reconstruction. The morphological component analysis (MCA) can decompose a signal into several components with outstanding morphological features to approximate the complex internal structure of data. A new dictionary combination (Shearlet+DCT) has been found under the MCA framework, and the block coordinate relaxation (BCR) algorithm has been used to get the optimal solution to obtain desired reconstruction results. Tests of real data have proven that the proposed method can produce good effects when used to reconstruct the SRS data.