基于联合加速近端梯度和对数加权核范数最小化的地震数据重建

Seismic Data Reconstruction Based on Joint Accelerated Proximal Gradient and Log-Weighted Nuclear Norm Minimization

由于地表障碍或经济限制,采样的地震数据通常是不完整的,因此地震数据重建是地震研究中的一个重要课题。本文提出一种基于联合加速近端梯度和对数加权核范数最小化的地震数据重建方法。首先通过纹理块算子对原始地震数据进行低秩预处理,然后使用加速近端梯度算法对低秩地震数据进行初步重建,最后提出对数加权核范数算法,用该算法解决优化问题并重建缺失数据。合成地震数据和真实地震数据对比实验结果表明,相比于奇异值阈值、加权核范数以及基于最大化最小化框架的非凸对数和函数算法,本文算法的重建结果在定量和定性分析上均有提升:在40%缺失率合成数据集上的信噪比为26.1357 dB,重建误差为6.7894;在30%缺失率Mobil Avo Viking Graben Line 12数据集上的信噪比为17.2478 dB,重建误差为4.7625;在60%缺失率Netherlands F3数据集上的信噪比为26.0581 dB,重建误差为7.4641。

Due to surface obstacles or economic constraints,seismic data recorded is often incomplete.Consequently,seismic data reconstruction is an important topic in seismic research.This study presents a seismic data reconstruction approach based on joint accelerated proximal gradient and log-weighted nuclear norm minimization.The process begins by subjecting the original seismic data to low-rank preprocessing through texture-patch operators.Subsequently,the accelerated proximal gradient algorithm is employed for an initial reconstruction of the low-rank seismic data.Finally,an algorithm based on the log-weighted nuclear norm is presented to tackle the optimization problem and reconstruct the missing data.For synthetic seismic data and real seismic data,the reconstruction results of the joint accelerated proximal gradient and log-weighted nuclear norm method have improved both in quantitative and qualitative analysis:The signal-to-noise ratio of the synthetic data set with a 40% missing rate is 26.1357 dB and the reconstruction error is 6.7894;The signal-to-noise ratio of the Mobil Avo Viking Graben Line 12 data set with a 30% missing rate is 17.2478 dB and the reconstruction error is 4.7625;The signal-to-noise ratio of the Netherlands F3 data set with a 60% missing rate is 26.0581 dB and the reconstruction error is 7.4641.