低秩矩阵恢复模型改进及其在石油测井中的应用

Low-rank Matrix Recovery Model Improved and Its Application in Oil Well Logging

传统的低秩矩阵恢复模型在去噪过程中通过将观测矩阵分解为低秩部分和稀疏部分达到噪声去除的目的,但该模型要求噪声矩阵必须是稀疏的。然而石油测井所获得的数据中噪声来源复杂,并不能完全保证噪声分布满足稀疏性的要求,使该模型在去噪时表现出一定的局限性,去噪效果不稳定,进而导致后续的数据处理准确率降低。为此,提出将加权范数的思想应用于传统的低秩矩阵恢复模型中,并在惩罚项中将F范数与待恢复矩阵的核范数相结合,构造改进的低秩矩阵恢复模型,使其能够在保证解的稳定性的同时,可以更好地挖掘观测矩阵的低秩性以及增强稀疏矩阵的稀疏性。通过非精确的拉格朗日乘子法分别对改进前后的模型进行求解,并对两种模型去噪后的测井数据分别采用支持向量机(SVM)和相关向量机(RVM)进行油气层识别,结果表明经改进的低秩矩阵恢复模型去噪后的测井数据在保证了油气层识别效率的同时,识别准确率上有了明显提升。

The classical low rank matrix recovery（ LRMR） model show that the observation matrix is decomposed into low rank part and sparse part during the de-nosing process,but the LRMR model requires that the noise matrix must be sparse. However,due to the complexity noise sources in the oil well logging data,the sparsity of noise cannot be fully guaranteed,and the model shows some limitations in de-noising process,which leads to the reduction of the accuracy of subsequent data processing. So,in the improved LRMR model,the weighted norm method is proposed to apply to classical LRMR model,and then the F norm is combined with the kernel norm of the matrix in penalty term,which can ensure the stability of the solution,mining the low rank of the observation matrix and enhance the sparsity of sparse matrix at the same time. Inexact Lagrange Multiplier（ IALM） algorithm is used to solve the LRMR model before improvement and the LRMR model after improvement,and then the logging data are used in oil and gas layer recognition by support vector machine（ SVM） and the relevance vector machine（ RVM） respectively,the application results show that compared with the classical LRMR model,the oil and gas layer recognition accuracy is improved remarkably by improved LRMR model,which can obviously improve the operation efficiency.