Research On The Denoising Of Logging Data Based On Low-Rank Matrix Recovery Algorithm

Low-rank matrix recovery is a method that can automatically identify the data disturbed and damaged by noise in the matrix,and restore the matrix damaged by noise to the original data matrix by solving the nuclear norm optimization problem.In recent years,low-rank matrix recovery theory has been widely applied to image denoising,video repair,face recognition,signal reconstruction and other fields.The limitation of low-rank matrix recovery algorithm is that,when the original matrix of the denoising matrix is low-rank and the noise matrix meets the strict sparse requirement,the denoising effect of low-rank matrix recovery algorithm is good.If the noise matrix does not meet the sparse requirement,the denoising effect of low-rank matrix recovery algorithm is not ideal.In this paper,the frequently-used low-rank matrix recovery algorithms were analyzed and compared by experiments.Aiming at the limitations of the low-rank matrix recovery algorithm,an improvement solution is proposed.The pre-improvement and post-improvement algorithms are used to carry out denoising experiments on uranium mine logging data to verify the denoising effect of the algorithm.The main research work or innovation of this paper as follows:(1)This paper studied the theory of low-rank matrix recovery and the mathematical principle and algorithm flow of frequently-used low-rank matrix recovery algorithms,and analyzes their advantages and disadvantages.The principle and flow of the three algorithms,namely the Exact Augmented Lagrange Multipliers,Inexact Augmented Lagrange Multipliers and Accelerated Proximal Gradient,are analyzed in detail.The three algorithms were run in Matlab to denoising the simulated data,and the operating efficiency and denoising effect of the three algorithms are compared.The experimental results show that the Inexact Augmented Lagrange Multipliers have the highest efficiency and the best denoising effect.In view of the limitations of low-rank matrix recovery algorithm,the algorithm model of low-rank matrix recovery is improved by introducing the idea of weighted norm and using F norm as the penalty term.Based on Matlab,the low-rank matrix recovery algorithm before and after improvement is realized by software,and the simulated data matrix is denoised,and the performance of the algorithm is compared and analyzed.The experimental results show that the running time of the improved algorithm is slightly increased than that of the frequently-used low-rank matrix recovery algorithm,but the error rate of the denoising result is greatly reduced compared with that of the frequently-used algorithm,with a maximum decrease of 23.13%.The denoising effect of the improved algorithm is better.(2)Based on the improved algorithm,the uranium mine logging data is de-noised.In the field of uranium mine logging data mining,because the uranium mine logging data are affected by various media in the formation during the acquisition process,there is noise in the uranium mine logging data,which affects the accuracy of data mining results.In order to improve the effect of uranium mine logging data mining,this paper de-noised the logging data of a uranium mine in Inner Mongolia,and then analyzed the de-noised data by using support vector machine and decision tree algorithm.Experimental results show that compared with several kinds of frequently-used low-rank matrix recovery algorithm,using support vector machines,decision tree to classify the uranium mine logging data de-noised by improved algorithm,the accuracy of classification results is the highest,79.17% and85.37% respectively,the improved algorithm has a good denoising effect.