基于无展开随机QR分解算法的地质雷达数据重建方法

GPR Data Reconstruction Method Based on Uncoiled Randomized QR Decomposition Algorithm

受到外业采集条件限制和施工环境的影响,通常很难采集到理想且完整的规则采样地质雷达数据。地质雷达数据的缺失和不规则采样容易对数据处理过程产生严重干扰,影响后续解释工作。本文给出了一种基于无展开随机QR分解(Uncoiled Randomized QR decomposition,URQR)的地质雷达数据重建方法。首先引入随机QR分解算法实现对地质雷达数据矩阵的降秩计算,并通过利用无展开求平均快速算法,来解决降秩后的Toeplitz矩阵对角线求平均效率低,内存占用量大的问题。然后基于凸集投影理论,实现了无展开随机QR分解算法的数据重建流程。最后,利用本文方法与随机奇异值分解(Randomized Singular Value Decomposition,RSVD)算法,对理论与实际地质雷达缺失道数据进行重建,通过对比质量因子Q值,说明了本文方法重建效果优于RSVD方法,对于大型地质雷达数据的重建,本文方法计算效率明显高于RSVD方法,验证了本文方法的有效性、可行性、效率高的特点。

Due to the limitation of field acquisition conditions and the influence of construction environment,it is usually difficult to collect ideal and complete regular sampling ground penetrating radar(GPR)data.The lack and irregular sampling of GPR data can easily cause serious interference to the data processing process and affect the subsequent interpretation work.This paper presents a GPR data reconstruction method based on uncoiled randomized QR decomposition(URQR)algorithm.Firstly,a randomized QR decomposition algorithm is introduced to calculate the rank reduction of the GPR data matrix,and by using a fast uncoiled averaging algorithm,it solves the problems of low efficiency and large memory consumption in the diagonal averaging of the reduced rank Toeplitz matrix.Sencordly,based on projection onto convex sets theory,the data reconstruction process of uncoiled randomized QR decomposition algorithm without expansion is realized.Finally,the proposed method and randomized singular value decomposition(RSVD)algorithm are used to reconstruct the theoretical and real missing trace GPR data.By comparing the quality factor value,the reconstruction effect of the proposed method is better than that of the RSVD method.For the reconstruction of large GPR data,the computational efficiency of the proposed method is significantly higher than that of the RSVD method.The results verify the effectiveness,feasibility and high efficiency of the proposed method.