基于加速Bregman方法和阈值迭代法的联合地震数据重建

Joint seismic data reconstruction based on the accelerated Bregman method and threshold iteration method

地震数据缺失道重建是数据处理的重要环节,但现今大部分重建算法收敛速度慢,计算成本高,难以满足海量数据处理的要求。为此,提出一种将加速线性Bregman方法(ALBM)与阈值迭代法(ISTA)进行联合的快速重建方法,并采用多尺度、多方向曲波变换作为稀疏基。ALBM能从未阈值化的曲波系数得到更多的有效信号,因此在迭代初期收敛速度快;后期因未阈值化的曲波系数带入更多噪声,会降低重建精度。ISTA则一直需要将曲波系数进行阈值化,迭代初期滤除了大部分有效系数,故收敛速度慢;但后期能恢复微弱有效信号,故重建精度较高。为了充分发挥两种算法的优势,文中给出了1~0范围的线性和指数两种加权参数公式,有效地将ALBM与ISTA两种算法进行线性组合,保证在迭代初期ALBM起主要作用,迭代后期ISTA作用大,从而使该联合算法既迭代速度快,且迭代精度高。联合过程中,采用软阈值公式,引入了指数阈值参数公式。理论模拟结果表明,相对于ALBM、ISTA及传统联合方法,所提加速联合方法的计算速度较快,重建效果明显。

The reconstruction of missing seismic data traces plays an important role in seismic data processing.However,the majority of the existing reconstruction algorithms,held back by their low convergence speed and high computational cost,can barely meet the needs of mass data processing.This paper proposed a rapid reconstruction method combining the accelerated linearized Bregman method(ALBM)with a threshold iteration method,namely the iterative shrinkage-thresholding algorithm(ISTA).Besides,multi-scale and multidirectional curvelet transform was adopted as the sparse basis.ALBM converges rapidly in the early stage of iteration as it can obtain more effective signals from unthresholded curvelet coefficients.Nevertheless,its reconstruction accuracy is weakened by the increasing noise brought by the unthresholded curvelet coefficients in the later stage.In contrast,ISTA needs to threshold the curvelet coefficients all along.Although its convergence speed is slow in the early stage of iteration as most of the effective coefficients are filtered out,its reconstruction accuracy is high in the later stage owing to the restoration of weak effective signals.To maximize the advantages of the two algorithms,this paper presented two weighting parameter formulas(linear and exponential)in the range of 0~1.In this way,ALBM and ISTA were effectively combined linearly to ensure that ALBM played a major role in the early stage of iteration while ISTA dominated the later stage of iteration and thereby to enable this joint algorithm to iterate rapidly and accurately. In the combination process,a soft thresholding formula was adopted,and an exponential thresholding parameter formula was introduced.The theoretical simulation results demonstrate that compared with ALBM,ISTA,and traditional joint methods,the proposed accelerated joint method delivers fast calculation and an evident reconstruction effect.