基于Curvelet的地震图像压缩感知重建研究

发布时间：2018-05-31 06:19

本文选题：地震图像 + Curvelet分析　；参考：《东北石油大学》2017年硕士论文

【摘要】：近年来随着石油勘探的不断发展,勘探地区的环境越来越复杂,加剧了地震勘探图像的不规则和不完整情况,影响对资料的处理和解释,最终影响油气判断。过去传统用的重建方法受Nyquist采样定理的限制需要较高的采样率,面对复杂的勘探情况不能做适当的采集调整,过去的勘探成本非常大,对于此现象,需要研究出一个良好的重建算法,尽量实现完整的地震图像重建,来使得地震资料的利用率得以提高。本文将Curvelet变换和压缩感知理论结合,提出相关算法实现对地震图像的重建,增强视觉质量。主要研究内容如下:1.基于Curvelet收缩阈值迭代算法的地震图像重建的研究。结合压缩感知理论,分析小波变换、DFT变换,Curvelet变换,并对地震图像进行重建,对比发现,Curvelet变换具有良好的多尺度几何分析能力,它能对具有曲线边缘的地震图像进行最优稀疏表达。把一个地震图像区域分为多个子区域,实现一定间隔的随机采样。最后根据Curvelet变换高频子带信息熵变化的特点,设计基于Curvelet变换的自适应双变量收缩阈值迭代重建算法。经过对比实验的分析可知,该算法应用在地震图像中有良好的重建效果。2.基于Bregman迭代算法的地震图像重建的研究。讨论了重建算法中的Bregman迭代算法,Bregman迭代算法的基本概念,Bregman距离,分别列举了常用的几个算法:Bregman迭代算法、线性Bregman迭代算法、残差Bregman迭代算法,比较它们优缺点和特性,从而提出了改进的Bregman迭代算法。在Bregman迭代框架中,采用软阈值作为阈值算子H,并且提出了基于H-curve准则的阈值参数选取,提高了地震图像重建的准确性。经过对比实验的分析可知,改进的Bregman迭代算法应用在地震图像中有良好的重建效果。3.基于压缩感知观测矩阵地震图像重建的研究。根据地震图像的特征,选取常用的几种观测矩阵,分析这五种观测矩阵的特点,将广义轮换矩阵作为主要的讨论对象。了解其构造的原理,广义轮换矩阵具有很强的稳定性,其性能比其它观测矩阵要好,除此之外广义轮换矩阵同样也是确定性观测矩阵,容易硬件实现和存储。通过研究发现它存在极强的列非相关性。也就是为了增强列与列之间非相关性可以修改观测矩阵每一行前半段部分元素系数,同时修改的系数值,强化了对低频段的采样。最后进行对地震图像重建的实验,对实验结果进行对比,发现广义轮换矩阵的作为观测矩阵时重建效果最好。
[Abstract]:In recent years, with the development of petroleum exploration, the environment of exploration area becomes more and more complex, which intensifies the irregular and incomplete situation of seismic exploration image, affects the processing and interpretation of data, and ultimately affects the judgment of oil and gas. The traditional reconstruction method used in the past is limited by the Nyquist sampling theorem and requires a high sampling rate. In the face of complex exploration conditions, it is impossible to make appropriate acquisition adjustment, and the exploration cost in the past was very large. It is necessary to develop a good reconstruction algorithm to realize the complete seismic image reconstruction as far as possible so as to improve the utilization ratio of seismic data. In this paper, Curvelet transform and compression sensing theory are combined to realize the reconstruction of seismic images and enhance the visual quality. The main research contents are as follows: 1. Research on seismic image reconstruction based on Curvelet shrinkage threshold iteration algorithm. Combined with the theory of compression perception, the wavelet transform DFT transform and Curvelet transform are analyzed, and the seismic images are reconstructed. It is found that the Curvelet transform has good multi-scale geometric analysis ability. It can perform optimal sparse representation of seismic images with curve edges. A seismic image region is divided into several sub-regions to realize random sampling at certain intervals. Finally, according to the characteristics of information entropy change in high frequency subband of Curvelet transform, an adaptive two-variable shrinkage threshold iterative reconstruction algorithm based on Curvelet transform is designed. The results of comparative experiments show that the algorithm has a good reconstruction effect in seismic images. Research on seismic image reconstruction based on Bregman iterative algorithm. In this paper, the basic concept of Bregman iterative algorithm and its basic concept, Bregman distance, are discussed. Several commonly used algorithms, such as: Bregman iterative algorithm, linear Bregman iterative algorithm, residual Bregman iterative algorithm, are listed respectively, and their advantages, disadvantages and characteristics are compared. Thus, an improved Bregman iterative algorithm is proposed. In the framework of Bregman iteration, the soft threshold is used as the threshold operator H, and the selection of threshold parameters based on H-curve criterion is proposed to improve the accuracy of seismic image reconstruction. The comparison experiment shows that the improved Bregman iterative algorithm has a good reconstruction effect in seismic images. Research on seismic image reconstruction based on compressed perceptual observation matrix. According to the characteristics of seismic images, several commonly used observation matrices are selected, the characteristics of these five observation matrices are analyzed, and the generalized rotation matrix is considered as the main object of discussion. Knowing the principle of its construction, the generalized rotation matrix has strong stability and its performance is better than that of other observation matrices. Besides, the generalized rotation matrix is also a deterministic observation matrix, which is easy to be implemented and stored in hardware. It is found that it has strong column noncorrelation. In other words, in order to enhance the non-correlation between the columns, the element coefficients of the first half of each row of the observation matrix can be modified, and the coefficient values can be modified at the same time, so that the sampling in the low frequency band can be strengthened. Finally, the experiment of seismic image reconstruction is carried out, and the experimental results are compared. It is found that the generalized rotation matrix is the best when it is used as the observation matrix.
【学位授予单位】：东北石油大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.4

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