基于稀疏表示的地震信号压缩方法研究
发布时间：2019-04-13 13:16
【摘要】：本文主要研究基于稀疏表示的地震信号压缩方法。对于地震学学者来说,地震数据的记录是很宝贵的资料,通过这些数据可以很好地学习地震的规律。人类对于地震数据的记录已经有100多年的历史,保存了大量的地震数据,其压缩是一个不得不考虑的问题。地震信号中存在着自相似性,针对这一特点,通过学习的方法获得过完备字典,并使用稀疏表示来解决地震信号的压缩问题。本文结合地震信号本身特点,从字典原子间的相干性和样本之间的相似性这两个角度出发,研究提高字典表达能力的方法,主要工作有两方面。第一种方法是通过减少字典原子间相干性来提高字典表达能力。合理降低字典原子间相干性,可以避免字典中出现相似的原子对,这样字典原子数在有限的情况下可以有效提高字典的表达能力。本文在字典更新时将含有r紧框架Φ的约束项加入到优化问题中,来平衡原子间相干性和字典对样本的表达误差,使得字典对地震信号的表达达到最佳效果。第二种方法考虑到训练样本中的相似性。通过聚类和字典学习两种手段结合,训练过完备字典。分段后的小段样本之间有很多相似性,通过聚类的手段,将小段样本进行聚类,并计算各类样本的权重系数。在优化问题中赋予各类样本相对应的权重系数,通过对目标函数的变换,原优化问题可以使用K-SVD算法解决。通过实验,验证了以上两种方法的字典在信号重构时的有效性。在传统的字典学习模型基础上,分别考虑字典原子间相干性以及样本间相似性这两个因素,从两个方向改进了字典学习模型,提高了字典的表达能力。在同等压缩比的条件下,地震信号重构效果得到提高。
[Abstract]:This paper mainly studies the seismic signal compression method based on sparse representation. For seismologists, the records of seismic data are very valuable data, through which the rules of earthquakes can be well learned. The records of seismic data have been recorded for more than 100 years, and a large number of seismic data have been preserved. The compression of seismic data is a problem that must be considered. There is self-similarity in seismic signals. According to this characteristic, the over-complete dictionary is obtained by means of learning, and sparse representation is used to solve the compression problem of seismic signals. In this paper, based on the characteristics of seismic signals and from the point of view of the coherence between atoms and the similarity between samples, the methods to improve the expression ability of dictionaries are studied. The main work is in two aspects. The first method is to improve the dictionary expression ability by reducing the interatomic coherence of dictionaries. A reasonable reduction of the coherence between dictionaries can avoid the occurrence of similar pairs of atoms in dictionaries, so that the number of atoms in dictionaries can effectively improve the expression ability of dictionaries under the condition that the number of atoms in dictionaries is limited. In this paper, the constraint with r-compact frame 桅 is added to the optimization problem when the dictionary is updated to balance the interatomic coherence and the expression error of the dictionary to the sample, so that the dictionary can get the best effect on the expression of seismic signals. The second method takes into account the similarity in training samples. Through the combination of clustering and dictionary learning, a complete dictionary has been trained. There are many similarities between the segmented samples. By means of clustering, the small segments of the samples are clustered and the weight coefficients of all kinds of samples are calculated. In the optimization problem, the corresponding weight coefficients are given to all kinds of samples. By transforming the objective function, the original optimization problem can be solved by using the K-SVD algorithm. The experimental results show that the dictionary of the above two methods is effective in signal reconstruction. Based on the traditional dictionary learning model, considering the coherence between atoms and the similarity between samples, the dictionary learning model is improved in two directions, and the dictionary expression ability is improved. Under the condition of the same compression ratio, the effect of seismic signal reconstruction is improved.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P315.6
[Abstract]:This paper mainly studies the seismic signal compression method based on sparse representation. For seismologists, the records of seismic data are very valuable data, through which the rules of earthquakes can be well learned. The records of seismic data have been recorded for more than 100 years, and a large number of seismic data have been preserved. The compression of seismic data is a problem that must be considered. There is self-similarity in seismic signals. According to this characteristic, the over-complete dictionary is obtained by means of learning, and sparse representation is used to solve the compression problem of seismic signals. In this paper, based on the characteristics of seismic signals and from the point of view of the coherence between atoms and the similarity between samples, the methods to improve the expression ability of dictionaries are studied. The main work is in two aspects. The first method is to improve the dictionary expression ability by reducing the interatomic coherence of dictionaries. A reasonable reduction of the coherence between dictionaries can avoid the occurrence of similar pairs of atoms in dictionaries, so that the number of atoms in dictionaries can effectively improve the expression ability of dictionaries under the condition that the number of atoms in dictionaries is limited. In this paper, the constraint with r-compact frame 桅 is added to the optimization problem when the dictionary is updated to balance the interatomic coherence and the expression error of the dictionary to the sample, so that the dictionary can get the best effect on the expression of seismic signals. The second method takes into account the similarity in training samples. Through the combination of clustering and dictionary learning, a complete dictionary has been trained. There are many similarities between the segmented samples. By means of clustering, the small segments of the samples are clustered and the weight coefficients of all kinds of samples are calculated. In the optimization problem, the corresponding weight coefficients are given to all kinds of samples. By transforming the objective function, the original optimization problem can be solved by using the K-SVD algorithm. The experimental results show that the dictionary of the above two methods is effective in signal reconstruction. Based on the traditional dictionary learning model, considering the coherence between atoms and the similarity between samples, the dictionary learning model is improved in two directions, and the dictionary expression ability is improved. Under the condition of the same compression ratio, the effect of seismic signal reconstruction is improved.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P315.6
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