基于压缩感知的小波域地震数据实时压缩与高精度重构

地震数据压缩是解决地震仪无线数据传输的一项关键技术。现有技术方案是对现场数据变换编码，消除其冗余达到压缩效果，再解码反变换恢复原始数据。这类方案需要对完整采集的地震数据进行操作，不仅时效性差，造成了硬件资源浪费，而且数据解码难以高精度恢复。针对以上问题，本文基于压缩感知理论（CS）提出一种新的地震数据压缩重构方案，通过构造混沌伯努利测量矩阵（CBMM）对地震数据小波变换后的稀疏系数进行压缩，在下位机端实时编码；为了提高重构精度，采用贝叶斯小波树结构CS重构算法（BTSWCS），根据小波树结构统计特性，构建一个分层贝叶斯CS先验模型，利用马尔科夫链蒙特卡洛推理对模型参数后验估计，在上位机端恢复原始数据。实际地震数据处理表明，使用本方法对总采样点为2⁸的数据压缩，压缩时间可缩短至1.0×10^-5s。低信噪比情况下，本文重构算法使峰值信噪比（PSNR）值至少提升5dB。

Seismic data real-time compression and high-precision reconstruction in the wavelet domain based on the compressed sensing

The seismic data compression is a key techno-logy in the data transmission of wireless seismic recording systems.The current technical scheme is to eliminate its redundancy with data transform coding to achieve the compression,and to restore the original data with reverse transform decoding.This scheme is inefficient due to acquired seismic data operation,which needs additional hardware resources.And high-precision data recovery cannot be ensured.To solve the above problems,we propose a new seismic data compression and reconstruction scheme based on the compressed sensing (CS) theory.By constructing the chaotic Bernoulli measurement matrix (CBMM),the sparse coefficients of seismic data wavelet transform are collected and compressed,and the real-time coding is achieved at the lower computer.In order to improve the reconstruction accuracy,we use the Bayesian tree-structured wavelet compressed sensing (BTSWCS) reconstruction algorithm,which builds a hierarchical Bayesian CS prior model according to the statistical characteristics of wavelet tree structure.The Markov chain Monte Carlo (MCMC) method estimates the model parameters and then the original data is restored at the superior machine.Based on our seismic data application,the compression time with the proposed scheme can be shortened to 1.0×10^-5s when the total sampling points are 2⁸.In the case of low signal-to-noise ratio (SNR),our reconstruction algorithm improves the peak signal-to-noise ratio (PSNR) value more than 5 dB.