基于压缩感知和Contourlet变换的地震数据重建方法

基于压缩感知技术的地震数据字典重建算法在训练字典时耗时较长,基于压缩感知技术的稀疏变换重建算法对稀疏基的要求较高,权衡信噪比和时间,采用目前已应用于地震数据重建的Contourlet稀疏基,提出了一种基于压缩感知技术和Contourlet变换的地震数据重建方法。首先根据设计的测量矩阵,在Contourlet域中采用快速迭代收缩阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm,FISTA)重建缺失的稀疏系数,然后进行Contourlet反变换完成地震数据的缺失重建。合成数据和实际地震数据测试结果表明,基于压缩感知技术的Contourlet变换能够很好地完成地震数据的缺失重建;与压缩感知技术中常用的短时傅里叶变换和小波变换方法相比,基于压缩感知的Contourlet变换重建结果信噪比更高,并且增加的耗时有限,在可以接受的范围之内。

Training a dictionary is time-consuming when using a standard algorithm for the reconstruction of dictionary learning based on compressed sensing.The algorithm for the reconstruction of sparse transforms based on compressed sensing is also problematic,as it has high requirements for sparse basis.Therefore,weighing the signal-to-noise ratio (SNR) and time consumption,introducing the Contourlet sparse basis which could be used in seismic data reconstruction,the paper proposes seismic data reconstruction using Contourlet transform based on compressed sensing.The method uses the fast iterative shrinkage-thresholding algorithm (FISTA) to reconstruct the missing sparse coefficients in the Contourlet domain according to the designed measurement matrix,and then performs a Contourlet inverse transform to reconstruct the missing seismic data.Testing on both synthetic data and field data indicates that the proposed method is effective.In comparison with the short-time Fourier transform and the wavelet transform,the proposed Contourlet transform based on compressed sensing has a higher SNR,and improved time efficiency.

国家自然科学基金项目(41304086)资助。