基于Shearlet稀疏变换基的压缩感知重建技术

Compressed sensing seismic data reconstruction with Shearlet transformation

压缩感知是一种新的地震数据表征框架,能够利用信号的稀疏性代替频带宽度更好地进行信号描述,为地震数据重建提供了有力的理论基础.本文在压缩感知理论框架下,构建了基于Shearlet稀疏变换基的地震数据重建算法,利用快速凸集投影(FPOCS)算法和指数阈值模型求取最优解,并采用地震数据指标参数(信噪比、峰值信噪比以及结构相似性)对重建结果进行定量评价.数值测试结果验证了本文方法的正确性和实用性,与Fourier变换基和Curvelet变换基相比,Shearlet变换基具有更敏感的方向性以及更优秀的稀疏表示能力,数据重建精度最高,引入的噪声较少.

Compressed sensing is a new framework for seismic data expression, uses the sparse property instead of frequency band to do signal description, which provides a powerful theoretical basis for seismic data reconstruction. In this paper, seismic data reconstruction algorithm with Shearlet sparse transformation base have been built under the framework of Compressed Sensing, which use the Fast Convex Projection(FPOCS) algorithm and exponential threshold model to obtain optimal solution, and apply seismic data index parameters(signal-to-noise ratio, peak signal-to-noise ratio and structural similarity) to quantitatively evaluate the reconstruction results. Numerical testing results verify the correctness and effectiveness of the proposed method, compared with the results of Fourier transform and Curvelet transform, the Shearlet transform have more sensitive directionality and anisotropy, higher sparse expression ability, therefore, the seismic data reconstruction using Shearlet sparse transform has higher reconstruction precision and less noise.