基于压缩感知的高分辨率平面波分解方法研究

平面波分解方法是地震资料处理中的一项关键技术，它广泛地运用在平面波偏移、各类Beam偏移等成像方法中.平面波分解不仅可以提高偏移成像的效率，而且可以压制地震资料中的随机噪音，提高地震数据的信噪比.线性Radon变换（LRT）是一种常见的实现平面波分解的方法，但常规的LRT存在以下两个缺点：（1）分辨率受测不准原理限制；（2）变换结果存在很多噪音和空间假频.为了克服LRT的上述缺点，本文提出一种基于压缩感知的高分辨率平面波分解方法，并利用加权匹配追踪（WMP）技术实现了该方法.该方法将LRT视为一个参数估计问题，并将LRT结果的稀疏性作为约束条件，在压缩感知理论的指导下利用WMP方法得到高分辨率、高信噪比的平面波分解结果.另外，该方法还可以用于提取地震数据的线性信号、压制随机噪音、实现高维地震数据规则化等地震资料处理技术.数值实验结果证明：WMP方法可以有效地提取地震数据中的线性信号，提高LRT的分辨率和信噪比，从而改善平面波分解的质量.

A research of high-resolution plane-wave decomposition based on compressed sensing

Plane-wave decomposition is a useful technique of seismic data processing, it is widely used in plane-wave migration and all kinds of Beam migration. Plane-wave decomposition can improve the efficiency of migration, attenuate the noise of field data and improve the signal to noise ratio of field data. Linear Radon Transform (LRT) is a most common method to realize plane-wave decomposition. But it has two defects which impact the effect of plane-wave decomposition: (1) The resolution of LRT is decided by uncertainty principle; (2) The result of LRT contains a lot of space aliasing and other noise caused by sample pattern. In order to overcome these defects and improve the quality of plane-wave decomposition, in this paper we present a new method to achieve high-resolution plane-wave decomposition based on compressed sensing, which is realized by weighted matching pursuit(WMP) algorithm. The presented method considers LRT as an inverse problem, and uses the sparsity of LRT's result as the constraint of this problem. Under the framework of compressed sensing theory, this method achieves high resolution and high signal to noise ratio plane-wave decomposition by WMP algorithm. In addition to plane-wave decomposition, this method can also be used to get the linear events of seismic data, attenuate noise of field data, realize high dimension seismic data regularization and other seismic data processing techniques. The numerical examples show that WMP algorithm can forecast the linear events of seismic data effectively, improve the resolution and signal to noise ratio of LRT's result and then get a high quality of plane-wave decomposition.