Sparse solutions of linear systems of equations are essential in many applications of seismic data processing. These systems arise in many denoising algorithms, such as those that use Radon transforms. We have developed a robust matching pursuit (RMP) algorithm for the retrieval of sparse Radon domain coefficients. The algorithm is robust to outliers and, hence, is applicable for seismic data deblending. The classic matching pursuit (MP) algorithm is often adopted to approximate data by a small number of basis functions. It performs effectively for data contaminated with well-behaved, typically Gaussian, random noise. However, MP tends to identify the wrong basis functions when the data are contaminated by erratic noise such as source interference encountered in common-receiver and common-channel gathers of simultaneous source surveys. Incorporating an $l_p$ space inner product into the MP algorithm significantly increases its robustness to erratic signals. Deblending experiments with synthetic and field data examples indicate a significant signal-to-noise ratio improvement when one adopts a Radon denoiser computed via our RMP solver. We determine in detail the steps required to implement our $l_p$ space RMP algorithm when the basis functions are not given in an explicit form, as is the case with the time-domain Radon transform.

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[数学]空间匹配追踪算法及其在时域拉顿变换中鲁棒地震数据去噪中的应用

线性方程组的稀疏解在地震数据处理的许多应用中至关重要。这些系统出现在许多降噪算法中，例如使用Radon变换的那些算法。我们已经开发了一种鲁棒的匹配追踪（RMP）算法，用于检索稀疏的Radon域系数。该算法对异常值具有鲁棒性，因此适用于地震数据去混合。通常采用经典的匹配追踪（MP）算法通过少量基函数来近似数据。对于表现良好的噪声（通常为高斯随机噪声）污染的数据，它可以有效执行。但是，当数据受到不稳定的噪声（例如在同时进行源调查的公共接收器和公共通道采集中遇到的源干扰）污染的数据时，MP倾向于识别错误的基函数。${升}_p$MP算法中的空间内部积显着提高了其对不稳定信号的鲁棒性。使用合成和现场数据示例进行的混合实验表明，当采用通过我们的RMP求解器计算的Radon降噪器时，信噪比有了显着提高。我们详细确定了实施我们的程序所需的步骤${升}_p$ 当基函数没有以显式形式给出时的RMP算法，时域Radon变换就是这种情况。