ABSTRACT Erratic noise often has high amplitudes and a non‐Gaussian distribution. Least‐squares–based approaches therefore are not optimal. This can be handled better with non–least‐squares approaches, for example based on Huber norm which is computationally expensive. An alternative method has been published which involves transforming the data with erratic noise to pseudodata that have Gaussian distributed noise. It can then be attenuated using traditional least‐squares approaches. This alternative method has previously been used in combination with a curvelet transform in an iterative scheme. In this paper, we introduce a median‐filtering step in this iterative scheme. The median filter is applied following the slope direction of the seismic data to maximally preserve the energy of useful signals. The new method can suppress stronger erratic noise compared with the previous iterative method, and can better deal with random noise compared with the single‐step implementation of the median filter. We apply the proposed robust denoising algorithm to a synthetic dataset and two field data examples and demonstrate its advantages over three different noise attenuation algorithms.

中文翻译：

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使用具有稀疏约束的迭代结构导向空变中值滤波抑制不稳定噪声

摘要 不稳定的噪声通常具有高振幅和非高斯分布。因此，基于最小二乘法的方法不是最佳的。这可以通过非最小二乘法更好地处理，例如基于计算成本高的 Huber 范数。已经发布了一种替代方法，该方法涉及将具有不稳定噪声的数据转换为具有高斯分布噪声的伪数据。然后可以使用传统的最小二乘法对其进行衰减。这种替代方法以前在迭代方案中与曲波变换结合使用。在本文中，我们在此迭代方案中引入了中值滤波步骤。中值滤波器沿着地震数据的斜率方向应用，以最大限度地保留有用信号的能量。与以前的迭代方法相比，新方法可以抑制更强的不稳定噪声，并且与中值滤波器的单步实现相比，可以更好地处理随机噪声。我们将所提出的稳健去噪算法应用于合成数据集和两个现场数据示例，并展示了其优于三种不同噪声衰减算法的优势。