Based on the fact that the Hankel matrix constructed by noise‐free seismic data is low‐rank, low‐rank approximation (or rank‐reduction) methods have been widely used for removing noise from seismic data. Due to the linear‐event assumption of the traditional low‐rank approximation method, it is difficult to define a rank that optimally separates the data subspace into signal and noise subspaces. For preserving the most useful signal energy, a relatively large rank threshold is often chosen, which inevitably leaves residual noise. To reduce the energy of residual noise, we propose an optimally damped rank‐reduction method. The optimal damping is applied via two steps. In the first step, a set of optimal damping weights is derived. In the second step, we derive an optimal singular value damping operator. We review several traditional low‐rank methods and compare their performance with the new one. We also compare these low‐rank methods with two sparsity‐promoting transform methods. Examples demonstrate that the proposed optimally damped rank‐reduction method could get significantly cleaner denoised images compared with the state‐of‐the‐art methods.

中文翻译：

---

基于低秩方法的地震信号增强

基于无噪声地震数据构成的汉克矩阵是低秩的事实，低秩近似（或秩减小）方法已被广泛用于消除地震数据中的噪声。由于传统低秩逼近方法的线性事件假设，很难定义一个将数据子空间最佳分离为信号和噪声子空间的秩。为了保留最有用的信号能量，通常选择相对较大的秩阈值，这不可避免地会留下残留噪声。为了减少残留噪声的能量，我们提出了一种最佳的阻尼秩降方法。最佳阻尼通过两个步骤进行。第一步，得出一组最佳阻尼权重。在第二步中，我们导出了一个最佳奇异值阻尼算子。我们回顾了几种传统的低等级方法，并将它们的性能与新方法进行了比较。我们还将这些低等级方法与两种稀疏促进变换方法进行了比较。实例表明，与最新方法相比，所提出的最佳阻尼降阶方法可以得到明显更清晰的去噪图像。