基于改进K-SVD字典学习的地震信号去噪
Seismic Signal Denoising Based on Improved K-SVD Dictionary Learning

字典学习作为近年来的研究热点，因其在稀疏表示方面的优势而受到广泛关注。该方法通过构建合适的稀疏字典，将地震数据表示为一组原子的线性组合，从而实现地震信号与噪声的有效分离。然而，传统的K-奇异值分解(K-SVD)字典学习算法在应用于地震数据去噪的过程中，尽管展现出了良好的适应性和去噪性能，但仍存在一些不足之处。本文在传统的K-SVD字典学习算法的基础上创新性地结合统计理论，在多个重要步骤对其进行改进，提出一种新的优化字典学习去噪算法。并通过对合成地震数据和实际地震数据的去噪实验验证：本文提出的优化字典学习算法与传统的K-SVD字典学习算法相比，在衡量去噪效果的多个维度都具有明显优势。
Dictionary learning, as a research hotspot in recent years, has received widespread attention due to its advantages in sparse representation. This method constructs a suitable sparse dictionary to represent seismic data as a linear combination of atoms, thereby achieving effective separation of seismic signals and noise. However, the traditional K-Singular Value Decomposition (K-SVD) dictionary learning algorithm, although exhibiting good adaptability and denoising performance when applied to seismic data denoising, still has some shortcomings. This article innovatively combines statistical theory with the traditional K-SVD dictionary learning algorithm, improves it in multiple important steps, and proposes a new optimized dictionary learning denoising algorithm. And through denoising experiments on synthetic seismic data and actual seismic data, it was verified that the optimized dictionary learning algorithm proposed in this paper has significant advantages compared to the traditional K-SVD dictionary learning algorithm in multiple dimensions of measuring denoising effectiveness.