基于改进的加权核范数最小化的地震资料去噪方法

Seismic Data Denoising Method Based on Improved Weighted Kernel Norm Minimization

摘要: 在实际的地震资料中含有各种不同类型的随机噪声，会降低地震资料的信噪比和对有效信号的分析，因此去噪是地震资料处理的首要步骤。加权核范数最小化(WNNM)作为地震资料去噪的有效方法之一，利用图像的非局部相似性，是一种低秩矩阵逼近方法，并且为不同的奇异值分配不同的权重。同时离散余弦变换(DCT)是试图对图像进行去相关，是一种稀疏变换。本文从地震数据的稀疏性和非局部相似性出发，利用局部地震资料的稀疏性和地震数据的空间信息，我们提出了一种使用稀疏性和低秩正则化的地震去噪方法(WNNM-DCT)。实验结果表明，本文提出的方法相对于WNNM和其他去噪方法，能更好的去除噪声，保留图像的有效信息。

Abstract: The actual seismic data contains a variety of different types of random noise, which will reduce the signal-to-noise ratio of the seismic data and the analysis of the effective signal, so denoising is the first step in seismic data processing. As one of the effective methods for denoising seismic data, the weighted kernel norm minimization (WNNM) is a low-rank matrix approximation method that uses the non-local similarity of the image and assigns different weights to different singular values. At the same time, the discrete cosine transform (DCT) is an attempt to decorrelate the image and is a sparse transformation. Starting from the sparsity and non-local similarity of seismic data, we propose an earthquake denoising method (WNNM-DCT) using sparsity and low-rank regularization using the sparsity of local seismic data and the spatial information of seismic data. Experimental results show that compared with WNNM and other denoising methods, the proposed method can better remove noise and retain the effective information of the image.