联合VMD和Shearlet变换的去噪方法研究

Research on Denoising Methods by Combining VMD and Shearlet Transform

地震数据中的噪声信号会很大程度上降低地震数据的信噪比,对后续的处理和解释工作造成一定的难度,因此研究一种去噪方法具有十分重要的意义。本文构建一种变分模态分解(Variational Mode Decomposition,VMD)和Shearlet变换联合去噪的方法,首先通过VMD将地震数据分解为一系列不同中心频率分布的模态分量(Intrinsic Mode Function,IMF),然后使用Shearlet变换对含噪的IMF分量进行去噪并对处理后的分量进行重构,最终达到去噪目的。该方法引入基于稀疏表示的地震数据去噪方法,兼顾VMD和Shearlet变换的优点,可以有效去除噪声。经过合成信号、模型及实际数据测试结果表明,本文方法处理合成信号结果显示,与VMD和小波变换方法相比,信噪比分别提高1.69、1.87,均方误差数值上减少近一半,在去除噪声的同时能更好地保留地震数据特征,提高地震资料的信噪比。

The noise signal in seismic data greatly reduces the signal-to-noise ratio of seismic data,which makes it difficult for the subsequent processing and interpretation,so it is of great significance to study a denoising method.This paper proposes a new denoising method based on variational mode decomposition(VMD)and Shearlet transform.Firstly,VMD is used to decompose seismic data into a series of intrinsic mode functions(IMF)with different center frequencies.Then,Shearlet transform is used to denoise the IMF components with noise and reconstruct the processed components.This method introduces a seismic data denoising method based on sparse representation,taking into account the advantages of VMD and Shearlet transform,and can effectively remove noise.The test results of synthetic signal,model and actual data show that the signal-to-noise ratio(SNR)of the proposed method is 1.69 and 1.87,higher than that of VMD and wavelet methods respectively,and the mean square error(MSE)value is reduced nearly half.The test results of analog signal and real data show that the proposed algorithm can better preserve the seismic data features while removing noise.