一种改进的非线性四阶PDE去噪模型

Improved Noise Removal Model Based on Nonlinear Fourth-Order Partial Differential Equations

针对已有的基于TV正则化的去噪方法会导致"阶梯效应"以及对纹理、细节等有用信息会过度地平滑等问题,文中通过结合Lysaker等人(2003)提出的LLT去噪模型与Gilboa等人(2006)提出的基于局部方差约束的变分去噪模型的优点,提出了一种基于非线性四阶偏微分方程(PDEs)的去噪模型,然后采用最速下降法对其进行求解.通过对数字图像进行去噪试验.结果表明:文中提出的方法可以有效地克服已有方法会带来"阶梯效应"以及对图像的纹理信息保持不好等缺陷;将文中提出的方法应用于地震资料去噪,实验结果表明:新方法在有效压制地震资料中随机噪声的同时,可以保持地震同相轴的横向连续性,恢复地震剖面中的弱同相轴,使得去噪后地震剖面的纹理结构更加清晰可见、同相轴的强弱对比更加分明.

The existing TV regularized denoising methods usually cause staircase effects and excessively smooth the information such as texture and details.The paper presents an improved noise removal model based on the nonlinear fourth order PDEs,which combines the advantages of LLT model and variational denoising model based on the local variance constraint.Then the proposed model is solved by the gradient descent method.Finally,some tests were conducted on the synthetic,real stacked and real prestack seismic data.Experimental results show that the proposed denoising method can effectively suppress the random noise in the seismic data,and can also preserve the lateral continuity of seismic events and well recover the weak events in the seismic profile,making the texture structure of the denoised seismic profile more visible and the contrast of the strong and weak events more distinct.