Seismic image, especially for the prestack image, performs a blurred version of the reflectivity image due to spatial aliasing, poor acquisition aperture, and nonuniform illumination. The blurring effects can be quantified by the point spread function (PSF). We herein adopt an explicit space-variant PSF formula, which can be defined as a sequential application of the modeling and migration operators with the asymptotic Green’s function. The deblurred images are restored using the nonstationary deconvolution with total variation regularization in which the blurred images are described by the convolution between the space-variant PSF and the reflectivity image. However, nonstationary deconvolution is computationally challenging. We introduce an extending primal–dual hybrid gradient (E-PDHG) method to decompose the complex problem into a sequence of simple subproblems that have closed-form solutions. Numerical results on synthetic data and field data demonstrate that the proposed E-PDHG method outperforms the basic PDHG method in the prestack seismic image deblurring.

中文翻译：

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具有总变化正则化的原始-对偶优化策略用于叠前地震图像去模糊

地震图像，特别是叠前图像，由于空间混叠，采集孔径差和照明不均匀而导致反射率图像模糊。可以通过点扩展函数（PSF）量化模糊效果。我们在这里采用显式的空间变量PSF公式，可以将其定义为具有渐近格林函数的建模和迁移算子的顺序应用。使用具有总变化正则化的非平稳解卷积来恢复去模糊的图像，其中，模糊图像是通过空间变量PSF和反射率图像之间的卷积来描述的。但是，非平稳反卷积在计算上具有挑战性。我们引入了扩展的原-对偶混合梯度（E-PDHG）方法，将复杂问题分解为具有封闭形式解的一系列简单子问题。综合数据和现场数据的数值结果表明，所提出的E-PDHG方法在叠前地震图像去模糊方面优于基本的PDHG方法。