• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.399-411
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• 2017

We first provide the linear operator equations corresponding to the Tikhonov regularization image denoising problems with different regularization terms, and then we propose how to choose Kronecker product preconditioners which are required for accelerating the $G{\ell}$-PCG method. Next, we provide how to apply the $G{\ell}$-PCG method with Kronecker product preconditioner to the linear operator equations. Lastly, we provide numerical experiments for image denoisng problems to evaluate the effectiveness of the $G{\ell}$-PCG with Kronecker product preconditioner.

• Geophysics and Geophysical Exploration
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• v.23 no.2
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• pp.72-88
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• 2020

Recent rapid advances in computer hardware performance have led to relatively low computational costs, increasing the number of applications of machine-learning techniques to geophysical problems. In particular, deep-learning techniques are gaining in popularity as the number of cases successfully solving complex and nonlinear problems has gradually increased. In this paper, applications of seismic data denoising methods using deep-learning techniques are introduced and investigated. Depending on the type of attenuated noise, these studies are grouped into denoising applications of coherent noise, random noise, and the combination of these two types of noise. Then, we investigate the deep-learning techniques used to remove the corresponding noise. Unlike conventional methods used to attenuate seismic noise, deep neural networks, a typical deep-learning technique, learn the characteristics of the noise independently and then automatically optimize the parameters. Therefore, such methods are less sensitive to generalized problems than conventional methods and can reduce labor costs. Several studies have also demonstrated that deep-learning techniques perform well in terms of computational cost and denoising performance. Based on the results of the applications covered in this paper, the pros and cons of the deep-learning techniques used to remove seismic noise are analyzed and discussed.