各项异性扩散
非线性系统
数学
波形
反问题
算法
反演(地质)
背景(考古学)
滤波器(信号处理)
降噪
数学分析
图像(数学)
计算机科学
计算机视觉
地质学
电信
雷达
古生物学
物理
量子力学
构造盆地
作者
Ludovic Métivier,Romain Brossier
出处
期刊:Inverse Problems
[IOP Publishing]
日期:2022-09-14
卷期号:38 (11): 115001-115001
被引量:6
标识
DOI:10.1088/1361-6420/ac8c91
摘要
Abstract Nonlinear anisotropic diffusion filters have been introduced in the field of image processing for image denoising and image restoration. They are based on the solution of partial differential equations involving a nonlinear anisotropic diffusion operator. From a mathematical point of view, these filters enjoy attractive properties, such as minimum–maximum principle, and an inherent decomposition of the images in different scales. We investigate in this study how these filters can be applied to help solving data-fitting inverse problems. We focus on seismic imaging using the full waveform, a well known nonlinear instance of such inverse problems. In this context, we show how the filters can be applied directly to the solution space, to enhance the structural coherence of the parameters representing the subsurface mechanical properties and accelerate the convergence. We also show how they can be applied to the seismic data itself. In the latter case, the method results in an original low-frequency data enhancement technique making it possible to stabilize the inversion process when started from an initial model away from the basin of attraction of the global minimizer. Numerical results on a 2D realistic synthetic full waveform inversion case study illustrate the interesting properties of both approaches.
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