Numerical differentiation of noisy, nonsmooth, multidimensional data
Numerical differentiation of noisy, nonsmooth, multidimensional data
复制标题
噪声、非平滑、多维数据的数值微分
DOI：
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发表时间：
2017
期刊：
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通讯作者：
R. Chartrand
中科院分区：
文献类型：
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作者：
R. Chartrand
我们考虑由噪声数据指定的多变量函数的微分问题。根据以前的工作单变量的情况下，我们正规化的微分过程，制定它作为一个逆问题的集成运营商作为正向模型。总变分正则化避免了有限差分方法的噪声放大，同时允许不连续的解决方案。与单变量的情况不同，我们使用交替方向，乘子算法的方法，为大型问题提供更高的效率。我们将该方法应用于合成数据和合成孔径雷达卫星图像。
We consider the problem of differentiating a multivariable function specified by noisy data. Following previous work for the single-variable case, we regularize the differentiation process, by formulating it as an inverse problem with an integration operator as the forward model. Total-variation regularization avoids the noise amplification of finite-difference methods, while allowing for discontinuous solutions. Unlike the single-variable case, we use an alternating directions, method of multipliers algorithm to provide greater efficiency for large problems. We apply the method to synthetic data and to synthetic-aperture radar satellite imagery.