An analysis of wavelet frame based scattered data reconstruction
An analysis of wavelet frame based scattered data reconstruction
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DOI：
10.1016/j.acha.2015.09.008
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发表时间：
2017-05
影响因子：
2.5
通讯作者：
Jianbin Yang;D. Stahl;Zuowei Shen
中科院分区：
文献类型：
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作者：
Jianbin Yang;D. Stahl;Zuowei Shen
在现实世界的应用中，许多信号都包含奇点，比如图像中的边缘。最近基于小波框架的方法被成功地应用于从这些函数重建散乱数据，同时保留了这些特征。在这篇文章中，我们提出了一种新的方法，它通过最小化一个ℓ1-正则最小二乘问题来确定移位不变子空间的近似值，该问题额外使用了小波框架变换来保持尖锐的边缘。我们给出了这种方法的详细分析，即近似误差如何表现依赖于数据密度和噪声水平。在此基础上，建立了基于小波框架的图像恢复模型，并分析了模型的收敛特性。最后，我们给出了一些数值例子，例如如何应用这种方法来处理分子动力学中的粗粒度模型。
In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this paper we present a recent approach which determines the approximant from shift invariant subspaces by minimizing an ℓ 1-regularized least squares problem which makes additional use of the wavelet frame transform in order to preserve sharp edges. We give a detailed analysis of this approach, ie, how the approximation error behaves dependent on data density and noise level. Moreover, a link to wavelet frame based image restoration models is established and the convergence of these models is analyzed. In the end, we present some numerical examples, for instance how to apply this approach to handle coarse-grained models in molecular dynamics.