Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion
Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion
复制标题
隐式不可压缩湍流运动的自相似先验基和小波基
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Harouna
中科院分区：
文献类型：
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作者：
P. Héas;F. Lavancier;S. Harouna
本文研究了从图像序列观测中估计湍流的不适定反问题。从贝叶斯的角度，选择无散度各向同性分数布朗运动（fBm）作为瞬时湍流速度场的先验模型。这种自相似先验准确表征了不可压缩各向同性湍流中速度场的二阶统计量。然而，相关的最大后验涉及到一个分数阶拉普拉斯算子，在实践中很难实现。为了解决这个问题，我们提出在选择好的小波基上分解无发散的fBm。作为第一种选择，我们建议设计小波作为白化滤波器。我们证明了这些滤波器是由勒雷投影组成的分数阶拉普拉斯小波。作为第二种选择，我们使用无散度小波基，它隐含地考虑了物理产生的不可压缩性约束。虽然后一种分解涉及到相关的小波系数，但我们能够在实践中处理这种相关性。基于这两种小波分解，我们最终提供了有效的算法来逼近最大后验。一个密集的数值评估证明了所提出的基于小波的自相似先验的相关性。
This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergent-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposition involves correlated wavelet coefficients, we are able to handle this dependence in practice. Based on these two wavelet decompositions, we finally provide effective and efficient algorithms to approach the maximum a posteriori. An intensive numerical evaluation proves the relevance of the proposed wavelet-based self-similar priors.
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DOI：
10.1007/978-1-4939-7647-8_1
发表时间：
2018
期刊：
Neuromethods
影响因子：
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作者：
Joshi,AnandA
通讯作者：
Joshi,AnandA