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首页> 外文期刊>Proceedings of the IEEE >A multiresolution methodology for signal-level fusion and data assimilation with applications to remote sensing
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A multiresolution methodology for signal-level fusion and data assimilation with applications to remote sensing

机译：用于信号级融合和数据同化的多分辨率方法及其在遥感中的应用

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This paper covers the design of multiscale stochastic models that can be used to fuse measurements of a random field or random process provided at multiple resolutions. Such sensor fusion problems arise in a variety of contexts, including many problems in remote sensing and geophysics. An example, which is used in this paper as a vehicle to illustrate our methodology, is the estimation of variations in hydraulic conductivity as required for the characterization of groundwater flow. Such a problem is typical in that the phenomenon to be estimated cannot be measured at fine scales throughout the region of interest, but instead must be inferred from a combination of measurements of very different types, including point measurements of hydraulic conductivity at irregular collections of points and indirect measurements that provide only coarse and nonlocal information about the conductivity field. Fusion of such disparate and irregular measurement sets is a challenging problem, especially when one includes the objective of producing, in addition to estimates, statistics characterizing the errors in those estimates. In this paper, we show how modeling a random field at multiple resolutions allows for the natural fusion (or assimilation) of measurements that provide information of different types and at different resolutions. The key to our approach is to take advantage of the fast multiscale estimation algorithms that efficiently produce both estimates and error variances even for very large problems. The major innovation required in our case, however, is to extend the modeling of random fields within this framework to accommodate multiresolution measurements. In particular to take advantage of the fast algorithms that the models admit, we must be able to model each nonlocal measurement as the measurement of a single variable of the multiresolution model at some appropriate resolution and scale. We describe how this can be done and illustrate its effectiveness for an ill-posed inverse problem in groundwater hydrology.
机译：本文涵盖了多尺度随机模型的设计，该模型可用于融合以多种分辨率提供的随机场或随机过程的测量。这种传感器融合问题出现在各种情况下，包括遥感和地球物理学中的许多问题。在本文中，用一个例子来说明我们的方法，它是估算地下水流特征所需的水力传导率变化的估计。这样的问题是典型的，因为无法在整个感兴趣区域中以精细尺度测量要估计的现象，而必须从非常不同类型的测量（包括在不规则的点集合处的水力传导率的点测量）的组合中推断出间接测量仅提供有关电导率场的粗略和非局部信息。这种不同的和不规则的度量集的融合是一个具有挑战性的问题，尤其是当除了估计之外还包括生成表征那些估计中的误差的统计数据的目的时。在本文中，我们展示了如何以多种分辨率对随机场进行建模，以实现测量的自然融合（或同化），从而提供不同类型和不同分辨率的信息。我们方法的关键是利用快速多尺度估计算法，即使对于非常大的问题，该算法也可以有效地产生估计值和误差方差。但是，在我们的案例中，主要的创新是在此框架内扩展随机字段的建模，以适应多分辨率测量。特别是要利用模型允许的快速算法，我们必须能够将每个非局部测量建模为在适当的分辨率和比例下对多分辨率模型的单个变量进行的测量。我们描述了如何做到这一点，并说明了其对地下水水文学中不适定反问题的有效性。

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