Bayes and empirical Bayes semi-blind deconvolution using eigenfunctions of a prior covariance
Bayes and empirical Bayes semi-blind deconvolution using eigenfunctions of a prior covariance
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DOI：
10.1016/j.automatica.2007.02.025
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发表时间：
2007-10-01
期刊：
影响因子：
6.4
通讯作者：
Bell, Bradley M.
中科院分区：
文献类型：
--
作者：
Pillonetto, Gianluigi;Bell, Bradley M.
我们考虑半盲去卷积问题;即，使用线性相关测量的有限集合来估计线性动态系统的未知输入函数，其中所述动态系统直到一些系统参数是已知的。如果没有进一步的假设，这个问题往往是不适定和病态的。我们克服了这个困难，建模的未知输入作为一个实现的随机过程的协方差已知的一些有限的协方差参数。我们首先提出了一种经验贝叶斯方法，其中未知参数通过最大化边际似然/后验来估计，随后通过Tikhonov估计器（参数设置为点估计）重建输入。接下来，我们介绍一种贝叶斯方法，该方法可以恢复未知参数和未知输入函数的后验概率分布，从而获得最小方差估计。这两种方法都使用随机过程协方差的特征函数来获得未知输入函数及其概率分布的有效表示。模拟案例研究被用来测试这两种方法，并比较它们的相对性能。(c)2007爱思唯尔有限公司保留所有权利。
We consider the semi-blind deconvolution problem; i.e., estimating an unknown input function to a linear dynamical system using a finite set of linearly related measurements where the dynamical system is known up to some system parameters. Without further assumptions, this problem is often ill-posed and ill-conditioned. We overcome this difficulty by modeling the unknown input as a realization of a stochastic process with a covariance that is known up to some finite set of covariance parameters. We first present an empirical Bayes method where the unknown parameters are estimated by maximizing the marginal likelihood/posterior and subsequently the input is reconstructed via a Tikhonov estimator (with the parameters set to their point estimates). Next, we introduce a Bayesian method that recovers the posterior probability distribution, and hence the minimum variance estimates, for both the unknown parameters and the unknown input function. Both of these methods use the eigenfunctions of the random process covariance to obtain an efficient representation of the unknown input function and its probability distributions. Simulated case studies are used to test the two methods and compare their relative performance. (c) 2007 Elsevier Ltd. All rights reserved.