Maximum-likelihood estimation of multiscale stochastic model parameters

K. C. Chou
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引用次数: 2

Abstract

We consider the class of multiscale stochastic models developed by Chou, Willsky and Benveniste (see IEEE Trans. on Automatic Control, vol.39, no.3, 1994) and by Luettgen, Karl, Willsky and Tenney (see IEEE Trans. Signal Processing, vol.41, no.12, 1993) for signal and image modeling. These are Markov random field models on trees that describe signals in a scale-recursive way. In particular, they are state-space models with dynamics with respect to scale and have available fast algorithms for smoothing data. We present a maximum likelihood (ML) procedure for estimating the state-space parameters of these models from data. The procedure uses the expectation-maximization (EM) algorithm to iteratively solve for the ML estimates. Each iteration consists of (1) an expectation step that takes advantage of the fast smoother available for these multiscale models and (2) a maximization step that is also fast. We present an example of using this procedure to identify parameters based on imagery data and, subsequently, to perform multiscale target detection.
多尺度随机模型参数的最大似然估计
我们考虑由Chou, Willsky和Benveniste开发的一类多尺度随机模型。自动控制,第39卷,no。Luettgen, Karl, Willsky和Tenney(参见IEEE Trans。信号处理,vol.41, no。12, 1993)用于信号和图像建模。这些是树上的马尔可夫随机场模型,用比例递归的方式描述信号。特别是,它们是相对于尺度具有动态的状态空间模型,并且具有用于平滑数据的快速算法。我们提出了一种极大似然(ML)方法来从数据中估计这些模型的状态空间参数。该过程使用期望最大化(EM)算法迭代求解ML估计。每次迭代包括(1)利用这些多尺度模型的快速平滑性的期望步骤和(2)同样快速的最大化步骤。我们提出了一个使用该程序来识别基于图像数据的参数并随后执行多尺度目标检测的示例。
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