Gauss-Markov随机场的伸缩递归表示与估计
Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields
摘要：
我们提出了\emph{telescoping}递归表示连续和离散索引非因果高斯马尔可夫随机场。我们的递归从边界（$\R^d$中的超曲面，$d \ge 1$）开始，向内收缩。例如，对于图像，伸缩表示将递归从$d = 2$减少到$d = 1$，即，到一维上的递归在适当的条件下，递归的随机场是线性随机微分/差分方程驱动的白噪声，我们推导出递归估计算法，扩展标准算法，如卡尔曼-布西滤波器和劳赫-董-Striebel平滑，非因果马尔可夫随机场。
英文摘要：
We present \emph{telescoping} recursive representations for both continuous and discrete indexed noncausal Gauss-Markov random fields. Our recursions start at the boundary (a hypersurface in $\R^d$, $d \ge 1$) and telescope inwards. For example, for images, the telescoping representation reduce recursions from $d = 2$ to $d = 1$, i.e., to recursions on a single dimension. Under appropriate conditions, the recursions for the random field are linear stochastic differential/difference equations driven by white noise, for which we derive recursive estimation algorithms, that extend standard algorithms, like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal Markov random fields.
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