Inf. Technol. Div., Alphatech Inc., Burlington, MA.
IEEE Trans Image Process. 1997;6(11):1517-29. doi: 10.1109/83.641412.
Recently, a class of multiscale stochastic models has been introduced in which random processes and fields are described by scale-recursive dynamic trees. A major advantage of this framework is that it leads to an extremely efficient, statistically optimal algorithm for least-squares estimation. In certain applications, however, estimates based on the types of multiscale models previously proposed may not be adequate, as they have tended to exhibit a visually distracting blockiness. We eliminate this blockiness by discarding the standard assumption that distinct nodes on a given level of the multiscale process correspond to disjoint portions of the image domain; instead, we allow a correspondence to overlapping portions of the image domain. We use these so-called overlapping-tree models for both modeling and estimation. In particular, we develop an efficient multiscale algorithm for generating sample paths of a random field whose second-order statistics match a prespecified covariance structure, to any desired degree of fidelity. Furthermore, we demonstrate that under easily satisfied conditions, we can "lift" a random field estimation problem to one defined on an overlapped tree, resulting in an estimation algorithm that is computationally efficient, directly produces estimation error covariances, and eliminates blockiness in the reconstructed imagery without any sacrifice in the resolution of fine-scale detail.
最近，一类多尺度随机模型被引入，其中随机过程和场由尺度递归动态树来描述。该框架的一个主要优点是，它为最小二乘估计提供了一种极其高效、统计最优的算法。然而，在某些应用中，基于之前提出的多尺度模型类型的估计可能不够充分，因为它们往往表现出视觉上令人分心的块状。通过放弃多尺度过程中给定层次上的不同节点对应于图像域的不相交部分的标准假设，我们消除了这种块状。相反，我们允许对应于图像域的重叠部分。我们将这些所谓的重叠树模型用于建模和估计。具体来说，我们开发了一种高效的多尺度算法，用于生成随机场的样本路径，其二阶统计量与预定的协方差结构相匹配，达到任意所需的保真度。此外，我们证明，在易于满足的条件下，我们可以将随机场估计问题提升到定义在重叠树上的问题，从而得到一种计算效率高的估计算法，直接产生估计误差协方差，并消除重建图像中的块状，而不会牺牲对细节的分辨率。
