A class of multiscale models describing stochastic processes indexed by the nodes of a tree has recently been introduced by Chou et al. (1994). Experimental and theoretical results indicate that this class of models is quite rich, and moreover these models lead to extremely efficient algorithms for optimal estimation based on noisy observations. This motivates further algorithmic development, and in particular, in this paper we present a likelihood calculation algorithm for this class of multiscale models. That is, we consider the problem of computing the log of the conditional probability of a set of data assuming that they correspond to a particular multiscale model. We exploit the structure of the multiscale models to develop an efficient, scale recursive algorithm that allows for multiresolution data and parameters which vary in both space and scale. We illustrate one possible application of the algorithm to a texture classification problem in which one must choose from a given set of models that model which best represents or most likely corresponds to a given set of random field measurements. Texture modeling with Gaussian Markov random field (GMRF) models is well documented. One difficulty in using GMRF models, however, is that the calculation of likelihoods may be prohibitively complex computationally if there is an irregular sampling pattern. It is shown here that GMRF models can be represented within our multiscale model class which allows us to approximately compute likelihoods for GMRF models based on measurements over arbitrarily sampled regions. As we demonstrate in the context of texture discrimination problems, the multiscale approach not only leads to computationally efficient implementations, but also to virtually the same performance as the optimal GMRF-based likelihood ratio test. We discuss further applications in the area of synthetic aperture radar imagery processing.>

Discusses a class of multiresolution models of random fields based on a generalization of the midpoint deflection construction of the 1D Brownian motion. The authors then present least squares (LS) algorithms for the estimation of parameters which define these models and hence provide a framework for synthesizing and analyzing images with fractal-like properties such as those found in statistical representation of natural terrain and other geophysical phenomena. The authors also briefly discuss possible applications of this modeling framework to target detection in images.>

A specific distributed decisionmaking problem is considered that reflects essential aspects of tactical command and control teams, particularly communications and limitations to human information processing induced because of time pressure. A constrained optimization problem is fonnulated to maximize overall team performance subject to individual limitations. The results of a systematic investigation of possible solutions are described in terms of performance and workload interactions. In particular, optimal solutions arise where team members act randomly and/or introduce errors. Though results obtained are specific to the case study, a number of more generally applicable principles are evident.

The problem of optimally controlling a large, stochastic, dynamical system has challenged control system designers for years, particularly when communication resources between ports of the system are quite scarce. Optimal control methods are known to lead to analytically intractable control laws due to the possibility of signaling through the system. A new formulation of the distributed control problem is presented which avoids such behavior by restricting the scope of each decision agent's knowledge of the underlying system dynamics. Within this framework techniques for solving the individual agents' problems can be developed. These techniques support coordination strategies as discussed in a companion paper.

Several mechanisms which can be used in the real-time distributed coordination of large-scale dynamical systems which display a subsystem structure are derived. A spectrum of approaches using varying degrees of types of communication to reduce the uncertainty of each agent concerning the events controlled by others is presented. The organizational requirements of each coordination strategy in terms of constraints on the interagent relationships are derived, and it is shown that while any of the mechanisms discussed here work well in hierarchical organizational structures, many are adaptable to much larger classes of structures.