Showing papers by "Michael I. Miller published in 1988"

On the existence of positive-definite maximum-likelihood estimates of structured covariance matrices

Abstract: It is shown that a sufficient condition for the likelihood function of a zero-mean Gaussian random vector with covariance R from some class of covariances R to be unbounded above over the set of positive-definite matrices in R is that some singular R/sub o/ exists in R whose range space contains the data. The results obtained imply that, for the spectrum estimation problem in which R is the class of Toeplitz covariances and only one long observation vector is available, by constraining the maximum-likelihood estimation problem to the class of Toeplitz matrices with nonnegative definite circulant extensions, a positive-definite solution is guaranteed to exist. >

Bayesian imaging using Good's roughness measure-implementation on a massively parallel processor

Abstract: A constrained maximum-likelihood estimator is derived by incorporating a rotationally invariant roughness penalty proposed by I.J. Good (1981) into the likelihood functional. This leads to a set of nonlinear differential equations the solution of which is a spline-smoothing of the data. The nonlinear partial differential equations are mapped onto a grid via finite differences, and it is shown that the resulting computations possess a high degree of parallelism as well as locality in the data-passage, which allows an efficient implementation on a 48-by-48 mesh-connected array of NCR GAPP processors. The smooth reconstruction of the intensity functions of Poisson point processes is demonstrated in two dimensions. >

Mapping Rule-Based And Stochastic Constraints To Connection Architectures: Implication For Hierarchical Image Processing

Abstract: Essential to the solution of ill posed problems in vision and image processing is the need to use object constraints in the reconstruction. While Bayesian methods have shown the greatest promise, a fundamental difficulty has persisted in that many of the available constraints are in the form of deterministic rules rather than as probability distributions and are thus not readily incorporated as Bayesian priors. In this paper, we propose a general method for mapping a large class of rule-based constraints to their equivalent stochastic Gibbs' distribution representation. This mapping allows us to solve stochastic estimation problems over rule-generated constraint spaces within a Bayesian framework. As part of this approach we derive a method based on Langevin's stochastic differential equation and a regularization technique based on the classical autologistic transfer function that allows us to update every site simultaneously regardless of the neighbourhood structure. This allows us to implement a completely parallel method for generating the constraint sets corresponding to the regular grammar languages on massively parallel networks. We illustrate these ideas by formulating the image reconstruction problem based on a hierarchy of rule-based and stochastic constraints, and derive a fully parallelestimator structure. We also present results computed on the AMT DAP500 massively parallel digital computer, a mesh-connected 32x32 array of processing elements which are configured in a Single-Instruction, Multiple Data stream architecture.

An EM Algorithm For Direction-Of-Arrival Estimation For Narrowband Signals In Noiset

Abstract: We derive a generalized EM algorithm for the maximum-likelihood estimation of the directions-of-arrival of multiple narrowband signals in noise, and prove that all of the limit points of the algorithm are stable and satisfy the neces-sary maximizer conditions. The deterministic signal model is considered here in which estimates of the unknown signal amplitudes are generated.

Application of Likelihood and Entropy for Toeplitz Constrained Covariance Estimation

Abstract: For the class of likelihood problems resulting from a complete-incomplete data specification in which the complete-data x are nonuniquely determined by the measured incomplete-data y via some many-to-one set of mappings y=h(x), it is shown that the density which maximizes entropy is identical to the conditional density of the complete data given the incomplete data which would be derived via rules of conditional probability. It is precisely this identity between the maxent density and the conditional density which results in the fact that maximum-likelihood estimation problems may be solved via an iterative joint-maximization of the sum of the entropy plus expected log-likelihood. It is demonstrated that for the problem of spectrum estimation from finite data sets, this view results in the derivation of the maximum- likelihood estimates of the Toeplitz constrained covariance parameters via an iterative maximization of the likelihood function.

Spectrum estimation via maximum likelihood estimation of Toeplitz constrained covariances

Abstract: The authors apply the maximum-likelihood (ML) method to the estimation of Toeplitz constrained covariances from Gaussian processes. An iterative expectation-maximization algorithm is used to generate the maximizers, and performance results are shown, demonstrating the superior mean-squared error properties of the ML estimator to conventional covariance estimates. >