The additive causal part of Burg's maximum entropy estimator anddata consistency

The additive causal part of Burg's maximum entropy (ME) estimator spectrum is calculated in closed form. An immediate corollary for data consistency is shown     

Iterative maximum entropy power spectrum estimation for multirate systems

In multirate systems, observations are generally insufficient to determine the power spectrum of the input signal. In this paper, we reformulate the problem using a novel matrix notation and the discrete entropy function. Then we present an iterative maximum entropy power spectrum estimation algorithm for the solution of this problem. Contrary to the existing solutions, the new algorithm is computationally efficient since it is based on fast Fourier transform (FFT) and simple matrix calculations. Furthermore, simulation results show that the new algorithm converges to the maximum entropy solution and can be successfully used in multirate statistical data estimation.     

Some detection and resolution properties of maximum entropy spectrum analysis

An experimental comparison between conventional spectral estimation techniques and a Maximum Entropy Spectral Analysis (MESA) algorithm is made. Three factors in the experimentation make the results of considerable interest to workers in acoustic signal processing, especially sonar and surveillance. These are the range of signal-to-noise ratio (SNR) studied, the comparisons based equal length observation intervals and the use of ensemble averaging after maximum entropy analysis. Results are presented, for both resolution and peak signal response, which tend to indicate that the Maximum Entropy Method (MEM) offers considerable promise in achieving the detection performance of long observation interval discrete Fourier transform (DFT) analysis at a much reduced length of observation time.     

On the method of maximum entropy spectrum estimation (Corresp.)

We derive the method of maximum entropy spectrum estimation by bordering techniques of linear algebra. Using bordering, we obtain the recursive solution to the Yule-Walker equations and the recursive equation for the Toeplitz determinant in terms of the partial correlation coefficients. Minimization of the forward and backward predictor errors is then done with respect to the partial correlation coefficients. The minimization is done stagewise, constraining higher partial correlation values to zero. Thus, the minimization is done for a maximum-entropy normal process; the Toeplitz determinant is a maximum.     

On the resolution properties of an adaptive algorithm for maximum entropy spectrum analysis

The resolution properties of the adaptive mean squares algorithm when used for maximum entropy spectrum estimation are compared with those of Burg's algorithm and the standard periodogram method using the FFT algorithm.     

An image model based on occluding object images and maximum entropy

This paper introduces a statistical image model based on occlusion and maximum entropy. The statistical model combines a fundamental property of image formation, occlusion, with both object-image shape and nonuniform object-image intensity. The model is a composition of individual object-images that have random positions, shapes, and intensities, and that occlude both background and one another. We derive the autocorrelation and second-order probability density functions of this model and give several examples.     

An information-theoretic view of network management

We present an information-theoretic framework for network management for recovery from nonergodic link failures. Building on recent work in the field of network coding, we describe the input-output relations of network nodes in terms of network codes. This very general concept of network behavior as a code provides a way to quantify essential management information as that needed to switch among different codes (behaviors) for different failure scenarios. We compare two types of recovery schemes, receiver-based and network-wide, and consider two formulations for quantifying network management. The first is a centralized formulation where network behavior is described by an overall code determining the behavior of every node, and the management requirement is taken as the logarithm of the number of such codes that the network may switch among. For this formulation, we give bounds, many of which are tight, on management requirements for various network connection problems in terms of basic parameters such as the number of source processes and the number of links in a minimum source-receiver cut. Our results include a lower bound for arbitrary connections and an upper bound for multitransmitter multicast connections, for linear receiver-based and network-wide recovery from all single link failures. The second is a node-based formulation where the management requirement is taken as the sum over all nodes of the logarithm of the number of different behaviors for each node. We show that the minimum node-based requirement for failures of links adjacent to a single receiver is achieved with receiver-based schemes.     

Resolution of maximum entropy array processor

An approximate expression for the resolution of the maximum entropy array processor is derived and compared with the resolution expression for the conventional linear array processor (beamformer).     

Application of the maximum entropy spectrum analysis technique to signals with spectral peaks of finite width

The Maximum Entropy Spectral Analysis technique is applied to signals with spectral peaks of finite width. The Burg and Least Squares algorithms are used and in each case the performance is compared to that of a conventional Fourier method.     

A new spectrum extension method that maximizes the multistepminimum prediction error-generalization of the maximum entropy concept

Given (n+1) consecutive autocorrelations of a stationary discrete-time stochastic process, how this finite sequence is extended so that the power spectral density associated with the resulting infinite sequence of correlations is nonnegative everywhere is discussed. It is well known that when the Hermitian Toeplitz matrix generated from the given autocorrelations is positive definite, the problem has an infinite number of solutions and the particular solution that maximizes the entropy functional results in a stable all-pole model of order n. Since maximization of the entropy functional is equivalent to maximization of the minimum mean-square error associated with one-step predictors, the problem of obtaining admissible extensions that maximize the minimum mean-square error associated with k-step (k⩽n) predictors, that are compatible with the given autocorrelations, is studied. It is shown that the resulting spectrum corresponds to that of a stable autoregressive moving average (ARMA) (n, k-1) process     

Extension to the maximum entropy method

The maximum entropy method provides an estimate of the power spectral density which maximizes the entropy of a stationary random process from the firstNlags of the autocorrelation function. The method is extended to accommodate weighted errors in the measured autocorrelation function.     

An information-theoretic analysis of cutaneous receptor responses

Two prevalent underlying assumptions related to cutaneous receptor research are that receptor responses are conditionally independent given the stimulus, and that stimulus information is encoded through a mean rate code. In this paper, an information-theoretic technique that can be used to test these assumptions is developed and presented. Results are presented from experiments designed to evaluate the efficiency of mean rate codes and the independence of receptor discharges recorded from cutaneous receptor afferent neurons.     

A two-dimensional maximum entropy spectral estimator

Using ideas from one-dimensional maximum entropy spectral estimation a two-dimensional spectral estimator is derived by extrapolating the two-dimensional sampled autocorrelation (or covariance) function. The method used maximizes the entropy of a set of random variables. The extrapolation (or prediction) process under this maximum entropy condition is shown to correspond to the most random extension or equivalently to the maximization of the mean-square prediction error when the optimum predictor is used. The two-dimensional extrapolation must he terminated by the investigator. The Fourier transform of the extrapolated autocorrelation function is the two-dimensional spectral estimator. Using this method one can apply windowing prior to calculating the spectral estimate. A specific algorithm for estimating the two-dimensional spectrum is presented, and its computational complexity is estimated. The algorithm has been programmed and computer examples are presented.     

The maximum entropy image of two targets

A theory has been developed which accounts for the empirically known facts of maximum entropy method's (MEM) sensitivity to the RF phase difference between targets, the effects of averaging with respect to variations of the phase difference, and the effect of noise. Of importance is the discovery from the theory that the effect of noise can be markedly reduced beyond what was previously believed to be the resolution limit suggested by Gabriel's data. Experimental evidence indicates a 7-15-dB improvement.     

最大熵原理在非结构化道路图像识别中的应用

根据非结构化道路环境的特点，结合最大熵理论在图像处理中的运用，提出了一种基于最大熵理论的非结构化道路图像识别的算法。对于以往划分道路时，阴影区域和道路与非路交界区域容易出现分类错误的现象，通过两次最大熵分类，把这些区域重新划分，最终将道路与周围的环境区分开来。同时满足实时性的要求。     

Multicriterion maximum entropy image reconstruction from projections

A solution algorithm for the image reconstruction problem with three criteria, maximum entropy, minimum nonuniformity and peakedness, and least square error between the original projection data and projection due to reconstruction is presented. Theoretical results of precedence properties which are respected by all noninferior solutions are first derived. These precedence properties are then incorporated into a multiple-criteria optimization framework to improve the computational efficiency. Comparisons of the new algorithm to the MART and MENT algorithms are carried out using computer-generated noise-free and Gaussian noisy projections. Results of the computational experiment and the efficiency of the multiobjective entropy optimization algorithm (MEOA) are reported.     

Extension to the maximum entropy method II

The maximum entropy method provides an estimate of the power spectral density which maximizes the entropy of a stationary random process from the firstNlags of the autocorrelation function. The method is applied to cases where some of the firstNautocorrelation function lags are unknown.     

Stable spectral estimates with maximum entropy estimation

The maximum-entropy-estimation technique has been found to give stable spectra at low and high signal/noise ratios with an unstable middle region.     

An information-theoretic and game-theoretic study of timing channels

This paper focuses on jammed timing channels. Pure delay jammers with a maximum delay constraint, an average delay constraint, or a maximum buffer size constraint are explored, for continuous-time or discrete-time packet waveforms. Fluid waveform approximations of each of these classes of waveforms are employed to aid in analysis. Channel capacity is defined and an information-theoretic game based on mutual information rate is studied. Min-max optimal jammers and max-min optimal input processes are sought. Bounds on the min-max and max-min mutual information rates are described, and numerical examples are given. For maximum-delay-constrained (MDC) jammers with continuous-time packet waveforms, saddle-point input and jammer strategies are identified. The capacity of the maximum-delay constrained jamming channel with continuous-time packet waveforms is shown to equal the mutual information rate of the saddle point. For MDC jammers with discrete-time packet waveforms, saddle-point strategies are shown to exist. Jammers which have quantized batch departures at regular intervals are shown to perform well. Input processes with batches at regular intervals perform well for MDC or maximum-buffer-size-constrained jammers.