Don R. Halverson

Towards digital video steganalysis using asymptotic memoryless detection

This paper studies the potential for passive steganalysis in correlated image frames using non-classical detection theory. In particular, an algorithm for digital video steganalysis, named MoViSteg for Motion-based Video Steganalysis, is developed that exploits the temporal correlation among individual image frames in video signals to enhance steganalysis performance. The method differs from prior art in the use of motion interpolation and non-classical asymptotic memoryless detection that we believe is well-suited for video steganalysis. Results and discussion are provide in order to demonstrate the potential of our ideas for intrusion detection in a broad class of emerging multimedia applications.

A differential geometric approach toward robust signal detection

Abstract A procedure for measuring the robustness of a signal detector by applying some techniques rooted in differential geometry is presented. This approach admits nonstationarity and, in some cases, dependent data in a manner which reflects the effects of essentially arbitrary perturbations in a distribution about a nominal. Numerous examples are provided of the computation of robustness for several detectors. It is shown how such a quantitative measure of robustness can be employed to design detectors which possess an optimized combination of performance and robustness subject to a linear cost criterion, thus admitting the judicious tradeoff of those two important quantities.

Asymptotic memoryless detection of random signals in dependent noise

Abstract Design of detectors for strong mixing signals in strong mixing noise is considered, where a large degree of dependency may occur between the signal and noise. Under the criterion of asymptotic relative efficiency, it is shown that this design reduces to determining the solution of an integral equation, where only knowledge of the second order statistics of the randon processes involved is required. In particular, if the signal is independent of the noise and has nonzero mean, the optimal detector is the same as in the known constant signal case. It is also shown that it is possible to delete several regularity conditions which may be difficult to check in practice in the slightly more restrictive case where the maximal correlation coefficients of the signal and noise tend to zero.

Average robustness in signal detection and estimation

Abstract We present a systematic approach toward the development of nonlocal robustness measures. Our approach offers the advantage of being far more versatile than local or “worst case” nonlocal methods, and provides the user with models appropriate to many practical situations in computing average nonlocal robustness for the design and evaluation of various algorithms.

Robustness of the sign detector in dependent noise

Abstract The sign detector is an easily implemented signal detector which has classic appeal especially in situations where a great deal of uncertainty exists regarding the underlying noise situations. However, actual success in the application of this detector is strongly influenced by its robustness to several factors which may violate textbook assumptions regarding the detector but which arise in practise nevertheless. In this paper we investigate the robustness of the sign detector to a variety of such factors and discuss how the detector may be modified to better admit dependent data by making use of the robustness measure we derive.

Applications of unbiased perturbations towards quantifying robustness with pragmatic geometric methods

Robustness of a system has been defined in various ways, and extensive work has been completed to model the robustness of a system, but quantifying or measuring robustness has always been very difficult. In this research, we consider a simple system of a linear estimator, and then attempt to model the system performance and robustness in a graphical manner, which admits an analysis using the differential geometric concepts of slope. We try to compare two different types of slopes, namely the slope with biased perturbations of a surface and the slope with unbiased perturbations, and observe the values to see which of them can alternately be used in the process of understanding or measuring robustness. In this process, we have worked on two different examples and taken readings for many points to find if there is any consistency in the two slopes.

Applications of curvature toward the measurement of robustness for data processors

A reality faced in the practical application of data processors is inexact statistical knowledge of the underlying random processes. Accordingly, it is often desirable for a processor to possess robustness. In this paper, we show how the concept of manifold curvature can be employed to admit measurement of robustness, thus allowing the degree of robustness to be a factor in the design of the processor. After showing how robustness measures can be obtained for a wide variety of processors, we then illustrate a specific application that can be applied to the area of parameter estimation.

Robust estimator design with an emphasis balance between performance and robustness

Abstract From a number of ML estimators (typically unbiased) of practical interest which include the variance for a Gaussian distribution, the standard deviation for a Laplace distribution, the variance for a Rayleigh distribution and a “spread parameter” for a Cauchy distribution, we design robust estimators according to an emphasis balance between normalized performance and normalized robustness. We measure performance with inverted MSE and robustness with a differential geometric approach.

Measuring performance of robust estimator for the variance of generalized Gaussian distribution

We consider the calculating performance of a robust estimator for the variance of a generalized Gaussian distribution. In detail, we apply an unbiased ML estimator and a robust estimator for the variance of a Gaussian distribution to the variance of a generalized Gaussian distribution and calculate the mean square error. Then, we determine how the performance (= inverted MSE) changes as the actual distribution varies over this generalized Gaussian distribution which represents a Gaussian, Laplace, or Cauchy distribution. Results indicate that, for robustness, heavy censoring (small k) should be employed for a small number of samples, while less censoring (large k) can be appropriate for a large number of samples.

Empirical Distribution Approach to the Robustness Measure for Non-stationary Data

This paper proposes the study of robustness measures for signal detection in non-stationary noise using differential geometric tools in conjunction with empirical distribution analysis. Our approach shows that gradient can be viewed as a random variable and therefore used to generate sample densities allowing one to draw conclusions regarding the robustness. As an example, we apply the geometric methodology to the detection of time varying deterministic signals in imperfectly known dependent non-stationary Gaussian noise.