Browsing by Author "Dabak, Anand Ganesh"

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    A geometry for detection theory
    (1993) Dabak, Anand Ganesh; Johnson, Don H.
    The optimal detector for a binary detection problem under a variety of criteria is the likelihood ratio test. Despite this simple characterization of the detector, analytic performance analysis in most cases is difficult because of the complexity of integrals involved in its computation. When the two hypotheses are signals in additive Gaussian noise, performance analysis leads to a geometric notion, whereby the signals are considered as elements of a Euclidean space and the distance between them being a measure of the performance. We extend this notion to non-Gaussian problems, assuming only that the nominal densities are mutually absolutely continuous. We adopt a completely non-parametric approach, considering the two hypotheses as points in the space of all the probability measures over the observation space. Employing the tools of differential geometry, we induce a manifold structure on this space of all probability measures, and enforce a detection theoretic specific geometry on it. The only Riemannian metric on this manifold is the Fisher information, whenever it exists. Because the detection theoretic covariant derivative is incompatible with this metric the manifold for the space of probability measures is non-Riemannian. We show that geodesics on this manifold are the exponential mixture densities. Despite not being able to define distance metric on our non-Riemannian manifold, we show that the Kullback information can play the role of "squared" distance. Because the Kullback information is asymptotically related to the performance of the optimal detector, geometry and performance are linked. We apply this geometry to solve some classic problems in detection theory. Using the Kullback information to define the contamination neighborhoods around the nominals, the likelihood ratio of the nominals is shown to yield the robust detector. We obtain a density "halfway" between the nominals to employ as the importance sampling biasing density. Using this density, we demonstrate that the importance sampling gain is inversely related to probability of error. In an M-ary hypotheses testing problem in communications, the M signals constitute a "signal constellation" in the space of all probability measures and the underlying geometry can be employed in signal set design.
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    Binaural localization using interaural cues
    (1990) Dabak, Anand Ganesh; Johnson, Don H.
    Major nuclei of the superior olivary complex--the lateral superior olive (LSO) and the medial superior olive (MSO) are presumed to play a major role in the localization of sound signals using interaural level and interaural phase differences between the signals arriving at the two ears. The present work develops a novel approach--function based modeling--for assessing the role of these nuclei in binaural localization. The interaural level difference is shown to be the sufficient statistic at high frequencies when only level cues are available. This level difference is processed optimally when the inputs are excitatory from one ear and inhibitory from the other ear. Response characteristics of LSO single units are remarkably similar to the optimal processor's, strongly supporting the notion that LSO units are intimately involved in high-frequency binaural hearing. For low frequencies the optimal processor makes use of the interaural phase difference cue by correlating the inputs to the two ears thus requiring that the two inputs be excitatory. Hence, high and low frequency localization systems are shown to differ greatly, suggesting separate pathways for each.