|Title||Control of false discovery rate in signal detection|
This dissertation investigates the application of multiple hypothesis testing procedures also known as multiple comparison problems), especially the control of the False Discovery Rate FDR), to several signal detection problems including distributed detection in wireless sensor networks, target detection in radars and Bayesian hypothesis testing with uncertain priors. The objective of the distributed detection problem is to design the local sensor decision rules and the fusion rule such that the system-level detection performance is optimized. Under the conditions that the local sensor performance metrics are unknown and the sensor and target locations are random, design of the optimum decision rules is an open and challenging research problem. In this dissertation, we propose a novel detection framework where the local sensor decision rules are obtained by controlling the FDR and the fusion rule is a randomized decision rule. The proposed approach is shown to provide substantial detection performance improvement over the present state of the art. In radar systems, the objective is to detect the presence of a target in clutter and noise. Conventional detection strategies involve hypothesis tests on each test cell at a pre-defined probability of false alarm. In this dissertation, we propose a novel approach where hypothesis tests are performed simultaneously on a number of test cells in a surveillance area SA) while controlling the FDR. Our approach thus proposes a shift from the conventional control of a cell-based statistic to the control of a region-based statistic for radar target detection. The proposed approach shows adaptivity to the unknown target density and provides improved detection performance in target-rich environments. However, control of a region-based statistic has several limitations, especially at very low and very high target densities. Hence, in this dissertation, we propose several solutions based on the concepts of decision fusion as well as algorithm fusion to overcome these limitations. We demonstrate that the proposed detection framework can distinguish between target-rich and target-starved regions and provides a more efficient and robust system design. In the Bayesian hypothesis testing problem, the objective is to minimize the average misclassification error while conducting multiple binary hypothesis tests with identical but unknown priors. It is further assumed that the prior is not a deterministic value but is a random variable with known density function. Under this problem setting, we propose a FDR based detection approach and demonstrate that the detection performance of the FDR based approach is close to that of a near-optimal Expectation-Maximization EM) based approach while requiring significantly less computation. Thus, the proposed approach is particularly suitable for Bayesian detection problems involving multiple binary hypothesis tests under real-time performance requirements.
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