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Multiple-channel detection is considered in the context of a sensor network where data can be exchanged directly between sensor nodes that share a common edge in the network graph. Optimal statistical tests used for signal source detection with multiple noisy sensors, such as the Generalized Coherence (GC) estimate, use pairwise measurements from every pair of sensors in the network and are thus only applicable when the network graph is completely connected, or when data are accumulated at a common fusion center. This thesis presents and exploits a new method that uses maximum-entropy techniques to estimate measurements between pairs of sensors that are not in direct communication, thereby enabling the use of the GC estimate in incompletely connected sensor networks. The research in this thesis culminates in a main conjecture supported by statistical tests regarding the topology of the incomplete network graphs.
Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.