Graduate Thesis Or Dissertation


Local Signal Detection on Irregular Domains via Bivariate Spline Public Deposited

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  • Local signal detection is useful in many scientific areas such as imaging processing and speech recognition, for extracting meaningful patterns from noisy signals. In this dissertation, we study estimation and local signal detection for spatial data distributed over irregular domains. In particular, we use bivariate splines defined on triangulations to approximate unknown signals on a complex domain nonparametrically. Subsequently, we propose a penalized polynomial spline method that simultaneously detects the null regions with signals and estimates the patterns on non-null regions. A smoothing proximal gradient (SPG) algorithm is used to find the estimator efficiently. In theory, the proposed estimator is shown to be consistent in estimating the true underling patterns. Furthermore, it is also able to detect the null signal region with probability approaching one. The numeric performance of the proposed method is evaluated through simulation studies and real data analysis. This validation shows that the proposed method and algorithm efficiently detect local signals on complex domains.
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