This research involves the development of statistical theories and methods related to the Generalized Cauchy density (GCD). The developed GCD?based theories and methods will be applied to a suite of contemporary problems not adequately addressed by traditional Generalized Gaussian density (GGD) and currently popular Alpha-Stable density based methods. The GCD combines the advantages of the GGD and Alpha -Stable distributions in that it possesses heavy algebraic tails (like Alpha-Stable distributions) and closed form expressions (like the GGD) across a flexible family of densities. This research thus develops a unified body of GCD?based theories/methods and applies them to a broad array of contemporary challenging applications dominated by heavy?tailed statistics.
Specifically, the investigators study the followings: (1) Density Fitting and Parameter Estimation ? Optimal methods for GCD fitting and density parameter estimation, and fast, accurate, suboptimal parameter estimation techniques, (2) Robust Detector/Estimator and Filter Design ? Optimal GCD?based detectors/estimators/filters based on statistical criteria, including maximum likelihood (ML), maximum a posterior (MAP), and general Bayesian approaches, (3) Error Norm Development ? Development and analysis of norms that arise naturally from the GCD family, (4) Applications ? The application of developed theory and algorithms to contemporary engineering problems: (a) Communications (powerline communications, atmospheric noise cancellation, robust amplitude/frequency estimation, and signal/noise modeling), (b) biomedical signal processing (ECG enhancement, speckle suppression, and protein sequence clustering), (c) networking (transferred and/or stored file size modeling, load?balancing, scheduling, routing and switching in the Internet), (d) adaptive signal processing (development of robust gradient adaptive algorithms and system identification), and (e) image processing (watermark detection, DCT/wavelet coefficients modeling and diffusion).
