Generalized Cauchy Distribution Theory for Statistical Signal Processing, Communications and Networking Applications

本研究涉及与广义柯西密度(GCD)相关的统计理论和方法的发展。发展的基于广义高斯密度(GCD)的理论和方法将被应用于传统的广义高斯密度(GGD)和当前流行的基于阿尔法稳定密度的方法所不能充分解决的一系列当代问题。GCD结合了GGD和Alpha稳定分布的优点，因为它具有重代数尾(如Alpha稳定分布)和跨灵活密度族的闭合形式表达式(如GGD)。因此，这项研究发展了一套统一的基于GCD的理论/方法，并将它们应用于以重尾统计为主导的一系列当代具有挑战性的应用。GCD拟合和密度参数估计的最佳方法，以及快速、准确、次优的参数估计技术，(2)稳健的检测器/估计器和滤波器设计？基于最大似然(ML)、最大后验概率(MAP)和一般贝叶斯方法的基于GCD？的最优检测器/估计器/过滤器，(3)误差范数开发？制定和分析GCD系列自然产生的规范，(4)应用？已开发的理论和算法在当代工程问题中的应用：(A)通信(电力线通信、大气噪声消除、稳健的幅度/频率估计和信号/噪声建模)，(B)生物医学信号处理(心电增强、斑点抑制和蛋白质序列聚类)，(C)联网(传输和/或存储的文件大小建模、负载平衡、调度、路由和互联网交换)，(D)自适应信号处理(发展稳健的梯度自适应算法和系统识别)，以及(E)图像处理(水印检测、DCT/小波系数建模和扩散)。

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).