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。发达的GCD？基于的理论和方法将被应用到一套当代的问题没有充分解决传统的广义高斯密度（GGD）和目前流行的阿尔法稳定的密度为基础的方法。GCD结合了GGD和Alpha -Stable分布的优点，因为它在一个灵活的密度族中拥有重代数尾（如Alpha-Stable分布）和封闭形式表达式（如GGD）。因此，本研究开发了一个统一的机构的GCD？的理论/方法，并将其应用于广泛的当代具有挑战性的应用为主的重？具体而言，研究者研究了以下内容：（1）密度拟合和参数估计？GCD拟合和密度参数估计的优化方法，以及快速、准确、次优的参数估计技术;（2）鲁棒检测器/估计器和滤波器设计？最优GCD？基于检测器/估计器/过滤器的统计标准的基础上，包括最大似然（ML），最大后验（MAP），和一般贝叶斯方法，（3）误差范数的发展？发展和分析从GCD家族中自然产生的规范，（4）应用？将已开发的理论和算法应用于当代工程问题：（a）通信（电力线通信，大气噪声消除，鲁棒幅度/频率估计和信号/噪声建模），（B）生物医学信号处理（ECG增强，斑点抑制和蛋白质序列聚类），（c）网络（传输和/或存储文件大小建模，负载？互联网中的平衡、调度、路由和交换），（d）自适应信号处理（稳健梯度自适应算法和系统识别的开发），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).