A Generalized Cauchy Distribution Framework for Problems Requiring Robust Behavior

• Published in: EURASIP journal on advances in signal processing Vol. 2010; no. 1
• Main Authors: Carrillo, Rafael E., Aysal, Tuncer C., Barner, Kenneth E.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2010; SpringerOpen
• Subjects: Engineering; Quantum Information Technology; Research Article; Robust Processing of Nonstationary Signals; Signal,Image and Speech Processing; Spintronics; Cauchy Distribution; Stable Distribution; Fusion Center; Sparse Signal; Influence Function
• ISSN: 1687-6180; 1687-6172; 1687-6180
• DOI: 10.1155/2010/312989

Statistical modeling is at the heart of many engineering problems. The importance of statistical modeling emanates not only from the desire to accurately characterize stochastic events, but also from the fact that distributions are the central models utilized to derive sample processing theories and methods. The generalized Cauchy distribution (GCD) family has a closed-form pdf expression across the whole family as well as algebraic tails, which makes it suitable for modeling many real-life impulsive processes. This paper develops a GCD theory-based approach that allows challenging problems to be formulated in a robust fashion. Notably, the proposed framework subsumes generalized Gaussian distribution (GGD) family-based developments, thereby guaranteeing performance improvements over traditional GCD-based problem formulation techniques. This robust framework can be adapted to a variety of applications in signal processing. As examples, we formulate four practical applications under this framework: (1) filtering for power line communications, (2) estimation in sensor networks with noisy channels, (3) reconstruction methods for compressed sensing, and (4) fuzzy clustering.