Poisson Point Processes

"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate:Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans)Various multi-target and multi-sensor tracking applicationsPractical applications in areas like distributed sensing and detectionRelated finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processesPerfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.

This overview of non-homogeneous and multidimensional Poisson point processes and their applications features mathematical tools and applications from emission- and transmission-computed tomography to multiple target tracking and distributed sensor detection.

Fundamentals.- Fundamentals.- The Poisson Point Process.- Intensity Estimation.- Cramér-Rao Bound (CRB) for Intensity Estimates.- Applications to Imaging, Tracking, and Distributed Sensing.- Tomographic Imaging.- Multiple Target Tracking.- Distributed Sensing.- Beyond the Poisson Point Process.- A Profusion of Point Processes.- The Cutting Room Floor.