Poisson Group Testing: A Probabilistic Model for Boolean Compressed Sensing

• Published in: IEEE transactions on signal processing Vol. 63; no. 16; pp. 4396 - 4410
• Main Authors: Emad, Amin, Milenkovic, Olgica
• Format: Journal Article
• Language: English
• Published: IEEE 15.08.2015
• Subjects: Adaptation models; Adaptive group testing; binomial group testing; Boolean compressed sensing; Cloning; Compressed sensing; dynamical group testing; Huffman coding; information-theoretic bounds; nonadaptive design; Probabilistic logic; semiadaptive algorithms; Signal processing algorithms; Testing; Upper bound
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2015.2446433

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including dynamic testing with diminishing relative rates of defectives. We consider both nonadaptive and semi-adaptive identification methods. For nonadaptive methods, we derive a lower bound on the number of tests required to identify the defectives with a probability of error that asymptotically converges to zero; in addition, we propose test matrix constructions for which the number of tests closely matches the lower bound. For semiadaptive methods, we describe a lower bound on the expected number of tests required to identify the defectives with zero error probability. In addition, we propose a stage-wise reconstruction algorithm for which the expected number of tests is only a constant factor away from the lower bound. The methods rely only on an estimate of the average number of defectives, rather than on the individual probabilities of subjects being defective.