A new pool control method for Boolean compressed sensing based adaptive group testing

In the adaptive group testing, the pool (a set of items to be tested) used in the next test is determined based on past test results, and its performance heavily depends on the control method of the pool. This paper proposes a new pool control method for Boolean compressed sensing based adaptive group testing. The proposed method firstly selects a pool size of the next test by minimizing the expectation of the approximated required number of tests after the next test based on the estimated number of remaining positive items. Then, when the selected pool size is one, an item having the highest probability of being positive will be selected as a pool, otherwise a pool with the selected size will be constructed by randomly selecting items. In addition, a new cardinality estimation method of positive items, that can be implemented in parallel with the proposed pool control method, is also proposed. Computer simulation results reveal that the adaptive group testing with the proposed method has better performance than that with the conventional methods for both with and without the information of cardinality of positive items.