Randomized recovery for boolean compressed sensing

We consider the problem of boolean compressed sensing, which is also known as group testing. The goal is to recover a small number of defective items in a large set from a few collective binary tests. This problem can be formulated as a binary linear program, which is NP hard in general. To overcome the computational burden, it was recently proposed to relax the binary constraint on the variables, and apply a rounding to the solution of the relaxed linear program. In this paper, we introduce a randomized algorithm to replace the rounding procedure. We show that the proposed algorithm considerably improves the success rate with only a slight increase in computational cost.