Pe'er, I.
(Ed.)

Combinatorial group testing and compressed sensing both focus on recovering a sparse vector of dimensionality n from a much smaller number 𝑚<𝑛 of measurements. In the first approach, the problem is defined over the Boolean field – the goal is to recover a Boolean vector and measurements are Boolean; in the second approach, the unknown vector and the measurements are over the reals. Here, we focus on real-valued group testing setting that more closely fits modern testing protocols relying on quantitative measurements, such as qPCR, where the goal is recovery of a sparse, Boolean vector and the pooling matrix needs to be Boolean and sparse, but the unknown input signal vector and the measurement outcomes are nonnegative reals, and the matrix algebra implied in the test protocol is over the reals. With the recent renewed interest in group testing, focus has been on quantitative measurements resulting from qPCR, but the method proposed for sample pooling were based on matrices designed with Boolean measurements in mind. Here, we investigate constructing pooling matrices dedicated for the real-valued group testing. We provide conditions for pooling matrices to guarantee unambiguous decoding of positives in this setting. We also show a deterministic algorithm for constructingmore »