Theoretical Bounds for Group Testing

COVID-19 Group Testing relies on the principle of Sparse Recovery via L1 optimization (or its variants). For Additive Gaussian Noise, theoretical bounds exist on the error of the recovered vector. However, the RT-PCR process involved in Group Testing leads to Multiplicative Gaussian Noise, for which no bounds exist. My team and I developed theoretical guarantees for acceptable error margins under this setting, with mild assumptions on the number of infected people in the sample. Our paper is up on arXiv.