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Group testing is a technique which avoids individually testing $n$ samplesfor a rare disease and instead tests $n < p$ pools, where a pool consists of amixture of small, equal portions of a subset of the $p$ samples. Group testingsaves testing time and resources in many applications, including RT-PCR, withguarantees for the recovery of the status of the $p$ samples from results on$n$ pools. The noise in quantitative RT- PCR is inherently known to follow amultiplicative data-dependent model. In recent literature, the correspondinglinear systems for inferring the health status of $p$ samples from results on$n$ pools have been solved using the Lasso estimator and its variants, whichhave been typically used in additive Gaussian noise settings. There is noexisting literature which establishes performance bounds for Lasso for themultiplicative noise model associated with RT-PCR. After noting that a recentgeneral technique, Hunt et al., works for Poisson inverse problems, we adapt itto handle sparse signal reconstruction from compressive measurements withmultiplicative noise: we present high probability performance bounds anddata-dependent weights for the Lasso and its weighted version. We also shownumerical results on simulated pooled RT-PCR data to empirically validate ourbounds.

Performance Bounds for LASSO under Multiplicative Noise: Applications to Pooled RT-PCR Testing