A Compressed Sensing Approach to Pooled RT-PCR Testing for COVID-19 Detection

We propose ‘Tapestry’, a single-round pooled testing method with application to COVID-19 testing using quantitative Reverse Transcription Polymerase Chain Reaction (RT-PCR) that can result in shorter testing time and conservation of reagents and testing kits, at clinically acceptable false positive or false negative rates. Tapestry combines ideas from compressed sensing and combinatorial group testing to create a new kind of algorithm that is very effective in deconvoluting pooled tests. Unlike Boolean group testing algorithms, the input is a quantitative readout from each test and the output is a list of viral loads for each sample relative to the pool with the highest viral load. For guaranteed recovery of
$k$
infected samples out of
$n \gg k$
being tested, Tapestry needs only
$O(k \log n)$
tests with high probability, using random binary pooling matrices. However, we propose deterministic binary pooling matrices based on combinatorial design ideas of Kirkman Triple Systems, which balance between good reconstruction properties and matrix sparsity for ease of pooling while requiring fewer tests in practice. This enables large savings using Tapestry at low prevalence rates while maintaining viability at prevalence rates as high as 9.5%. Empirically we find that single-round Tapestry pooling improves over two-round Dorfman pooling by almost a factor of 2 in the number of tests required. We evaluate Tapestry in simulations with synthetic data obtained using a novel noise model for RT-PCR, and validate it in wet lab experiments with oligomers in quantitative RT-PCR assays. Lastly, we describe use-case scenarios for deployment.