Recovery Algorithms for Pooled RT-qPCR Based Covid-19 Screening

We consider the problem of sparse signal recovery in a non-adaptive pool-test setting using quantitative measurements from a non-linear model. The quantitative measurements are obtained using the reverse transcription (quantitative) polymerase chain reaction (RT-qPCR) test, which is the standard test used to detect Covid-19. Each quantitative measurement refers to the cycle threshold, a proxy for the viral load in the test sample. We propose two novel, robust recovery algorithms based on alternating direction method of multipliers and block coordinate descent to recover the individual sample cycle thresholds and hence determine the sick individuals, given the pooled sample cycle thresholds and the pooling matrix. We numerically evaluate the normalized mean squared error, false positive rate, false negative rate, and the maximum sparsity levels up to which error-free recovery is possible. We also demonstrate the advantage of using quantitative measurements (as opposed to binary outcomes) in non-adaptive pool testing methods in terms of the testing rate using publicly available data on Covid-19 testing. The simulation results show the effectiveness of the proposed algorithms.