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.

中文翻译：

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基于混合 RT-qPCR 的 Covid-19 筛查的恢复算法


我们使用非线性模型的定量测量来考虑非自适应池测试设置中的稀疏信号恢复问题。定量测量是使用逆转录（定量）聚合酶链反应（RT-qPCR）测试获得的，这是用于检测 Covid-19 的标准测试。每个定量测量均指循环阈值，它代表测试样本中的病毒载量。我们提出了两种基于乘法器交替方向方法和块坐标下降的新颖、鲁棒的恢复算法，以恢复个体样本周期阈值，从而在给定池样本周期阈值和池矩阵的情况下确定患病个体。我们对归一化均方误差、假阳性率、假阴性率以及无差错恢复可能达到的最大稀疏度进行数值评估。我们还使用 Covid-19 测试的公开数据证明了在非自适应池测试方法中使用定量测量（相对于二元结果）的优势，即测试率。仿真结果表明了所提算法的有效性。