Fast testing can help mitigate the coronavirus disease 2019 (COVID-19) pandemic. Despite their accuracy for single sample analysis, infectious diseases diagnostic tools, like RT-PCR, require substantial resources to test large populations. We develop a scalable approach for determining the viral status of pooled patient samples. Our approach converts group testing to a linear inverse problem, where false positives and negatives are interpreted as generated by a noisy communication channel, and a message passing algorithm estimates the illness status of patients. Numerical results reveal that our approach estimates patient illness using fewer pooled measurements than existing noisy group testing algorithms. Our approach can easily be extended to various applications, including where false negatives must be minimized. Finally, in a Utopian world we would have collaborated with RT-PCR experts; it is difficult to form such connections during a pandemic. We welcome new collaborators to reach out and help improve this work!

中文翻译：

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用于病毒检测的噪声聚合 PCR

快速测试有助于缓解 2019 年冠状病毒病 (COVID-19) 大流行。尽管对单个样本分析具有准确性，但传染病诊断工具（如 RT-PCR）需要大量资源来测试大量人群。我们开发了一种可扩展的方法来确定合并患者样本的病毒状态。我们的方法将组测试转换为线性逆问题，其中误报和否定被解释为由嘈杂的通信渠道产生，并且消息传递算法估计患者的疾病状态。数值结果表明，与现有的嘈杂组测试算法相比，我们的方法使用更少的汇总测量来估计患者的疾病。我们的方法可以很容易地扩展到各种应用，包括必须最小化假阴性的应用。最后，在乌托邦世界中，我们会与 RT-PCR 专家合作；在大流行期间很难形成这种联系。我们欢迎新的合作者伸出援手并帮助改进这项工作！