Recovery of Noisy Pooled Tests via Learned Factor Graphs with Application to COVID-19 Testing

The ongoing pandemic and the necessity of frequent testing have spurred a growing interest in pooled testing. Conventional recovery methods from pooled tests are based on group testing or compressed sensing tools which rely on simplistic modeling of the pooling process, and may not be reliable in the presence of complex and noisy measurement procedures and highly infected populations. In this work, we propose a strategy for pooled testing designed for noisy settings, which bypasses the need for a tractable acquisition model. This is achieved by combining deep learning, for implicitly learning the measurement relationship from data, with factor graph inference, which exploits the structured known pooling pattern. Learned factor graphs provide a quantitative readout corresponding to the infection severity, as opposed to group testing which only detects the presence of infection. The proposed scheme is shown to achieve improved robustness to noise compared with previous approaches and to reliably estimate in highly infected populations.