Compressed sensing-based SARS-CoV-2 pool testing

TL;DR

This paper introduces a compressed sensing-based method for SARS-CoV-2 pool testing that is non-adaptive, noise-robust, and reduces the number of tests needed, offering faster and more efficient detection during pandemics.

Contribution

It presents a novel non-adaptive, noise-robust compressed sensing approach with a tuning-free algorithm for efficient large-scale COVID-19 testing.

Findings

Achieves the same number of tests as current methods but with higher empirical performance.

Significantly reduces the number of tests needed compared to traditional group testing.

Demonstrates potential for error correction in sparse error scenarios.

Abstract

We propose a compressed sensing-based testing approach with a practical measurement design and a tuning-free and noise-robust algorithm for detecting infected persons. Compressed sensing results can be used to provably detect a small number of infected persons among a possibly large number of people. There are several advantages of this method compared to classical group testing. Firstly, it is non-adaptive and thus possibly faster to perform than adaptive methods which is crucial in exponentially growing pandemic phases. Secondly, due to nonnegativity of measurements and an appropriate noise model, the compressed sensing problem can be solved with the non-negative least absolute deviation regression (NNLAD) algorithm. This convex tuning-free program requires the same number of tests as current state of the art group testing methods. Empirically it performs significantly better than theoretically guaranteed, and thus the high-throughput, reducing the number of tests to a fraction compared to other methods. Further, numerical evidence suggests that our method can correct sparsely occurring errors.