Robust Recovery of Sparse Support in Constrained Group Testing

Abstract

In the early stage of a pandemic, rapidly identifying a small number of infected individuals through large-scale screening is critical for pandemic control. Group testing has been widely used to improve testing efficiency and numerous studies have investigated the problem under noisy measurements, typically modeled as bit-flipping of test outcomes. However, these methods do not consider the constraints imposed by dilution, pool size, and the limit of detection (LOD), which can lead to false negatives when the viral load in a pool falls below the LOD. In addition, liquid dispensing errors, common in laboratory settings, affects diluted viral loads in a nonlinear manner. In this work, we introduce a novel measurement model that characterizes the process of sample pooling and dilution, incorporating LOD-induced binary quantization as well as liquid dispensing errors. For the case with known sparsity level, we propose a low-complexity decoding algorithm and provide theoretical guarantees for exact support recovery under both noiseless and noisy settings. For the case with unknown sparsity level, we develop a blind support recovery algorithm, along with a heuristic variant to enhance robustness, which can achieve exact support recovery with only O(klogn) measurements. Extensive simulations show that the proposed algorithms outperform existing combinatorial group testing algorithms, validating the effectiveness, efficiency and robustness in large-scale screening.