约束组检测中稀疏支持集的鲁棒恢复
Robust Recovery of Sparse Support in Constrained Group Testing
- College of Control Science and Engineering, Zhejiang University（浙江大学控制科学与工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对组检测中稀释和检测限导致的假阴性问题，提出新测量模型及低复杂度解码和盲支持恢复算法，实现稀疏支持集的鲁棒精确恢复。
AI中文摘要：
在疫情初期，通过大规模筛查快速识别少量感染者对疫情防控至关重要。组检测已被广泛用于提高检测效率，大量研究在噪声测量下（通常建模为检测结果的比特翻转）探讨了该问题。然而，这些方法未考虑稀释、池大小和检测限（LOD）带来的约束，当池中的病毒载量低于LOD时可能导致假阴性。此外，实验室中常见的液体分液误差会以非线性方式影响稀释后的病毒载量。在本工作中，我们引入了一种新颖的测量模型，刻画了样本合并与稀释过程，包含LOD引起的二元量化以及液体分液误差。对于稀疏度已知的情况，我们提出了一种低复杂度解码算法，并在无噪声和有噪声设置下提供了精确支持集恢复的理论保证。对于稀疏度未知的情况，我们开发了一种盲支持恢复算法，并辅以启发式变体以增强鲁棒性，该算法仅需O(klogn)次测量即可实现精确支持集恢复。大量仿真表明，所提出的算法优于现有的组合组检测算法，验证了其在大规模筛查中的有效性、效率和鲁棒性。
英文摘要：
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.
