In this paper, we propose an efficient multi-stage algorithm for non-adaptive Group Testing (GT) with general correlated prior statistics. The proposed solution can be applied to any correlated statistical prior represented in trellis, e.g., finite state machines and Markov processes. We introduce a variation of List Viterbi Algorithm (LVA) to enable accurate recovery using much fewer tests than objectives, which efficiently gains from the correlated prior statistics structure. Our numerical results demonstrate that the proposed Multi-Stage GT (MSGT) algorithm can obtain the optimal Maximum A Posteriori (MAP) performance with feasible complexity in practical regimes, such as with COVID-19 and sparse signal recovery applications, and reduce in the scenarios tested the number of pooled tests by at least $25\%$ compared to existing classical low complexity GT algorithms. Moreover, we analytically characterize the complexity of the proposed MSGT algorithm that guarantees its efficiency.

翻译：本文提出了一种高效的用于非自适应分组测试（GT）的多阶段算法，该算法适用于具有一般相关先验统计信息的情况。所提出的解决方案可应用于任何以网格表示的关联统计先验信息，例如有限状态机和马尔可夫过程。我们引入了一种列表维特比算法（LVA）的变体，能够利用比目标所需少得多的测试实现精确恢复，并充分利用相关先验统计信息的结构。数值实验表明，所提出的多阶段分组测试（MSGT）算法能在实际场景（如COVID-19检测和稀疏信号恢复应用）中以可行的复杂度实现最优最大后验（MAP）性能，并在测试场景中将混合检测数量至少减少25%，优于现有经典低复杂度分组测试算法。此外，我们从理论上表征了MSGT算法的复杂度，保证了其高效性。