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：本文提出了一种针对具有一般相关先验统计的非自适应群组检测(GT)的高效多阶段算法。所提出的解决方案可应用于任何以网格图表示的相关统计先验，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，使其能够使用远少于目标数量的测试实现精确恢复，从而有效地利用相关先验统计结构。数值结果表明，所提出的多阶段群组检测(MSGT)算法能够在实际应用场景（如COVID-19检测和稀疏信号恢复）中以可行的复杂度获得最优的最大后验概率(MAP)性能，并且在测试场景中，与现有经典低复杂度GT算法相比，将合并测试的数量减少了至少$25\%$。此外，我们通过分析刻画了所提MSGT算法的复杂度，从而保证了其高效性。