Compressed sensing, which involves the reconstruction of sparse signals from an under-determined linear system, has been recently used to solve problems in group testing. In a public health context, group testing aims to determine the health status values of p subjects from n<<p pooled tests, where a pool is defined as a mixture of small, equal-volume portions of the samples of a subset of subjects. This approach saves on the number of tests administered in pandemics or other resource-constrained scenarios. In practical group testing in time-constrained situations, a technician can inadvertently make a small number of errors during pool preparation, which leads to errors in the pooling matrix, which we term `model mismatch errors' (MMEs). This poses difficulties while determining health status values of the participating subjects from the results on n<<p pooled tests. In this paper, we present an algorithm to correct the MMEs in the pooled tests directly from the pooled results and the available (inaccurate) pooling matrix. Our approach then reconstructs the signal vector from the corrected pooling matrix, in order to determine the health status of the subjects. We further provide theoretical guarantees for the correction of the MMEs and the reconstruction error from the corrected pooling matrix. We also provide several supporting numerical results.

翻译：压缩感知涉及从欠定线性系统中重建稀疏信号，最近已被用于解决群体检测问题。在公共卫生背景下，群体检测旨在通过n<<p次池化测试确定p个受试者的健康状况值，其中池化定义为将部分受试者样本的等体积微量混合物。这种方法在疫情或其他资源受限场景中可显著减少检测次数。在时间紧迫的实际群体检测中，技术人员可能在池化制备过程中无意产生少量误差，导致池化矩阵出现错误，我们称之为"模型失配误差"(MMEs)。这给从n<<p次池化测试结果中确定受试者健康状况值带来了困难。本文提出一种算法，可直接根据池化测试结果和现有（不精确的）池化矩阵来校正池化测试中的MMEs。随后通过校正后的池化矩阵重建信号向量，从而确定受试者的健康状况。我们进一步为MMEs的校正及基于校正后池化矩阵的重建误差提供了理论保证，并提供了若干支持性数值结果。