Correction of Pooling Matrix Mis-specifications in Compressed Sensing Based Group Testing

2026-01-20

AI Summary

This work addresses the challenge of model mismatch in compressed sensing-based group testing, where experimental errors often lead to inaccuracies in the pooling matrix, thereby degrading the reliability of individual health status inference. To tackle this issue, the paper proposes a novel algorithm that jointly corrects pooling matrix errors and reconstructs the underlying sparse signal directly from noisy test outcomes and an inaccurate pooling matrix. Notably, this is the first method within the compressed sensing framework to explicitly account for and correct pooling matrix mismatches, accompanied by theoretical guarantees for both error correction and signal recovery. Extensive numerical experiments demonstrate that the proposed algorithm consistently achieves high accuracy and robustness across a variety of practical scenarios.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

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.

Problem

• compressed sensing
• group testing
• pooling matrix
• model mismatch errors
• sparse signal reconstruction

Innovation

• model mismatch errors
• compressed sensing
• group testing
• pooling matrix correction
• sparse signal reconstruction