Non-adaptive pooling strategies for detection of rare faulty items

TL;DR

This paper investigates non-adaptive pooling strategies for efficiently detecting rare faulty items, demonstrating that sparse binary matrices with minimal measurements can be constructed using random spatially coupled designs, applicable in genetic screening.

Contribution

The paper introduces a novel random spatially coupled design for sparse binary pooling matrices that minimizes measurements needed for signal reconstruction.

Findings

Low measurement count achievable with spatially coupled design

Robustness of the design against matrix element errors

Potential applications in genetic screening and genotyping

Abstract

We study non-adaptive pooling strategies for detection of rare faulty items. Given a binary sparse N-dimensional signal x, how to construct a sparse binary MxN pooling matrix F such that the signal can be reconstructed from the smallest possible number M of measurements y=Fx? We show that a very low number of measurements is possible for random spatially coupled design of pools F. Our design might find application in genetic screening or compressed genotyping. We show that our results are robust with respect to the uncertainty in the matrix F when some elements are mistaken.