Copyright © 2012 Linxia Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss the relaxation of the SNR. By defining nonnegative restricted isometry/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and the relaxation share the common unique solution. Besides, we show that any solution to the SNR must be one of the extreme points of the underlying feasible set.