  In this paper, we derive mutual information based upper and lower bounds on
the number of nonadaptive group tests required to identify a given number of
"non defective" items from a large population containing a small number of
"defective" items. We show that a reduction in the number of tests is
achievable compared to the approach of first identifying all the defective
items and then picking the required number of non-defective items from the
complement set. In the asymptotic regime with the population size $N
\rightarrow \infty$, to identify $L$ non-defective items out of a population
containing $K$ defective items, when the tests are reliable, our results show
that $\frac{C_s K}{1-o(1)} (\Phi(\alpha_0, \beta_0) + o(1))$ measurements are
sufficient, where $C_s$ is a constant independent of $N, K$ and $L$, and
$\Phi(\alpha_0, \beta_0)$ is a bounded function of $\alpha_0 \triangleq
\lim_{N\rightarrow \infty} \frac{L}{N-K}$ and $\beta_0 \triangleq
\lim_{N\rightarrow \infty} \frac{K} {N-K}$. Further, in the nonadaptive group
testing setup, we obtain rigorous upper and lower bounds on the number of tests
under both dilution and additive noise models. Our results are derived using a
general sparse signal model, by virtue of which, they are also applicable to
other important sparse signal based applications such as compressive sensing.
