  We investigate non-negative least squares (NNLS) for the recovery of sparse
non-negative vectors from noisy linear and biased measurements. We build upon
recent results from [1] showing that for matrices whose row-span intersects the
positive orthant, the nullspace property (NSP) implies compressed sensing
recovery guarantees for NNLS. Such results are as good as for
$\ell_1$-regularized estimators but do not require tuning parameters that
depend on the noise level. A bias in the sensing matrix improves this
auto-regularization feature of NNLS and the NSP then determines the sparse
recovery performance only. We show that NSP holds with high probability for
biased subgaussian matrices and its quality is independent of the bias.
