  We propose a method of reduction of experimental noise in single-pixel
imaging by expressing the subsets of sampling patterns as linear combinations
of vertices of a multidimensional regular simplex. This method may be also
directly extended to complementary sampling. The modified sampling consists
only of non-negative patterns. The measurement becomes theoretically
independent of the ambient illumination, and in practice becomes more robust to
the varying conditions of the experiment. We show how the optimal
dimensionality of the simplex depends on the level of measurement noise. We
present experimental results of single-pixel imaging using binarized sampling
and a real-time reconstruction with the Fourier domain regularized inversion
method.
