  In this paper we consider the problem of linear unmixing hidden random
variables defined over the simplex with additive Gaussian noise, also known as
probabilistic simplex component analysis (PRISM). Previous solutions to tackle
this challenging problem were based on geometrical approaches or
computationally intensive variational methods. In contrast, we propose a
conventional expectation maximization (EM) algorithm which embeds importance
sampling. For this purpose, the proposal distribution is chosen as a simple
surrogate distribution of the target posterior that is guaranteed to lie in the
simplex. This distribution is based on the Gaussian linear minimum mean squared
error (LMMSE) approximation which is accurate at high signal-to-noise ratio.
Numerical experiments in different settings demonstrate the advantages of this
adaptive surrogate over state-of-the-art methods.
