In this paper we study the unmixing problem which aims
to separate a set of structured signals from their superposition.
In this paper, we consider the scenario in which
the mixture is observed via nonlinear compressive measurements.
We present a fast, robust, greedy algorithm called
Unmixing Matching Pursuit (UnmixMP) to solve this problem.
We prove rigorously that the algorithm can recover the
constituents from their noisy nonlinear compressive measurements
with arbitrarily small error. We compare our algorithm
to the Demixing with Hard Thresholding (DHT) algorithm
[1], in a number of experiments on synthetic and real data.