Inference of signals with unknown correlation structure from non-linear measurements.

We present a method to reconstruct auto-correlated signals together with their auto-correlation structure from non-linear, noisy measurements for arbitrary monotonous non-linearities. In the presented formulation the algorithm provides a significant speedup compared to prior implementations, allowing for a wider range of application. The non-linearity can be used to model instrument characteristics or to enforce properties on the underlying signal, such as positivity. Uncertainties on any posterior quantities can be provided due to independent samples from an approximate posterior distribution. We demonstrate the methods applicability via three examples, using different measurement instruments, non-linearities and dimensionality for both, simulated measurements and real data.