Inference of signals with unknown correlation structure from nonlinear measurements

Abstract: We present a method to reconstruct autocorrelated signals together with their autocorrelation structure from nonlinear, noisy measurements for arbitrary monotonous nonlinear instrument response. In the presented formulation the algorithm provides a significant speedup compared to prior implementations, allowing for a wider range of application. The nonlinearity 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 simulated and real measurements, using different measurement instruments, nonlinearities and dimensionality.