  Successful detection of weak signals is a universal challenge for numerous
technical and biological systems and crucially limits signal transduction and
transmission. Stochastic resonance (SR) has been identified to have the
potential to tackle this problem, namely to enable non-linear systems to detect
small, otherwise sub-threshold signals by means of added non-zero noise. This
has been demonstrated within a wide range of systems in physical, technological
and biological contexts. Based on its ubiquitous importance, numerous
theoretical and technical approaches aim at an optimization of signal
transduction based on SR. Several quantities like mutual information,
signal-to-noise-ratio, or the cross-correlation between input stimulus and
resulting detector response have been used to determine optimal noise
intensities for SR. The fundamental shortcoming with all these measures is that
knowledge of the signal to be detected is required to compute them. This
dilemma prevents the use of adaptive SR procedures in any application where the
signal to be detected is unknown. We here show that the autocorrelation
function (AC) of the detector response fundamentally overcomes this drawback.
For a simplified model system, the equivalence of the output AC with the
measures mentioned above is proven analytically. In addition, we test our
approach numerically for a variety of systems comprising different input
signals and different types of detectors. The results indicate a strong
similarity between mutual information and output AC in terms of the optimal
noise intensity for SR. Hence, using the output AC to adaptively vary the
amount of added noise in order to maximize information transmission via SR
might be a fundamental processing principle in nature, in particular within
neural systems which could be implemented in future technical applications.
