Detection of transient events in the presence of background noise.

We describe a method to detect and count transient burstlike signals in the presence of a significant stationary noise. To discriminate a transient signal from the background noise, an optimum threshold is determined using an iterative algorithm that yields the probability distribution of the background noise. Knowledge of the probability distribution of the noise then allows the determination of the number of transient events with a quantifiable error (wrong-positives). We apply the method, which does not rely on the choice of free parameters, to the detection and counting of transient single-molecule fluorescence events in the presence of a strong background noise. The method will be of importance in various ultra sensing applications.