Forward-backward non-linear filtering technique for extracting small biological signals from noise

A novel and computationally efficient, non-linear signal processing technique for reducing background noise to reveal small biological signals is described. The signal estimate is formed by weighting the outputs of a set of causal (forward) and anti-causal (backward) predictors. The weights used to combine the predictors are adaptively determined at each data point to reflect the performance of the respective predictor within a short analysis window. The method is specifically designed for revealing fast transient signals dominated by noise, such as single-channel or post-synaptic currents. Markovian and exponentially decaying signals embedded in the amplifier noise were extracted using this method and compared with the original signals. The results of such simulations demonstrate the advantage of this non-linear method over low-pass filtering. Brief pulses imbedded in a broad-band amplifier noise can be reliably recovered using our non-linear filtering technique. Moreover, the kinetics of a single channel and the time constant of exponentially decaying signals can be measured with acceptable accuracy even when the signals are dominated by noise.