A noise reduction method for chaotic signals

An iterative method for reducing noise in contaminated chaotic signals is proposed. This method estimates the deviation of the observed signal from the nearest noise-free signal satisfying the system dynamics in order to get a noise-reduced (or enhanced) signal. To calculate the deviation we minimize a cost function composed of two parts: one containing information that represents how close the enhanced signal is to the observed signal and another including constraints that fit the dynamics of the system. This method has a simple structure and is flexible in the choice of the parts of the cost function. The proposed method is compared with Farmer's method which is known to have good performance in mild signal-to-noise ratios but has a more complex structure.