Simple denoising algorithm using wavelet transform

We have presented a new and alternative algorithm for noise reduction using a discrete wavelet transform. We believe that the algorithm will be beneficial in various noise-reduction applications, and that it shows promise in developing techniques that can resolve an observed signal into its various intrinsic components. In the method the threshold for reducing noise comes out automatically. The algorithm has been applied to three model flow systems - the Lorenz, Autocatalator, and Rossler systems - all evolving chaotically. The method is seen to work quite well for a wide range of noise strengths, even as large as 10% of the signal level. We have also applied the method successfully to noisy time series data obtained from the measurement of pressure fluctuations in a fluidized bed, and also to that obtained by conductivity measurement in a liquid-surfactant experiment. In all the illustrations we have been able to observe that there is a clean separation in the frequencies covered by the differentiated signal and white noise. However, if the noise is colored, a certain degree of overlap between the signal and noise may exist, even after differentiation. The method needs to be improved upon for this complex situation.