Complex diffusion process for noise reduction

Signal de-noising and restoration is an essential step for many signal processing algorithms and applications. One of the most common problems is the removal of some interesting structures in the signal during the restoration process. The capability of methods based on partial differential equations (PDEs) in image restoration and de-noising prompted many researchers to search for an improvement in the technique. In this paper, a new method is presented for signal de-noising, based on PDEs and Schrodinger equations, named as complex diffusion process (CDP). This method assumes that variations on signals are like geometric heat flow, in which heat transfers from a warm environment to a cooler one, until temperatures of the two environments are balanced. In this model, sudden variations in a signal not explained by PDEs are considered as noise. Results of our study show that CDPs are very suitable for signal de-noising. To evaluate the performance of the proposed method, a number of experiments have been performed using Sinusoid, multi-component and FM signals cluttered with noise. The results indicate that the proposed method outperforms the approaches for signal de-noising known in prior art.