In Signal Processing and Communication, Signals are usually contaminated with noise. It is therefore important to remove noise and keep some original features of the signal such as carrier signals and discontinuities separating some portions of a signal. In this research, I have developed a method based on anisotropic diffusions to remove noise and preserve carrier signals and discontinuities in noisy signals. Some intermediate results of our iterative method are shown as a movie in this clip for a signal with one carrier frequency.
Our approach has also been extended for signals with any number of carrier signals. The following figure also shows the end result of our algorithm removing noise from a signal with two carrier signals by keeping both carrier signals and all discontinuities.