An Introduction of Chen-Mobius Transform and its Application

摘要

The purpose of this paper is to introduce a new transform, the Chen-Mobius transform, and the application of which in Chen-Mobius communication system and image processing is also presented. To evaluate the application results of the Chen-Mobius transform, simulations are done by the MATLAB software on the computer and the results are discussed in some detail. In the communication system, the discussions of which include the analog and the digital that are quite different from the traditional ones, hence the Chen-Mobius communications are built in. Simulation results show that the new application has excellent performances that signals, whether analog or digital, can be restored from intense noise and outperforms their traditional counterparts. While in the image processing, the idea of modulation and demodulation in communication system is applied to reduce image noise and to prevent the image and the information it contains from being stolen. In the image de-noising, the data is modulated on a modulation wave for some period and recorded by a certain means, then the data can be carried everywhere. To make such a processing, the Chen-Mobius inverse transformed functions act as the "modulation" waveforms and the receiving end is coherently "demodulated" by the often-used digital waveforms. Simulation results show that the application also has excellent performances that the digital image signals can be restored from intense Gaussian noise and well encrypted. To prove the performance of application of the transform, the results are compared with some of the other existent methods or algorithms to some degree. The simulation results and the application indicate that the Chen-Mobius transform can be used in a variety of different areas, especially in the secret and security communication system the hardware realization of which is also expected in the near future.