Multiple-Parameter Discrete Fractional Transform and its Applications

In recent years, several special multiple-parameter discrete fractional transforms (MPDFRTs) have been proposed, and their advantages have been demonstrated in the fields of communication systems and information security. However, the general theoretical framework of MPDFRTs has not yet been established. In this paper, we propose two separate theoretical frameworks called the type I and II MPDFRT that can include existing multiple-parameter transforms as special cases. The properties of the type I and II MPDFRT have been analyzed in detail and their high-dimensional operators have been defined. Under the theoretical frameworks, we can construct new types of transforms that may be useful in signal processing and information security. Finally, we perform two applications about image encryption and image feature extraction in the type I and II MPDFRT domain. The simulation results demonstrate that the typical transforms constructed under the proposed theoretical frameworks yield promising results in these applications.