Two-dimensional analytic signal construction

This paper provides a brief overview of the approaches for two-dimensional analytic signal construction. According to the basis of definition for one-dimensional analytic signal, a set of desirable properties is determined as the guideline to measure a new definition for two-dimensional analytic signal. To appreciate this guideline, several important definitions are brought out, such as total analytic signal, partial analytic signal and Hahn's two-dimensional analytic signal, etc. It is a pity that these definitions cannot satisfy the main properties in the guideline. A chance to solve this problem is provided by the quaternion theory. Based on the Quaternionic Fourier Transform (QFT), a novel definition called quaternionic analytic signal is introduced. This novel definition fulfills most properties in the guideline.