Generalized amplitude-phase demodulation for isotropic image decomposition and analysis

It is well known that the amplitude-phase demodulation based on Hilbert transform (HT) plays a fundamental role in signal processing. Also, the Bedrosian principle (BP), the key to HT, determines the exponential form of the complex signals out of real ones. In this paper, the novel BP on 2D HT was proposed in details. At first, a few 2D BPs would be revisited with some new interpretation for 2D time-frequency analysis. Then the new generalized BP (GBP) with new spirit of Riesz transform (RT) were derived with novel features. On one hand, various BPs would be employed jointly for image pattern analysis via our particular design. On the other hand, various π/2 phase shifting operations for the multiplicative signal would be systematically performed in 2D images through BPs so that we could obtain more rational image features. Furthermore, the amplitude-phase demodulation method based on GBP for the isotropic image decomposition would be presented as well. The theoretical analysis and comparison experiments on composite and natural images have been presented to demonstrate the efficiency of our contributions in time-frequency analysis and pattern recognition along with feature extraction.