The construction of two dimensional Hilbert Huang transform and its application in image analysis

Hilbert Huang Transform is a new developed method for signal processing especially suitable for non-stationary signal processing. In this paper, we propose a two dimensional Hilbert-Huang Transform based on Bidimensional Empirical Mode Decomposition (BEMD) and quaternionic analytic signal. Bidimensional Empirical Mode Decomposition is adaptive signal decomposition method and its decomposition results are almost monocomponent. Quaternionic analytic signal satisfies most of the two dimensional extension properties and is especially suitable for the monocomponent. In detail, the image is first decomposed to several comoponents by Bidimensional Empirical Mode Decomposition. Then by the Quaternionic analytic method, we get the two dimensional Quaternionic analytic signal. Two dimensional Hilbert spectral characters are got include the instantaneous amplitude, the instantaneous phase, and the instantaneous frequencies. We illustrate the techniques on natural images, and demonstrate the estimated instantaneous frequencies using the needle program. These features inflect the intrinsic characters of image and form the basis for a general theory of image processing.