Two Dimensional Hilbert Spectral Characters Analysis Based on Bi-orthant Analytic Signal

Abstract

Two dimensional Hilbert spectral characters (2DHSC) are important part of two dimensional Hilbert-Huang Transform. In this paper, we propose a two dimensional Hilbert spectral analysis method based on Bi-orthant analytic signal. Bi-orthant analytic signal is based on a new proposed two dimensional Hilbert Transform-Bi-orthant Hilbert Transform, which satisfies most of the two dimensional extension properties and is especially suitable for the monocomponent. Definitely, the image is first decomposed by Bidimensional Empirical Mode Decomposition (BEMD). Then using the Bi-orthant Hilbert Transform, we get the two dimensional Bi-orthant analytic signal. Two dimensional Hilbert spectral characters are got include the instantaneous amplitude, the instantaneous phase, and the instantaneous frequencies. We demonstrate the techniques on both synthetic and natural images, and depict the estimated frequencies using the needle program. These features reflect the intrinsic characters of image and form the basis for a general theory of image processing in the modulation domain.