Image decomposition and texture analysis via combined bi‐dimensional Bedrosian's principles.

Image decomposition is an important issue in image processing. The existing approaches including the bi‐dimensional empirical mode decomposition (BEMD) still fail to separate monocomponents in multicomponents in many cases. To solve this problem, this study proposes a new image decomposition method based on the new derived combined bi‐dimensional Bedrosian's principle that has not been reported anywhere else for image processing. First, this study investigates a few bi‐dimensional Bedrosian's principles according to the bi‐dimensional Hilbert transforms. Second, based on the derived bi‐dimensional Bedrosian's principles and the original multicomponents, the authors provide the combined bi‐dimensional Bedrosian's principle and the assisted components obtained through projections via optimisation so that these monocomponents in multicomponents can be separated in the case that the existing methods fail. Third, an iterative image decomposition method is proposed via the above principles to decompose the multicomponent image into true monocomponents. The proposed method can solve the problems caused by the cross‐angle and amplitude ratio and frequency ratio between these components that BEMD fails to solve. Also, the phase and amplitude are estimated for texture analysis after the decomposition is demonstrated. Experiments are shown to support the proposed methods. [ABSTRACT FROM AUTHOR]