Image decomposition is an important issue in image processing all along. How to obtain the true monocomponents in multicomponents is still an open question in images by far, which is of much importance to image understanding, analysis and further applications. The existent approaches including the bi-dimensional empirical mode decomposition (BEMD) still fail to separate the monocomponents in multicomponents in many cases. To solve this question, this paper proposes a new image decomposition method based on new derived combined bi-dimensional Bedrosians principle that has not been reported anywhere else for image processing. First, this paper investigates a few bi-dimensional Bedrosians principles according to the bi-dimensional Hilbert transforms . Second, based on the derived bi-dimensional Bedrosians principles and the original multieomponents, we provide the combined bi-dimensional Bedrosians principle and the assisted components obtained through multiple projections in bi-dimensional Fourier transform domains via optimization so that these monocomponents in multicomponents can be separated in the case that the existent 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 and so on between these components that BEMD fails to solve. Also, that the phase and amplitude are estimated for texture analysis after the decomposition is demonstrated. Experiments on composite and real-world textures including support the proposed methods.