In this paper, we propose a method to embed the color information of an high dimension image in its corresponding grey-level image. The objective of this work is to allow a free and rapid access to the grey-level image and give color image access to secret key owners. This method is made of two steps which are the fast high-dimension color image decomposition (in a grey-level image and its associated color information) and the data-hiding. The two main contributions of this paper are the energy function proposed to model the decomposition of the color image and the fast optimization. The optimization of the proposed energy function leads to the achievement of an index image and a color palette. The good properties of that decomposition are an index image which is similar to the luminance of the color image and a color palette which is well suit for the data-hiding. The obtained results confirm the model quality and the real-time property.