Abstract: Directional decompositions of the Contourlet transform do not take into account the characteristics of the image itself and the number of directional decompositions in each high-frequency sub-band is fixed. To address these problems, we take entropy as the criterion for describing image texture/edge characteristics of high-frequency sub-bands in order to achieve optimal directional decomposition with Contourlet. After the wavelet transform, complete directional decomposition is carried out for each of the image's high-frequency sub-bands, and the sub-bands are then analyzed with respect to their changing entropy for different directional decompositions. The optimal number of directional decompositions can be determined using the minimum entropy principle. Next, we combined this optimal Contourlet directional decomposition method with the SPECK image-coding algorithm, wherein each sub-band is assigned a different weight according to its visual sensitivity band-pass characteristics, such that visually important information can be transmitted in advance. The experimental results show that the peak signal-to-noise ratio of the reconstructed image is significantly improved, and the distortion of local texture is effectively reduced.