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It is well known that the implementation of Tchebichef transforms (TT) does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. Therefore, it can be effectively used in the analysis of images processing area. However, the direct computation of discrete orthogonal TT is very expensive. In this study, we introduce a new framework for TT based on the discrete Tchebichef polynomials and develop a new block-based directional Tchebichef transforms (BDTT) to compensate for the defects of the direct computation TT in the application of image description. Moreover, this new algorithm is integrated into the compressed sensing (CS). By choosing the best directional mode of TT, the proposed methods simultaneous realizes sampling, compression of image, and better image description. Several numerical experiments demonstrate that the proposed algorithm has better performance than the conventional methods.