The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The DTT transform kernel does not depend on the input data and fast algorithms can be developed to real-time applications. However, the DTT fast algorithm presented in literature possess high computational complexity. In this paper, we introduce a new low-complexity approximation for the DTT. The fast algorithm of the proposed transform is multiplication free and requires a reduced number of additions and bit-shifting operations. Image and video compression simulations in popular standards show good performance of the proposed transform. Regarding hardware resource consumption for FPGA shows a 43.1 reduction in configurable logic blocks and ASIC place and route realization shows a 57.7 reduction in the area-time figure compared with the 2D version of the exact DTT.
@cite_69: In this letter, we introduce a low-complexity approximation for the discrete Tchebichef transform (DTT). The proposed forward and inverse transforms are multiplication-free and require a reduced number of additions and bit-shifting operations. Numerical compression simulations demonstrate the efficiency of the proposed transform for image and video coding. Furthermore, Xilinx Virtex-6 FPGA based hardware realization shows 44.9 reduction in dynamic power consumption and 64.7 lower area when compared to the literature.
To the best of our knowledge, the only DTT approximation archived in literature was proposed in @cite_69 . That approximation was obtained by means of a parameterization of integer functions combined with a normalization of transformation matrix columns. The derived approximation in @cite_69 furnishes good coding capabilities, but it lacks orthogonality or near-orthogonality properties. As a consequence, the forward and inverse transformations are quite distinct and possess unbalanced computational complexities.