Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms. The DCT is employed in a multitude of compression standards due to its remarkable energy compaction properties. Multiplier-free approximate DCT transforms have been proposed that offer superior compression performance at very low circuit complexity. Such approximations can be realized in digital VLSI hardware using additions and subtractions only, leading to significant reductions in chip area and power consumption compared to conventional DCTs and integer transforms. In this paper, we introduce a novel 8-point DCT approximation that requires only 14 addition operations and no multiplications. The proposed transform possesses low computational complexity and is compared to state-of-the-art DCT approximations in terms of both algorithm complexity and peak signal-to-noise ratio. The proposed DCT approximation is a candidate for reconfigurable video standards such as HEVC. The proposed transform and several other DCT approximations are mapped to systolic-array digital architectures and physically realized as digital prototype circuits using FPGA technology and mapped to 45 nm CMOS technology.

In this paper, 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.

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A low-complexity orthogonal multiplierless approximation for the 16-point discrete cosine transform (DCT) was introduced. The proposed method was designed to possess a very low computational cost. A fast algorithm based on matrix factorization was proposed requiring only 60 additions. The proposed architecture outperforms classical and state-of-the-art algorithms when assessed as a tool for image and video compression. Digital VLSI hardware implementations were also proposed being physically realized in FPGA technology and implemented in 45 nm up to synthesis and place-route levels. Additionally, the proposed method was embedded into a high efficiency video coding (HEVC) reference software for actual proof-of-concept. Obtained results show negligible video degradation when compared to Chen DCT algorithm in HEVC. standards, such as JPEG [10], MPEG-1 [11], MPEG-2 [12], H.261 [13], H.263 [14], and H.264 [15].Moreover, numerous fast algorithms were proposed for its computation [16][17][18][19][20][21][22].Designing fast algorithms for the DCT is a mature area of research [17,[23][24][25]; thus it is not realistic to expect major advances by means of standards techniques. On the other hand, the development of low-complexity approximations for DCT is an open field of research. In particular, the 8-point DCT was given several approximations, such as the signed DCT [26], the level 1 DCT approximation [27], the Bouguezel-Ahmad-Swamy (BAS) series of transforms [4,5,7,28,29], the rounded DCT (RDCT) [8], the modified RDCT [30], the multiplier-free DCT approximation for RF imaging [31], and the improved approximate DCT proposed in [9]. Such approximations reduce the computational demands of the DCT evaluation, leading to low-power consumption and highspeed hardware realizations [9]. At the same time, approximate transforms can provide adequate numerical accuracy for image and video processing.

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 work, 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 shows good performance of the proposed transform. Regarding hardware resource consumption for FPGA shows 43.1% reduction of configurable logic blocks and ASIC place and route realization shows 57.7% reduction in the area-time figure when compared with the 2-D version of the exact DTT. KeywordsApproximate transforms, discrete Tchebichef transform, fast algorithms, image and video coding * Paulo A. M. Oliveira is with the Signal Processing Group,