An orthogonal 16-point approximate discrete cosine transform (DCT) isintroduced. The proposed transform requires neither multiplications norbit-shifting operations. A fast algorithm based on matrix factorization isintroduced, requiring only 44 additions---the lowest arithmetic cost inliterature. To assess the introduced transform, computational complexity,similarity with the exact DCT, and coding performance measures are computed.Classical and state-of-the-art 16-point low-complexity transforms were used ina comparative analysis. In the context of image compression, the proposedapproximation was evaluated via PSNR and SSIM measurements, attaining the bestcost-benefit ratio among the competitors. For video encoding, the proposedapproximation was embedded into a HEVC reference software for direct comparisonwith the original HEVC standard. Physically realized and tested using FPGAhardware, the proposed transform showed 35% and 37% improvements of area-timeand area-time-squared VLSI metrics when compared to the best competingtransform in the literature.
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