  An orthogonal 16-point approximate discrete cosine transform (DCT) is
introduced. The proposed transform requires neither multiplications nor
bit-shifting operations. A fast algorithm based on matrix factorization is
introduced, requiring only 44 additions---the lowest arithmetic cost in
literature. 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 in
a comparative analysis. In the context of image compression, the proposed
approximation was evaluated via PSNR and SSIM measurements, attaining the best
cost-benefit ratio among the competitors. For video encoding, the proposed
approximation was embedded into a HEVC reference software for direct comparison
with the original HEVC standard. Physically realized and tested using FPGA
hardware, the proposed transform showed 35% and 37% improvements of area-time
and area-time-squared VLSI metrics when compared to the best competing
transform in the literature.
