Design of Fast Transforms for High-Resolution Image and Video Coding

We study factorization techniques and performance of Discrete Cosine Transforms of various sizes (including nondyadic and odd numbers). In our construction we utilize an array of known techniques (such as Heideman's mapping between odd-sized DCT and DFT, Winograd fast DFT algorithms, prime-factoring, etc), and also propose a new decimation strategy for construction of even-sized scaled transforms. We then analyze complexity and coding gain of such transforms with sizes 2-64 and identify ones that show best complexity/performance tradeoffs.