Design of fast transforms for high-resolution image and video coding

We review design of 4-, 8-, and 16-point transforms currently used in image and video coding standards, and compare them with fast implementations of Discrete Cosine Transform of various other sizes (including non-dyadic even and odd numbers) in the range of 2-64. We show that among such transforms there exist few that offer better complexity/coding gain tradeoffs than current dyadic-sized transforms. In our construction and analysis we utilize an array of known techniques (such as Heideman's mapping between DCT and DFT, Winograd short length DFT modules, prime-factorand common-factor algorithms), and also offer a new factorization scheme for even-sized scaled transforms.

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