A Preliminary Case for Hirschman Transform Video Coding

The use of Hirschman transforms for video coding has not been considered previously, primarily due to the lack of any previous construction of a real-valued Hirschman transform. In this paper, we introduce a new 2D separable 8×8 Hirschman transform that, for the first time, is inherently real and integer-valued. We apply this new transform to perform block-based video coding. Our preliminary results on the well-known Foreman sequence show significantly superior coefficient quantization performance relative to both the 2D DCT and the H.264 8×8 integer transform. We also study the energy compaction characteristics of the new transform. Preliminary results indicate that, in contrast to the DCT, the Hirschman transform coefficients tend to cluster around a few integer values on average, suggesting that m-ary run-length coding may provide a particularly efficient encoding after quantization of the Hirschman transform coefficients.