A butterfly structured design of the hybrid transform coding scheme

The hybrid transform coding scheme that alternates amongst the asymmetric discrete sine transform (ADST) and the discrete cosine transform (DCT) depending on the boundary prediction conditions, is an efficient tool for video and image compression. It optimally exploits the statistical characteristics of prediction residual, thereby achieving significant coding performance gains over the conventional DCT-based approach. A practical concern lies in the intrinsic conflict between transform kernels of ADST and DCT, which prevents a butterfly structured implementation for parallel computing. Hence the hybrid transform coding scheme has to rely on matrix multiplication, which presents a speed-up barrier due to under-utilization of the hardware, especially for larger block sizes. In this work, we devise a novel ADST-like transform whose kernel is consistent with that of DCT, thereby enabling butterfly structured computation flow, while largely retaining the performance advantages of hybrid transform coding scheme in terms of compression efficiency. A prototype implementation of the proposed butterfly structured hybrid transform coding scheme is available in the VP9 codec repository.