Fast Computation of Integer DCT-V, DCT-VIII, and DST-VII for Video Coding

Joint exploration model (JEM) reference codecs of ISO/IEC and ITU-T utilize multiple types of integer transforms based on DCT and DST of various transform sizes for intraand inter-predictive coding, which has brought a significant improvement in coding efficiency. JEM adopts three types of integer DCTs (DCT-II, DCT-V, and DCT-VIII), and two types of integer DSTs (DST-I and DST-VII). The fast computations of Integer DCT-II and DST-I are well known, but few studies have been performed for the other types such as DCT-V, DCT-VIII, and DST-VII for all transform sizes. In this paper, we present fast computation methods of N-point DCT-V and DCT-VIII. For this, we first decompose the DCT-VIII into a preprocessing matrix, the DST-VII and a post-processing matrix to quickly compute it by using the linear relation between DCT-VIII and DST-VII. Then, we approximate integer kernels of N = 4, 8, 16, and 32 for DCT-V, DCT-VIII, and DST-VII with norm scaling and bit-shift to be compatible with quantization in each stage of multiplications between decomposed matrices for video coding. In various experiments, the proposed fast computation methods have shown to effectively reduce the total complexity of the matrix operations with little loss in BDBR performance. In particular, our methods reduce the number of addition and multiplication operations by 38% and 80.3%, respectively, in average, compared to the original JEM.