An Analytic Transform Kernel Derivation Method for Video Codecs

Abstract

In the standardization of versatile video coding (VVC), discrete cosine transform (DCT)-2, discrete sine transform (DST)-7, and DCT-8 are regarded as the primary transform kernels. However, DST-4 and DCT-4 can also be considered as the transform kernels instead of using DST-7 and DCT-8 owing to their effectiveness in smaller resolution test sequences. To implement these different block size transform kernels, a considerable amount of memory has to be allocated. Moreover, memory consumption to store different block size transform kernels is regarded as a major issue in video coding standardization. To address this problem, a common sparse unified matrix concept is introduced in this study, where any block size transform kernel matrix can be obtained after some mathematical operations. The proposed common sparse unified matrix saves approximately 80% of the static memory by storing only a few transform kernel elements for DCT-2, DST-7, and DCT-8. Full-required transform kernels are derived using the stored transform kernels and generated unit-element matrices and a permutation matrix. The static memory required is only for 1648 elements instead of 8180 elements, each with 8-bit precision. The defined common sparse unified matrix is composed of two parts: a unified DST-3 matrix and a grouped DST-7 matrix. The unified DST-3 matrix is used to derive different points of DCT-2 transform kernels, and the grouped DST-7 matrix is used to derive different points of DST-7 and DCT-8 transform kernels. The new technique of grouping concept is introduced, which shows the relationship between different rows of DST-7 transform kernels with various block sizes. The proposed grouping concept supports the fast algorithm of DST-7 by implementing the proposed method of the “one group one feature” principle. The simulation was conducted using the VTM-3.0 reference software under common test conditions. The simulation result of the all intra (AI) configuration is Y = 0.00%, U = −0.02%, V = 0.00% with an encoding time of 100%, and a decoding time of 100%. Similarly, the simulation results of random access (RA) configuration are Y = −0.01%, U = 0.09%, V = 0.06%, and the encoding and decoding times are 101% and 100%, respectively. The simulation result of the low delay B (LDB) configuration is Y = 0.01%, U = 0.08%, and V = −0.27%, for encoding and decoding times of 101% and 100%, respectively.