Fast DST-VII/DCT-VIII With Dual Implementation Support for Versatile Video Coding

The Joint Video Exploration Team (JVET) recently launched the standardization of the next-generation video coding named Versatile Video Coding (VVC) with the inherited technical framework from its predecessor High-Efficiency Video Coding (HEVC). The simplified Enhanced Multiple Transform (EMT) has been adopted as the primary residual coding transform solution, termed Multiple Transform Selection (MTS). In MTS, only the transform set consisting of DST-VII and DCT-VIII remains, excluding the other transform sets and the dependency on intra prediction modes. Significant coding gains are achieved by introducing new DST/DCT transforms, but the full matrix implementation is relatively costly compared to partial butterfly in terms of both software run-time and operation counts. In this work, we exploit the inherent features existing in DST-VII and DCT-VIII. Instead of repeating the element-wise additions and multiplications in full matrix operation, these features can be leveraged to achieve more efficient implementations which only use partial elements to derive the identical results. Existing transform matrices are further tuned to utilize these (anti-)symmetric features. A partial butterfly-type fast algorithm with dual-implementation support is proposed for DST-VII/DCT-VIII transform in VVC. Complexity analysis including operation counts and software run-time are conducted to validate the effectiveness. In addition, we prove the features are perfectly supported by theory. The proposed fast methods achieve noticeable software run-time savings without compromising on coding performance by comparing with the VVC Test Model VTM-3.0. It is shown that under Common Test Condition (CTC) with inter MTS enabled, an average of 9%, 0%, and 3% decoding time savings are achieved for All Intra (AI), Random Access (RA) and Low Delay B (LDB), respectively. Under low QP test condition with inter MTS enabled, the proposed fast methods achieve 1%, 2% and 4% decoding time savings on average for AI, RA, and LDB, respectively.