Hardware-friendly DST-VII/DCT-VIII approximations for the Versatile Video Coding Standard

Versatile Video Coding (VVC) is the next generation video coding standard expected by the end of 2020. The new concept of Multiple-Transform Selection (MTS) has been introduced in VVC. MTS enables the VVC encoder to select the transform that minimizes the rate-distortion cost among a set of pre-defined trigonometric transforms including the well known Discrete Cosine Transform (DCT)-II, DCT-VIII and Discrete Sine Transform (DST)-VII. Unlike the DCT-II that has fast computing algorithms, the DST-VII and DCT-VIII rely on more complex matrix multiplication.This paper tackles the problem of DST-VII and DCT-VIII approximations based on the DCT-II and an adjustment stage. This latter consists in a multiplication by a band-matrix with low number of non-zero coefficients per row. The approximation problem is first modeled as a constrained integer optimization problem minimizing both error and orthogonality. The genetic algorithm is then used to solve the optimization problem and find the adjustment band-matrix that minimizes a trade-off between error and orthogonality. The proposed solution enables to preserve the coding gain achieved by the MTS and considerably reduces the complexity in terms of required number of multiplications by coefficient. Moreover, the proposed approach is hardwarefriendly and will provide a lightweight shared hardware module for DST-II, DST-VII and DCT-VIII transforms.