Down-sampling in DCT domain using linear transform with double-sided multiplication for image/video transcoding

This paper proposes a designing framework for downsampling compressed images/video frames with arbitrary ratio in the discrete cosine transform (DCT) domain. We first derive a set of DCT-domain down-sampling methods which can be represented by a linear transform with double-sided matrix multiplication (LTDS) in the DCT domain, and show that the set contains a wide range of methods with various complexity and visual quality. Then, based on a pre-selected spatial- domain method, we formulate an optimization problem for finding an LTDS to approximate the given spatial domain method for achieving the best trade-off between the visual quality and the complexity. By selecting a spatial-domain reference method with the popular Butterworth lowpass filtering and bicubic interpolation, the proposed framework discovers LTDSs with better visual quality and lower computational complexity as saving 20%~70% execution time when compared with state-of-the-art methods in the literature.