Mathematical Relation between APBT-Based and DCT-Based JPEG Image Compression Schemes

—A novel linear transform, called All Phase Biorthogonal Transform (APBT), was generated from All Phase Digital Filter (APDF) theory. APBT can be used in image compression instead of the conventional Discrete Cosine Transform (DCT), and the corresponding image compression scheme is called APBT-based JPEG (APBT-JPEG) which can achieve better coding performance, especially at low bit rates. With in-depth mathematical analysis on the emerging APBTJPEG and conventional DCT-based JPEG (DCT-JPEG), we bring forward a unique insight into the relation between them. The relation is that APBT-JPEG can be implemented by DCTJPEG, using a new quantization table deduced from mathematical analysis. To the best of our knowledge, it is the first time to reveal it, which can be considered to the main contribution of this paper. Finally, experiment results obtained with the test images have verified our proposed conclusion both in terms of objective quality and subjective effect.