Abstract—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 APBT-JPEG 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 DCT-JPEG, 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.

Index Terms—Image compression, All Phase Biorthogonal Transform (APBT), Discrete Cosine Transform (DCT), quantization table, JPEG, All Phase Digital Filter (APDF)

Cite: Qiming Fu, Xiao Zhou, Chengyou Wang, and Baochen Jiang, “Mathematical Relation between APBT-Based and DCT-Based JPEG Image Compression Schemes," Journal of Communications, vol. 11, no. 1, pp.84-92, 2016. Doi: 10.12720/jcm.11.1.84-92